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<h2>SL Paper 2</h2><div class="specification">
<p>Let <em>f</em>(<em>x</em>) = ln <em>x</em> − 5<em>x</em> , for <em>x</em> &gt; 0 .</p>
</div>

<div class="question">
<p>Solve<em> f '</em>(<em>x</em>)<em> = f "</em>(<em>x</em>).</p>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) =&nbsp; - 0.5{x^4} + 3{x^2} + 2x">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>0.5</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>4</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>3</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>2</mn>
  <mi>x</mi>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p>&nbsp;</p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
  <mi>x</mi>
  <mo>=</mo>
  <mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
  <mi>x</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span>. There is a maximum at A where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
  <mi>x</mi>
  <mo>=</mo>
  <mi>a</mi>
</math></span>, and a point of inflexion at B where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
  <mi>x</mi>
  <mo>=</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> , the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b"> <mi>x</mi> <mo>=</mo> <mi>b</mi> </math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) =&nbsp; - {x^4} + a{x^2} + 5">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>4</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mi>a</mi>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>5</mn>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> is a constant. Part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> is shown below.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.47.40.png" alt="M17/5/MATSD/SP2/ENG/TZ2/06"></p>
</div>

<div class="specification">
<p>It is known that at the point where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2">
  <mi>x</mi>
  <mo>=</mo>
  <mn>2</mn>
</math></span> the tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> is horizontal.</p>
</div>

<div class="specification">
<p>There are two other points on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> at which the tangent is horizontal.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-intercept of the graph.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f'(x)">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 8">
  <mi>a</mi>
  <mo>=</mo>
  <mn>8</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(2)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-coordinates of these two points;</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the intervals where the gradient of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f(x)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> is positive.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of possible solutions to the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 5">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>5</mn>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = m">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>m</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m \in \mathbb{R}">
  <mi>m</mi>
  <mo>∈</mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>, has four solutions. Find the possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
  <mi>m</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Contestants in a TV gameshow try to get through three walls by passing through doors without falling into a trap. Contestants choose doors at random.<br>If they avoid a trap they progress to the next wall.<br>If a contestant falls into a trap they exit the game before the next contestant plays.<br>Contestants are not allowed to watch each other attempt the game.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The first wall has four doors with a trap behind one door.</p>
<p style="text-align: left;">Ayako is a contestant.</p>
</div>

<div class="specification">
<p>Natsuko is the second contestant.</p>
</div>

<div class="specification">
<p>The second wall has five doors with a trap behind two of the doors.</p>
<p>The third wall has six doors with a trap behind three of the doors.</p>
<p>The following diagram shows the branches of a probability tree diagram for a contestant in the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfwAAAFLCAYAAAAznT7eAAAgAElEQVR4Ae29D3CT15X//bW8Q5PUKHkJtEg4vzLUY5MMztLguv0VdjF2IuO3my1jCmyIHad2gewGQmFjCxzT5NcQNzYsDISQNMQuYJosEHugbBcsQDUtJMRr85Ka38bSeFh+bx3JXQgvKBpKmFp65zzSY8tCtmVbkvXn+8x4JD26z33u/Zxrneeec8+5SW632w0eJEACJEACJEACcU1AE9e9Y+dIgARIgARIgAQUAlT4HAgkQAIkQAIkkAAEqPATQMjsIgmQAAmQAAlQ4XMMkAAJkAAJkEACEKDCTwAhs4skQAIkQAIkQIXPMUACJEACJEACCUCACj8BhMwukgAJkAAJkAAVPscACZAACZAACSQAASr8BBAyu0gCJEACJEACVPgcAyRAAiRAAiSQAAQSQ+E7zDDqk5CUNNhfFozma4CrE/X5euiNZjjGJHwHrCd3onJfJ1wB67kGszELSfn1sPoX6GvrUtRbbw+8eoTtc1nrkZ+k1nMb1vqlge858C78FJCAC05rCz7YWgJ93zjSY4FxD5rMVjgDXhPNJ4cYg9JsZRzqkV/vP4ZdcJgrPQwCjF/PmPP+Pw3bfb8xqYzvtAD3HLaixC7Q95sx2O+b57zyuxbUb4hXLvpKmB3+P1DDoea4Go7QeH6fGArfS1hXcRo33W7I9gED/9pQkzsZ0MxEabMNtppcaMciFUcb6kpeR3vvYJVMQla+AbqOLnQ7B/5DuXqu4CK+h5zvfQZL90A14ur6EAdNehTnPzq29g3WLJ4flIDrsyNYm7MGx5JXor1XHT+d+MXjThwtWozn6y/FoNIftLuA9lHkF+vRYbH59esOeq50ATk5+N5d4/c2us6egElnQH7WpCEq51chJaDNRY1NHZNuuG+eRoUO8P+9C/537R6klx6C21aNXG2IVQTHVUhFP9LKQizNkd4+UctrkJKahky7Cc1t130geH4wO4qfw/PzvkRD8x98LA0uOLu70MEfUx9ekXp7DS07q1GfuQ4vrZ0LXd9/jRbpT/wjXtr8MPZXvYfWEc+GItX+0dwnBakZM2BvOIU23365ruDswc9Q/Hwp5sF//DrRbbkMXfHjyAq1ohhNF3hNFBLguBpPofT9dI1nI6Lm3gPMXarpMh/GPa+jRHEJeE2VTivM9UYs6DPt5sNYb4ZVZutiXpuZh1q7Haayh5E8iFlMk/Y9LDPcwMUr1/rN/uqPaX4+DPkGYMCP7XW0NZtgz0xDaoqI7Q7s7U3YWpLZ76pYYER9TJqXo2YEBG6I6xquXLQF/g6BZ0Mueyv2GfO9shHTfz3MVj9HkcuO9n3940hfsh0nB5RxwGquh3GB3luPzzhTWqOaT9+EubWhv5y+BFtPDnQzuOztaOpzR2SiZOuvcaHny0H6JKfvQdq8hTDYu3Cl505fOcXK1DEf+YZ85Bdj4EOp4w9obrAhM0OPFLlC+te01fu/I2blQTj01c43ESPQcwHH+8ZDEgaOPT+Tvte9s8C4s+/3RnV7clxFTGIhuREV/rAYTWg4q8NGay96bQexMluD9rfXo+jMI3jri17FNdBrexHJDSux5pAVLjGvdYpJTQdD3afoHcwsppmOecseg+ngh+jyWvU9JvtpyEjVQpv1OIrh82OrKJ0bMCz7HtI0Ljjb38TyJ48i+XkTehUXxZewbboPDXnr8Xb7jWF7xQIjIKCZgfxVhdCZypDzo634oKnF83A3SBWuz5qwYk4ZzFN/Cpti/u/EWxnnUJRTiabPvMrT9X/QtMKArL3JWGO5Cbf7JszzL6Gkr4wDnfXrkFN0BlNr2hUZ99p+iqln1iLjyR1o93UFmV7Dq41fRdmxbrjdX8J2YAZ+Y/AZB85WbFu+DG9c/QFalDF7Di/N6MJv9l8apAee056H0gs4ePaK96HUa7JXHjonK24pXLyCHnX8ijvKPg/L5k2HBjfQvm0Fnjx6L55v/9LjQuv9D2xKPoi8VXUD2z9kK/hlOAjY95/EhRkbYZXfjt5uHJh2AoYh5WJHS8MnmLTxHNy9f0LLyixoOa7CIZqw1plQCt9em4f7+2bl6gKX4RYYzUFxyfcxM0UDje6b+OZ9/41PTnYic/53kK7MtAGN7glU/7YLzaUzETzQCZg6Pc3Hj+812RsWYl7aPV4f6mf9P7ZOGywdj3l/TK+j9dCvYCkuQVm2znvPCdDlLEOxoRMnP+nptxqEdfgkSuUTMK2wGi2mbXjiZDmWLF6AjInJSEqSGXeT38w9kPlfi5mlNThQfB6rd55V3DSurtP4Rf1XULFpPQrTZcWIFjN/+DSK0YRfNF+Gy9GGX1a1omDXz7DWK2ONbi7WvbEDFZYtqJSHSxW/7llsemmRdzxOgC7rb5Ctu+AdBy44Wo9gm2WpTxkt0gvXY1PFHLWGwK+ayZg++wEfP76Y7D/zPnRqPA+lHSdwtksWl/qNX8cFHNrWg+KSZcjWTfDUr5mGnGeXwdDyET6x9VsNAt+cZ8NJQFdhxEuFMz2WmCDloit+Gj+cqQU0X0P6N1M4rsIpoDDVHbx+ClMDIlmt/yIWz8I974K9YBuimYq/fmImTFW/xJFW8xhWaHt/MPv8oGKyP4NMZQYvjRFf1zSvBcAFR9spNCAN06fKj+dk5Na0wVaThR7zUTQ1NaGpaQ+MebkoM90KticsNyIC4q9fh322L2Fr+w0aG3+FLc/YUFu2GHkZc1GiLtpTzNrt0M2ejqkD/rt8fZe3PIvbMAMZqYrx29MSZfGVDc2l6XCKvO0PY+6srw98iEzRIyMTPko4QCcGlPF3BanlPe1RPwV+9Swu7XMtKX2b5n3olCEqbVEtAJ77QO230pc21GRfh1kZn01oqjciL6MMpsA349lxJ3D5roXCgzeJ42pwNtH7zYCfpOhtZjS17AHMefE9WA58Bzcaa7A4LwMTR+ubVFasfsXjx/f/MVV9qMpK6NueldF9i6FccHbuQ4n+fmTk7cbHN2Su9zXkv9WEOsMwyiCaUMZkWyZAN+f/RmHhcry4rwPuLz5FY4Ue+8t+hkM+YZR3W5PuRUbZ4SB77FkJbx+itN3HlD5EMWDI9QdDXglAfSgV19Jtz0NnptcCJZd63VLKSn7lPl/xiSARl0QZ9BMzkPfGx1CcTA8U4K22d2DASBTLcG3k9+NCgONqXLCP9aZU+KMiqEV6biFKa5o9PtO2Xfh+z3bk5bw+wrjV/lm81XYFF31/TOX3VBb2ZZ5B88etnpXRajiey4pDazfiZEEjunubUVP6QxQW/gC5+luwdAylJkbV2YS/aMjY8pSZWFS2DAac7Xe/wLt+467wT3eQoU5ed88Q5O+2IAxSWDHL6wf5MojTfbN4C2xX/o+PBUqu9Szsy2w4hY/bfo+DspjPG47nsn6AtWWtKGi8gt7f1qC0sBCFhX8L/c3/QkcQt2WRKCfAcRXlAgrcPCr8wFxGcFZmfIuwsuRJ6PxWNA9fiXcldMcF/NuRY+hQzaHqhcoMajoutp/H/+6QxXxe86/izwcy5z7iEyIGuL64gWvqtXwNGQHP4jXbwBXpd9XuXaymxhmf+0/Y+5zsUvgG2rf+nTfxkVfu/jNdb5RIUv5e9HzrcRTrPsW5S3/q99VLNars1ZXwd7XD/8RgOR88IXT+pe/6rM7i/3czjhy8gtnTJw9wMXgeSrvQ/rtP0NEXQeL158PfJfEXfHHDL1LhrhvyRGwQ4LiKDTkNbCUV/kAew3/yZgNbYGzqX6nttOJUcztQ+g/IlwV3yqzoPk9dt5zwXVDtfwPPD2YTyjf+0cccqpaSmd430LFxI7b5zv69SsXUcBAtds/iJ5f9HHZUvox6TvBVeKF71aRj6Y6f44mGtViztQntXuae0MgGbFxVjTtbXsTS9HuU9RU5L1Si4PjLqNxxzqv0HbA21eLFcmBLdSHSNWK9yYdx44OoffVNmJX67sDechANpsc8Zf6vLPxoczaOr/4pdrTaPUrfeQn1a9aiNqMc1UvTByjewTurgTZnFXYVHEPRmgZ0KoNR2rMNr9a2D35Z3zfeWfy2jdjoM4Pv+1qZ6V3GxvImn9m/1xWgO4uGvb/3MrgDe+seVK5+ExyiffRi+A3HVSwKjwp/pFLTzMSzew9izZSjyFFWaichaeISHJ2yCsc2/x2mCVHNDBQYi3FH4vC/WopDyirmQW6kmsYCJtRRfzjhtwhsMnJ+sht7sz9Env4rSox26oaP8FDJbjQOt/J6kGbw9FAENEiZWYJftu9F4aSP8aKXeVLSVzBn55/w7U3/jmMvZntWPIv4py3CjpYdmN/zM+iTJRrkfuQcnYQ1bXuwfs4DnhtppiF38160PXsLryr1fQX6V2/h2b4ysrJ/O1oOzEePcQ6SJbpk4j/DMn8HLMfWYo43QmSoVvd9p/kGCnc0Yl+mGbnKmJ2JVR8/jDVbFvUVGeqNZup0zJbMbX1rSHxLe2d60A+c/Wvn4SfHapD9UYmXwRxs+N1klBw5rGSB862B72OUAMdVzAkuyS1L1XmQAAmQAAmQAAnENQHO8ONavOwcCZAACZAACXgIUOFzJJAACZAACZBAAhCgwk8AIbOLJEACJEACJECFzzFAAiRAAiRAAglAgAo/AYTMLpIACZAACZAAFT7HAAmQAAmQAAkkAAEq/AQQMrtIAiRAAiRAAlT4HAMkQAIkQAIkkAAEqPATQMjsIgmQAAmQAAlQ4XMMkAAJkAAJkEACEKDCTwAhs4skQAIkQAIkQIXPMUACJEACJEACCUCACj8BhMwukgAJkAAJkAAVPscACZAACZAACSQAASr8BBAyu0gCJEACJEACVPgcAyRAAiRAAiSQAASo8BNAyOwiCZAACZAACVDhcwyQAAmQAAmQQAIQoMJPACGziyRAAiRAAiRAhc8xQAIkQAIkQAIJQIAKPwGEzC6SAAmQAAmQABU+xwAJkAAJkAAJJAABKvwEEDK7SAIkQAIkQAJU+BwDJEACJEACJJAABKjwE0DI7CIJkAAJkAAJUOFzDJAACZAACZBAAhCgwk8AIbOLJEACJEACJECFzzFAAiRAAiRAAglAgAo/AYTMLpIACZAACZAAFT7HAAmQAAmQAAkkAAEq/AQQMrtIAiRAAiRAAlT4HAMkQAIkQAIkkAAEqPATQMjsIgmQAAmQAAlQ4XMMkAAJkAAJkEACEKDCTwAhs4skQAIkQAIkQIXPMUACJEACJEACCUCACj8BhMwukgAJkAAJkAAVPscACZAACZAACSQAASr8BBAyu0gCJEACJEACVPgcAyRAAiRAAiSQAASo8BNAyOwiCZAACZAACVDhcwyQAAmQAAmQQAIQoMKPWSG74DBXQp+UhKTB/vSVMDtcQfXQZa1HftJS1FtvK+X9PwdVyYBCt2GtX4qkEbRBudxpxcmtr2Gftx0DquQHEiABEiCBUROgwh81umi5cA4qTl+F2+2++89WjVzteIn4HqSXHoJ7RG1wwdG6FyXln6A3WvCyHSRAAiQQJwTGSxvECT52gwRIgARIgARigwAVfmzIaYytvAN7exO2lmT2m/8XGFFvtsIZbM1OK8z1Rizocx/kw1hvhtU5mMvAz6TvMMOo1yN/z0m07uuvR1+yHSetDgDioqjCzLyfw47DKMu4F3qjGfIN4IDVXA/jAr23/cPdO9hOsRwJkAAJJA4BKvy4l7ULzvY3sfzJo0h+3oRexfT/JWyb7kND3nq83X4jCAI30P72ehSdeQRvfdGruA56bS8iuWEl1hyyYjCVf3fFdphWbkXjxB/hmLSjtxsHpp2AYVUd2p2ANnczOk9vhA5LUGf5M2w1udDCgc76dcgpOoOpNe1K+3ttP8XUM2uR8eQOtA/6wHH33XmGBEiABBKZABV+zEu/HbV5U/pn7uoMvG+x3HW0HvoVLMUlKMvWwSPwCdDlLEOxoRMnP+kZXmG7evDJyU5kzv8O0lM8NWh0T6D6t11oLp3prTM4kLoKI14qnIkUKa7RIevxOdC1fIRPbHcCV+Bowy+rWlGw62dY622/RjcX697YgQrLFlSO6IEj8C14lgRIgAQSgcBfJUIn47uPsmjvBGpyJw/SzcnIrWmDTTGLH8WpG7Ic7nN8/MbLqG0BDMsGucz3tGYq/vqJmSir+iWOzMoHnKkw5KZ7lLZvuRG/1yAlNQ2ZMMHS7QTSJ/nV4IKj7RQa7A9j86yvD3ywSNEjIxNosNjgxExo/a7kRxIgARIggYEEOMMfyCMOP7ng7NyHEv39yMjbjY9viAH+a8h/qwl1BqBDUZjDdfsBzHnxPVgOfAc3GmuwOC8DE5P0WGCsh1nxvw93/Wi/v4OeK12wD3G5/eIV9ATvUxiiJn5FAiRAAvFNgAo/vuULuKw4tHYjThY0oru3GTWlP0Rh4Q+Qq78FS8dQqtQfjBbpuYUorWmG2/0lbG278P2e7cjLeT3oWH//Gof/PAFTp6dBN0RB3ezpmMpRPAQhfkUCJEACHgL8qYz3keC0wdIBZM59BDofabu+uIFro+77BOjmLMLKkiehs3fhSs8g/vdR169eqIE263EU6z7FuUt/GrjWQO1Xhj4ErgX1fnwlARIggfgl4KMC4reTCd0z7aPIL9bD1HAQLXaPYnbZz2FH5cuoD3aC7+pEfX4aFhib+sPwnFacam4HSv8B+Wn3hAix6tOX6ly45bwFlzYLP9qcjeOrf4odrXaP0ndeQv2atajNKEf10vSBvv0QtYTVkAAJkEC8EaDCj0KJ/vnPf0ZTUxNMJlMIWjcZOT/Zjb3ZHyJP/xVlNX/qho/wUMluNFbMCa5+zUw8u/cg1kw5ipyJyZ6IgIlLcHTKKhzb/HeYFsJRpEnLh3HjTZRlfBVfXfyv6HJpMbN0O1oOzEePcQ6SJQph4j/DMn8HLMfWYo43aiC4jrAUCZAACSQugSS35GTlETUEzp07h3Xr1iEnJwcbNmzApEn+K9ejpqlsCAmQAAmQQAwRYFhelAjLarViy5YtuHr1Kg4cOID09PQoaRmbQQIkQAIkEA8EqPDHWYrXr1/He++9h/379ysz+sLCwnFuEW9PAiRAAiQQjwRC6H2NRzzh7ZP46RcuXKjc5MyZM6CyDy9v1k4CJEACiUyAM/xxkP7FixfxyiuvKGZ7mu/HQQC8JQmQAAkkIAEq/AgKvbu7Gzt37oT468vLyzF37twI3p23IgESIAESSGQCUbNKPykpaVzlEM5gBQmzO3z4MEpKStDY2IiCggLce++949pf3pwESIAESCCxCESND18U7nj+hUvsEks/f/58yOz+888/V/z0VPbhos16SYAESIAEBiNAk/5gZMZ4PiJhdk4rTr59GLa//2eUpIcq290YO87LSYAESIAEopJA1Mzwo5LOKBolYXbV1dUoKirCkiVLcOTIkTDF1LvgaN2LkvJPIBve8iABEiABEiCBoQhQ4Q9FZwTfqelwJcwuNTUVEmZnMBhGUAOLkgAJkAAJkED4CFDhh4CtpMN96qmncP78eSUH/jPPPBPmRXkuOMxVmJn3c9hxGGUZ90JvNMPhMMOol33qd2JrSaaS8145jzuwtzf1nZMFkkkLjKg3W+FU+i/1VUKftBR7zCex3XttUlI+jPtaYed+8yEYJayCBEiABMaXABX+GPjLQryKigolJa7E1dfW1iqz+zFUGeSlGmhzN6Pz9EbosAR1lj/DVpMLrXK1HS0Nn2DSxnNw9/4JLSu/BU37m1j+5FEkP29Cr7I48kvYNt2Hhrz1eLv9hs89D2Nl0QFAKdeLLyyrgL3LsXxbq/fBwKco35IACZAACcQUASr8UYhLzPe7du1SVtx/97vfxfvvv4/Zs2ePoqbwXKIrfho/nKkFNF9D+jd70XroV7AUl6AsW+fdSnYCdDnLUGzoxMlPenz2mZ+F0l0/w1qlnAYp6Yvw0qalsGw7glYHp/nhkRZrJQESIIHIEKDCHyFnNcxOLjtx4kQMhNlNRm5NG2w1WegxH1VcDk1Ne2DMy0WZ6ZZf7x/G3Flf99lf3rs/vd2E5rbrfmX5kQRIgARIIJYIUOEHKS0Js1u0aJGSQEfS4a5evTpGtq51wdm5DyX6+5GRtxsf35CZ+teQ/1YT6gxAh8UWhLnehotXrvlYAoKExmIkQAIkQAJRQ4Bx+MOIQsLsXn/9dbS0tGD79u2xlw7XZcWhtRtxsqAR3XsKMU19xJMFfh12IChPhB6zp0/2mfkPA41fkwAJkAAJRB0B9ec/6ho23g1Sw+wefPBBzJo1Swmzi8nc904bLB1A5txHoPORtuuLG7h2F+TLsHR71u17vnLB2d2FDp0B+VmT7irNEyRAAiRAArFDwEcFxE6jw91SCbOTdLgSZifpcMMfZjeaHnn968qlLtxy3gpsctc+ivxiPUwNB9Fiv+MpbT+HHZUvo97uf9921L66DU1WBwBxBTRgTdExFOxahRwth4o/LX4mARIggVgiwF9xH2mJn14NsxM/vYTZTZoUvTNbTVo+jBtvoizjq/jq4n9FV8CUe5OR85Pd2Jv9IfL0X1Fi81M3fISHSnajsWKOT+/lrQEVxQ/j8mtzkZSUjIm5ZmTua8SOwm/QnO9Hih9JgARIINYIRM1ueeMJTvz07733Hvbv348NGzYoK+/Hsz2Rv7eayKcLmy37Ucq8/JEXAe9IAiRAAmEmkPAz/KamJkg6XDkkHW5hYWGYkbN6EiABEiABEog8gYRdpX/x4kVIdrz09HSI+V5eeZAACZAACZBAvBJIOJO+GmYn/vry8vLYC7OL15HIfpEACZAACYSVQMKY9CXMTnz0EmanpsONyTC7sA4HVk4CJEACJBCvBBJC4avpcGWzGwmzEz/9vffeG68yZb9IgARIgARI4C4Cce3DF7P9li1bcPXqVfrp7xI9T5AACZAACSQSgbhU+OKnf/vtt3HkyBFs3rwZBoMhkWTKvpIACZAACZDAXQTiyqSvpsOVMDutVquE2VHZ3yVzniABEiABEkhAAnEzw5d0uGK+l/A6ia1PTU1NQHGyyyRAAiRAAiQQmEDMK3xZiLdz506Iv17i6mfPDmr7t8A0eJYESIAESIAE4pRAzJr0xXy/a9cuZcW9GmZHZR+no5TdIgESIAESGDOBmFT4apidw+HAiRMnGGY35mHACkiABEiABOKdQEyZ9NXd7KZMmcIwu3gfmewfCZAACZBASAnEhMJX0+G2tLRg+/btTIcb0iHAykiABEiABBKBQFSb9NUwO0mHO2vWLCXMjulwE2FYso8kQAIkQAKhJhC1M3wJs1u3bh1ycnKUdLiTJk0Kdd9ZHwmQAAmQAAkkDIGoU/jip3/33XeVMLt33nmHYXYJMxTZURIgARIggXASiBqTvvjpJcyuqKhI2c1O0uIyzC6comfdJEACJEACiUQgKhS+ZMaTdLhynDlzRgmzSyQhsK8kQAIkQAIkEG4C42rSv3jxopIdT9LhHjhwQEmLG+4Os34SIAESIAESSEQC46LwGWaXiEONfSYBEiABEhhPAhE16UuY3f79+yFhdpIOV8z3DLMbT/Hz3iRAAiRAAolCIGIKX8Ls5s+fD9ns5vPPP2c63EQZYewnCZAACZBAVBAIu0lfwuxk29qrV6/STx8VImcjSIAESIAEEpFA2Gb44qevrq5WwuyWLFkCCbOTxXk8SIAEYpSAwwyjPglJSYP9ZcFovhZk527DWr8USfn1sLoAuDpRn5+G/PpOyMdRHUodeuiNZjiCrsAFp7UZWyvf87Qj6OtYkARij0DIFb6aDlfC7LRareKnNxgMsUeGLSYBEghIQFdxGjfdbrjv+mtDTe7kgNdE5KRmJkqbbbDV5EIb9A2vo7XuJZS33w76ChYkgVglEFKTvm+YncTWp6amxioXtpsESIAESIAE4opASGb4shCvoqJCial/5ZVXUFtbS2UfV8OEnSGBERJw2dHetBUlfS4APRYY62G2Bmtsd8Bqrodxgd7rQgji+gEmfRcc5krok5Zij7kF+4z53noyUbK1GVanOA6uwWxciLzadsBUhoxkH5eE0wpzvRELVPfFAiPqzVY4R4iBxUkgmgiMSeGL+V7S4RYWFiphdu+//z7T4UaTdNkWEhgXAjfQvm0Fnjx6L55v/9Jj+u/9D2xKPoi8VXVoV5TtUA1zwdleh1VF55DxVufA69d8MEJf+2GsfNWEiWWHlXp6bdsw7TfPY9XbbXBiMnJrTuB0xRzAUAdLr9cl4byE+ucXo+jM/0CNTdr/JWw1/wNninLw5NZWKv2hRMfvoprAqBW+LMqTMDuJqxfzvSj9e++9N6o7y8aRAAmMnYC9Ng/3qzPfvlef2bHjAg5t60FxyTJk6yZ4bqiZhpxnl8HQ8hE+sd0ZphF3YPvkI7RkzsW8dK83XjMNudXNcDeXIn1Ev1pzULFpPQq99Wh038Lj2Q+g5eQl2AKuDnTB0foeqk7Ox67qFd72T4Au+x/xxoFnYSnfikNW+vuHESC/jlICI/rX8e2DbFd74sQJZftaUfYSZ8+DBEgg/gkEXrTns2BPm4saWxtqsq/D3NSkTAia6o3IyyiDKSg8E6D/6/+JHNNu1B35PcxNLV4TfFAXD1MoBakZM4COLnQHtDRcR1uzCfbMxzBLfVhRatQgJTUNmbgMSzcN+8NA5tdRSmDUCl/6I0pf/PWyja3E2osfX+LueZAACSQyAQc668ugn5iBvDc+xg1B8UAB3mp7B4agFKYGKXPW4phlK75z49/w6uIFyJiYjKRI+NFd13Dlom0I4dlw8cq10YcODlEzvyKBcBMYk8JXGyfb2EqcvaTLle1txa8vJn8eJEACiUfAZf0Aa8taUdB4Bb2/rUFpYSEKC/8W+pv/hY6gcWiQkp6DwtIa/NbtRq+tDY3f70FV3nK8GnSsf9A36y+omYzps/X9n+96p8fs6ZMRkh/Ou+rmCRIIL4GQjlsx7Ut+fDkkDl98+7KwjwcJkECiEHDB2d2FDovblocAACAASURBVDyMubO+7qMY/4IvbgS7Qv9uVhrdHBSuLEGxLtwz7EnIyjdA13EBl+y+aw3Ufs1ARmrK3Q3kGRKIAQIhVfjSX1m4t3r1akXZnz9/Hk899RQkPp8HCZBAIhDQQJv1OIp1Z9Gw9/ewKwvj7sDeugeVq9+EPSgE3ix8CyrR1BfG54D11Cm0ohCr8mf4PEgEVeEQhbw+faXEbTidLmizl2PzE2ewunIPWhWl74KzswFrivYiY8uLWJp+zxD18SsSiF4CIVf4alcl6Y7498vLy5X4fPHvS7w+DxIggegjYDKZkJ2dHRqLnHYefnKsBtkflUCfLGl452DD7yaj5MhhVOiC6fs9SH92B9rWTMLRnPu98fP3I+foJKw59hIWTfOu/A+mqmHL3IO0ghXYeKcKGckzsPhQF1wps1D6ZiMOzP9/YdR/BUlJyZj4j/+J+QdacOzFbHB+PyxUFohSAkluyY8Z5kPM+sePH8frr7+OZ555BmVlZQzhCzNzVk8CwRCQRbbyMD5lyhTl4Zz7XQRDjWVIIDYJREThq2hkId97772nxO5v2LBBid1Xv+MrCZBA5AjI/6I8gLe0tGD79u2YO3du5G7OO5EACYwLgbCZ9AP1RsL4xL9/4MABZca/aNEihvEFAsVzJBAmAurmVg8++CBmzZqlLLKlsg8TbFZLAlFGIKIzfP++S7KedevWKcl7ZMYvDwQ8SIAEwkOA/2/h4cpaSSBWCIyrwhdIqn9/8eLF2LdvH5YsWUL/fqyMHrYzJgiIn/7dd99VrGmykJZ++pgQGxtJAiEnEFGTfqDWSxifxO9//vnnyip+yc8vK4Z5kEC4CST15YGXleSR/wt3/8RPL0mwJBmWJMWS5FhU9uGmzvpJIHoJjPsM3x+NzEYkTe/Vq1eVsD7+QPkT4mcSGJ6AJL1iVMzwnFiCBBKJQNQpfBW+zPKrqqogC/uee+45+vdVMHwlgSEISJKrV155RZnJ//jHP+aMfghW/IoEEo3AuJv0BwNuMBiUFcSSwEdWFDNN72CkeJ4EoOxdIfH0K1euVOLpw+Ord8B6cicq93Vy8xgOOhKIQQJRq/CFpfj3JVGP+PclTa/497kNbwyOMjY5bARk0ev+/fuVh2Lx08teFmELs3O0oa7kdbT3hq07rJgESCCMBKJa4av9Vrfhlfh98e+vWLGC8fsqHL4mLAFxe8lDsKSslodiWfwqD8k8SIAESCAQgZhQ+GrDZQGfrDQuKCjgNrwqFL4mHAFZ2CoPvbt371aSWFVWVoZ/jYvDDOPMPNTa7TCVPYxkfSXMjv+G2Zil7FO/Z2sJ9BLpoJx3AS472pu2okSvRj/oscBYD3PfZjjXPNfmvwnz+Tf7yy0wYl+7nS6DhBvV7HAkCMSUwleBcBtelQRfE4mAhNlVV1crD7uSryKiYXbaXNR0nkaFTgdD3afotVUjV+v9+Wj5d5ydVA6r+0vYWlYhW+tA+7YVePLovXi+/UvIdh3u3v/ApuSDyFtVh3ansoWeR3Sm1Sh6C95yN2FZk4y9WSuwrf1GIomWfSWBiBCISYUvZAJtw0v/fkTGDG8SYQJqOtyFCxdCq9UqfnpZ1Bo1h+5JlPzwEaRgAnTp30CK4wIObetBcckyZOu8O9tppiHn2WUwtHyET2w++8zrnseu6hXeclqkF67HpooebDt0AY6o6SAbQgLxQeCvYr0b6ja8ajjS0aNHwXCkWJcq268SkIdYWbci7iyJVJHxHvWHWANsbYDTCnPT76DM1W98jDfKatGCJVjm24HMxzBLfShQznv2p7dXnULbSzn9VgTfa/ieBEhgVARidobv39vZs2fj/fffVzKKSWYxyTAmMyMeJBCLBGQhnoTZibKXuHoJs4sJZa/AdqCzvgz6iRnIe+Njj8J/oABvtb0DAy7D0u0cXiT2Llzp8bEEDH8FS5AACQxDIG4UvvRTTdN74sQJpduygllmRTxIIFYIyEOqPKzKOhUJs5OHWHmYjaXDZf0Aa8taUdB4Bb2/rUFpYSEKC/8W+pv/hY5gO6JLw/SpXndAsNewHAmQwJAE4krhqz313YZX4vclW5+Y/HmQQDQTUMPsHA4H5KE1NsPsXHB2d6EDD2PurK+j/wfmL/jiRgCvfEcXun0X8cGJbstl6IofR5a6KDCahca2kUAMEej/f4yhRgfbVPF7iim0vLxcMYuKiVRMpTxIIJoISJidPJQePnw4cmF2owGQokdG5n2eK285MUBP99WngTbrcRTrzqJh7+9hVxbk34G9dQ8qV78Je1857xv7Xrz62hFYlcrEFWBEUcN3seuFedD6l+VnEiCBMRGIa4WvkpHMY6p//6GHHlIyk9G/r9Lh63gRkDA7eQiVNSfyULpnz57ozn2vmYECYzHuSBz+V0txqGuQNTLaefjJsRpkf1QCfbLE4c/Bht9NRsmRw6jQ+dHOKUbxty/jtfRkJCXdj9wzs7CvpRqF02jO9yPFjyQwZgJRu3nOmHs2SAXyI/v2228rMcybN29GVIU3DdJmno4vAvKwefz4cSxevBj79u2DxNQnXoY8SbyzEHkX/wmW46VIT4ipR3yNY/Ym9ggk3L+Z+PclM5mk6RUTqphSxaTKgwQiQUDC7GQxqawtkXS4sldE4in7SJDmPUiABPwJxHwcvn+Hgv0s/n0xocoPsJhUc3JysGHDhvCnKA22gSwXVwTkofLdd99VHi7feeedmFt5H1fCYGdIIEEJJJxJP5CcxcQqs/2SkhI0NjYqufo56wpEiudGSkDGVl1dnbJuRB4oZeU9DxIgARIYDwIJZ9IPBFmUO7fhDUSG58ZCQHJAiPleDtm2lsp+LDR5LQmQwFgJcIYfgKCYX2X19JQpU5TV02L+50ECwRJQ0zzLuGGa52CpsRwJkEC4CVDhD0FYEqFUVVUpC/uee+45+veHYMWvAIkAef3119HS0oLt27dDwkF5kAAJkEC0EKBJfwhJSMiemGIlh/mDDz6opOll/P4QwBL0KxkT+/fvV8aIpMOVMUNln6CDgd0mgSgmQIU/jHBU//4f//hHJZTqqaeeUlb2D3MZv04QAmqYnWRwlDC72EyHmyDCYjdJIMEJ0KQ/wgFA/+wIgcVpcVnnITvZXb16VUnfzHUecSpodosE4ogAFf4ohSkrsMVfK6v7ly9fTv/+KDnG2mXM1BhrEmN7SYAEVAI06askRvgqplvx1cqxcOFCbsM7Qn6xVlz89PKQJ7LWarWK7JmWOdakyPaSQGIT4Aw/BPL3zaL2yiuvMItaCJhGUxW+bpwXXnhBWcQZTe1jW0iABEggGAJU+MFQCrKMLOASv674c6kYgoQWxcVkId7OnTuVdLh8kItiQbFpJEACQRGgST8oTMEV8t2GV0z+u3btAsP4gmMXTaVEZiI7kaGE2cnWyrNnz46mJrItJEACJDBiAlGj8JOSZN/s8fsbMblBLpAwPlEUJ06cgMPhUFKrSgIfHrFBQGQl6XBFdiJDkSX3VYgN2bGVJEACQxOgSX9oPmP+luFbY0YYkQqYTjkimHkTEiCBcSQQNTP8cWQQ1luLP1+24S0vL1e24ZUc/RLaFerDZa1HvlhI9JUwO1yhrt5Tn6sT9fl66I1mOAa9wzWYjVlIyq+HNUzNGPTWo/hCZFFdXa3IRmQksmJM/ShA8hISIIGoJ0CFHyERiX9fwvjEJyxpeiUVa+j8+7fRdfYEOtb/HD/PPIPmttA/UCiYNDNR2myDrSYX2ghxC9dt1DA7kYWkTmY63HCRZr0kQALRQoAKP4KSUP37koJVVoCLrzgk/n3Hh6iruozi7z+NwmXTUFvz65iYXUcQ/YBbqelwz58/r6TDleRJ9NMPQMQPJEACcUiACn8chDpp0iRUVlbiwIED2L17N1asWKGEfo2uKS442k6hAQbkZ01D2ryFMJhO4GzXbW91t2GtXxrAxO6Cw1wJfZ8LwAWn1Yx6Y7538aQeC4z1MFt9jPcBTPouezuatpZAryy4zETJ1l/jQs+XPl3xrzcJSQuMqDdb4fQpFYm3qp9eQiffeecdJSWuyIIHCZAACSQCASr8cZSy+IqPHDmCJUuWKD5k8SWP3L9/HW3NJqD4cWRpNdCkfQ/LDBdw8OwVeFzo9wR4CJBO+14HODsb8HzOWpyZ+lPYet1w97ajZuoZFGUsx9b2G4EpOVuxbfkyvHH1B2j5ohdu9zm8NKMLv9l/qb+8sw1vr6rAmYx/wRduN9zuL2HbdB8a8qpwyKo+lPQXD8c7NcyuqKhIcakIc4bZhYM06yQBEohmAlT4USCdsWzD67L+GjW1QHH+ox6/umY65i17DKaq/WjxLt5THwIafv2H/lm14w9oblCvu47WX76BkwX/C9Vr50Ino0KjQ/a6f8GBih6UVzYFcBG44Gg9gm2Wpdj00iKkp8hFWqQXrsemijl9VF22SzjZMgPz56UhRTk7Abrcl/Fb9yGUpt/TVy5cbyQdrrhO5FDD7MJ1L9ZLAiRAAtFMgAo/SqQjPmTxJYt/X3zLoqQkpevQh2exnkkn5nzVNO2d0dtN/Yv3NDOQv2ohLNuOoFV5CLiDz041oSHjaSzNngQoyt+GzLmPeJR9301TkJoxA+joQrfTf8m9x0Jgz0xDqqLs1Yu813g/avSz8ETOWVTV/Rtazf820EWgXhKGV2G3aNEihaW4TlavXs0NjsLAmVWSAAnEDgEq/CiTlfiUa2trFR/zfffdN3TrXFdw9uBZwP5z5N2f3Je4KDmjDCa0o6H5D97wuQmY9nghiuF9CHBdRvMvTiCzuADfStHA1XMFF+1D3MrehSs9dwYWcF3DlYu2gecCfUrJxovHWnDgO/8fGl9dibyM+5GUlA9jvRnWux4iAlUwsnPiEpHQx5UrVyqhkMKSYXYjY8jSJBB9BLzhvkMkZxs6XHhgjzxhzEtRr7gVB1vnNPCaIT8FWN80ZHn1S6cVJ7e+hn0Rcm9S4avgo+xVfMxDKyoXHC37UWWahzrLn+FW/OPiI5e/Xtw8vRGofRsfqANJ+yjyi6E8BNzo+hAHTY9h2bzpkAGgmTods3VDANClYfrUCQMLaCZj+mz9wHODfUpJR27hCtT81gZ3rw1tjU+gpyoPOa+2DBHPP1hlgc+Ln15CHSXMTkIfGWYXmBPPkkBME9BtxOmbsl5I/a3rfx3XcOFRhSyLW3QvSso/QW+EhEKFHyHQob+Nd9Fd6T8gP83fF66BNutxFOvO+izem4SsfAPQ0IR3m47BZFiIeep1ysOAHh3n/hP2AZZ7J7otl4G7zPbSG099urvM/d5rBuuwRoc5hc+ipHgO7BevoGfA/Qa7aOjzapjdpUuXFJcI0+EOzYvfkgAJJCYBKvxYlbu66O7pv8W0QFLUPoal6x+D6eCH6FKUqgba7EVYn9GE8o0fw7Dse0jru24Ssn+0Bk8cfxmVO855lb4DnfVGFNVOxZbqQqT3lVWBaaDNWYVdBcdQtKYBnYp53gFr0za8WtuuFoLHdJYPY1Ond8GghOn9Ds2tQOmqPJ829F0S9BsJs5OQRgmzEz+9mO8ZZhc0PhYkgTglcAf29iZsLcnsc3OOLBR4FKHE/iZ9hxlGvR75e06idZ8RC7yuCH3JdpxUQp0lLLoKM/N+DjsOoyzjXp8Mpg5YzfUwLtB72x86F+hdP+NxOgLirFu3Yf3gbdSqi+4C9u4BfOvvC2Ew7UZdyzVPiZRH8ffF8wBdIVblz1DM+Z4vNEiZWYw3W3Zgfs/PoE+WTYxm4h8tc3HA8h5enPNAwDtA8w0U7mjEvkwzcifKGoKZWPXxw1izZVFfeU16Efa2rcKUo0swURn0yZiYcxRT1vwCmxd9w6cNfZcM+8Y3Ha6ENEqY3dDuj2GrZAESIIG4IOCCs/1NLH/yKJKfN6F3QCjwerw9WIixb99DFkpsh2nlVjRO/BGOSTt6u3Fg2gkYVtWh3Qloczej8/RG6LBEcct6XBIy0VqHnKIzmFrTrrS/1/ZTTD2zFhlP7kD7WNc9uXmQQIwQuHXrlruxsdH97W9/2/3GG2+45TMPEiCBRCBw1X26Yo4bQMA/XcVp900Fg6dc/2cvm95P3XWGb7oNdZ+6e91ud6+lzm3AEned5c9ut/vPbkvdEjcMdW5Lr/93QbJV6te5++5787S7Qof+z0o1ve6bpze6dX339f/sdruV62a5SxuvKO3su7tyXtfX/r7zI3zzV74PNnxPAtFM4Pjx41i8eDH27dunhDBGc1vZNhIggTAQkEV7nZuRqx3MOD0ZuTVtsEHM4kdx6oYsh/scH7/xMmpbAMOy4dvkCSWuUkKJZ+XfA2fq3yI3PRS7h2iQkpqGTJhg6XYC6Wootdomb9ZU+8PYPOvrA62fKXpkZAINFhucmDnqvUwGo6a2gK8kEDUEZDGexWLB73//eyXGXnz4PEiABEign4ALzs59KNHfj4y83fj4hixg+hry32pCnQHoUBRmf+mA7yIcStzfhjvoudKFISOkx7jQmQq/nzbfxQAB8dVHYrvhGEDBJpIACfgTcFlxaO1GnCxoRHdvM2pKf4jCwh8gV38Llo6hVKlfRREIJfa7I4AJmDo9DUNGSM+ejqlj0NpjuPTu5vIMCUSKgLrd8KxZs5TYe0mhG7rthiPVC96HBEggpAScNlg6cFfWUNcXN+Bdujzy24UhlDhwI9Rw6k9x7tKfvHuheEuq/crQe1OUB65huLNU+MMR4vdRSyBQOmKJyedBAiSQoAS8OUVMDQfRYvdkB3XZz2FH5cuoD3KCH85Q4oFSUX36ctaFW85bcGmz8KPN2Ti++qfY0Wr3KH3nJdSvWYvajHJUL00f6NsfWOGwn6jwh0XEAtFOQE1HLLH4EpM/tu2Go723bB8JxBcBdTfL0KzJmYycn+zG3uwPkaf/ihLHnrrhIzxUshuNPpt6DUUwHKHEg91Pk5YP48abKMv4Kr66+F/R5dJiZul2tByYjx7jHCRLKPPEf4Zl/g5Yjq3FnAH7lgxW6+Dnk2RV/+Bf8xsSiD0CJpMJVVVVysK+5557jsl4Yk+EbHGCEFD/V2XjsOXLl/N/Ncxy5ww/zIDDWn2EN14Ia19CWLm63bBWq8XChQtB/34I4bIqEggBAZnNy26Whw8fVrJkcjfLEEANogrO8IOAFJ1F1NSMXdhs2R+RveWjk8PQreru7sbOnTshPzDl5eWQxX48SIAExoeAZMl8/fXX0dLSgu3bt/P/McJi4Aw/wsB5u8gSSE1NVXLsv/LKK4p/X7bODY2vMLL94N1IIJYJiJ9eLG2ym6VE1nA3y/GRJhX++HAf413V2b3fxgveDRsWGHf2bRzh2SN6uM0kpL5K6JOWYo/5JLb3bTqRD+O+Vr8d9MbY9HG6XLYblpz7snVuUVERdu3aBZlt8CABEggvAXU3y/Pnzyu7WYq/XiJseESeABV+5JmH4I6aQTZekKrtaGn4BJM2noO7909oWfktaILeTOIwVhYdAJRNJ3rxhWUVsHc5lm9r9e50F4Kmj3MVkq3vxIkTSitU//44N4m3J4G4JCCWNLGocTfL6BEvFX70yCJkLdEVP40fztQCmq8h/Zu9aD30K1iKS1CWrfPGcE6ALmcZig2dOPlJj0+Ch1ko3fUzrFXKaZCSvggvbVoKy7YjaHWEYOP6kPVwbBVJGJ8sEpIwPpl1yOKhixcvjq1SXk0CIyCQ5N0udbxeR9DUERcVy5lY0MSSJhY17mY5YoRhu4Cb54QNbbRUPJLNJB7G3AGbNngTQ9h3o7ltPXJzJ0dLp0LSDknTW1tbCzE5io9fPr/wwgsQvz8PEggngXiNhhY/vSzKE7O9+Olpug/nKBp53Zzhj5xZjF0Rgs0kYMPFK9d8LAExhmCY5srK/ffff1+ZjYjJX2YnTNM7DDR+TQI+BMRCJpYysZiJ5UwsaKFV9i44rc3YWvkerPFjbPQhGJm3VPiR4Tx+dwnJZhJ6zJ4+eUwpHccPQHB3lh8n1b/vcDgwf/58SFIQHiRAAoMTEPO9+OlXrlyphL2KxUwsZaE/rqO17iWUt98OfdUJVCMVfrwLW910Ye4j0PlIO/BmEpc9+zT3MXHB2d2FDp0B+Vn+ezf3FYqrN+Lfr6ysVGYpkhREZi0M44srEbMzISAgFrD9+/crYXbip2eYXQigRqAKHxUQgbvxFiEkEGDjhUC1j2gziXbUvroNTVaHspmDs7MBa4qOoWDXKuRoE2uocBveQIOJ50gAiuVLLGCS1Orzzz9XLGOhNd/7U74Gs3Eh8mrbAVMZMpKzYDT/tzeUOB/GPa+jRJ+EpCQ5L3viMQzZn6D6ObF+xdVex8nrXRsv9Abq2Eg2kzCgovhhXH5tLpKSkjEx14zMfY3YUfiNuDbnB6KmnlO34ZVZjCQNkVkN/fsqHb4mEgGxdMnGVLt371YsYGIJE4tY+A9ZeHwCp2XzG0MdLL1tqOlbQGxCw1kdNlp70Ws7iJXZD8DJMOTBRSKb5/BIdAK97punN7p1WOKus/w50WEM2v/PP//cXV5e7v72t7/tPnv27KDl+AUJxBMBGfevvfaaMu6bm5vHqWtX3acr5rhhqHNbeqUJ6m/WHHfF6as+bfKU01Wcdt/0Oevu/dRdZ/im21D3qbu379pZ7tLGK26lOqWst07dRvfpm/1nfauJ9fec4Q/+LMRvSGAAAW7DOwAHP8Q5ATUdriSoko2oxE8vG1NF9+ENQ67JQo/5qJLOt6lpD4x5uSgz3fJr+mBhyCY0t8VnFk4qfL8hwI8kMBwB8e9LMpElS5YoyUWqq6uZpnc4aPw+pghIboqnnnpKCbOT2PrQh9mFCwfDkIciy8Q7Q9FJmO8kVW81bO6E6XBIOiqznb/5m79RtvgU/35jYyMKCgpCHH8ckqayEhIIioDv7pKSjEr2oIipwzcMeU8hpqlTWtlnpMMOBNWd+A1DVnHElEzZWBKIFgKyOlmyislqZUk6IquXZXbEgwRiiYCY7yXhlOSikAWqkogq5pS9AGcY8pDDjgp/SDz8kgSCI6D699955x1uwxscMpaKEgKSYEoeVCXhlGwsJUo/vGF2o+l4ClIzZngvvA2n8y+BK2EYcmAu3rNU+EPi4ZckMDIC3IZ3ZLxYevwISJidJJaSBFOSDjdyYXaj6fM9SCtYgY13qpCRPAOLD3UhYBQyGIY8FN0kCTMYqgC/IwESGB0BMZPW1dUpsfsbNmygf390GHlViAlIOlzZ4KalpQXbt2+H5JpIrMMFh7kKM/O6sNmyH6Xp9yRM9znDTxhRs6ORJiBmUVndLKucxb8vq565DW+kpcD7qQTUMDtZYDpr1iymw1XBJNArV+knkLDZ1fEhINvtchve8WHPu3oIyELSdevWIScnR1lgGpkMeaQfbQRo0o82ibA9cU1AZlnHjx/v2zO8rKwsChdIxbUIEqpz4qd/9913lQ2gYjLMLqGkFf7O0qQffsa8Awn0ERAzv7oNr5yU1dFi8udBAqEkIH56CbMrKipSwuwkUVRMhtmFEgrrStg9USh6EhhXAmJSFf++rI6WGT+34R1XccTVzeUBUtLhyiHpcOUBkwcJCAGa9DkOSCAKCPj6WGVFP32sUSCUGGuCLAgVs72kfv7xj3+svMZYF9jcMBOgwg8zYFZPAsESUP37ixcvxr59+5Rc/dGXACXY3rBcpAgwzC5SpGP/PvThx74M2YM4IaD69yVNr+Q0F/++ZEHjQQKBCMgD4v79+yFhdpIOV8z3iRdTH4gMzw1GgAp/MDI8TwLjREDM+ZL1TPz7kgWN/v1xEkQU31ZcQPJAKA+G8oAYnelwoxhggjaNJv0EFTy7HTsEZJZfVVWlKP7nnnuO/v3YEV3IWyphdlu2bMHVq1eV3A7ir+dBAsES4Aw/WFIsRwLjREC24RVzrSTwEfOtrMIWcy6PxCEgfvrq6molzG7JkiWQMDsq+8SRf6h6SoUfKpKshwTCSED8+9yGN4yAo7RqebBTw+y0Wq3y4CcPgDxIYDQEaNIfDTVeQwLjTEBMuxUVFZgyZQrKy8s52xtneYTj9r5hdi+88IJi4QnHfVhn4hCgwk8cWbOncUhAZn+y85nM/pcvX07/fhzIWBbi7dy5k+lw40CW0dYFmvSjTSJsDwmMgICszhb/vhySXY3+/RHAi7KiYr6XdLgiUwmze//995kON8pkFOvNocKPdQmy/aMmkJSUhPH8G3XD/S4U/77/NrwStsUjdghIJIaE2TkcDpw4cYJhdrEjuphqKU36MSUuNpYEhifg6/tlitXheY1nCa7FGE/6iXdvzvATT+bscZwTkF3RxBwsZmHZLU3MxCEP43N1oj5fj6SkLBjN18JE9Das9UuRpK+E2eEa5B4uOMyV0CctRb319iBlou+0b5idLLrcs2cPF15Gn5jirkVU+HEnUnaIBAA1Ta+Yh+UI9Ta8rq4PcbCjEFt+/hAamv8AR1ig34P00kNw26qRq42Pnyo1zE7yKUheBabDDcvAYaWDEIiP/6JBOsfTJJDoBHy34T1//rySrU9M/mM7rqGlbjc6igvx48InkVn7Nj6Iodn12Po++qvVdLgiB0mHK5EV8mDGgwQiRYAKP1KkeR8SGEcCkpWttrZWidmXLVQlhl/Cv0Z1OP6A5gagOP9RPJD2PSwzXMDBs1fQZ3RXzP1pyK/v7D+n3OgazMYs6I1mr0XAAau5HsYF4hqQBZT5MNabYXWqNQUw6bvsaG/aihK9Z8GlvmQbjl/4bGA3nFaY641Y0Lco07/egcXD/Un100tK3HfeeUeRA7c/Djd11h+IABV+ICo8RwJxSkB2U1P9+w899JCy29rI/PsuONpOoQEG5GdNAjTTMW/ZYzAd/BBdqp4OdE54+jwoaOFAZ/065BSdwdSadvS63ei1/RRTz6xFxpM70N6n9H0FcQPt21Yg643r+EHLTbjdvbC+NAMXfnMS9r5iN9D+9noUnXkEb33RctykFQAAFc1JREFUC7dS74tIbliJNYesfg8gfReF5Y0aZifrKGQ9haTDlfUVPEhgvAhQ4Y8Xed6XBMaJgOrfH9U2vC4rPqjZCxQ/jizFr34P0uYthMG0G3Ut6uI99VwTfv3/3PD20u9BwdGGX1a1omDXz7A2Wwf5IdLo5mLdGztQYdmCykDK2XEBh7b1oGLTehSma+UKpKQvwkubnoVOZenqwScnO5E5/ztIT/H8vGl0T6D6t11oLp2p3EctGs5XyYcg6ybkUMPswnk/1k0CwRCgwg+GEsuQQBwSCLQNr6weH+pQFuuZ9Io5X1SuHBrFrG8bsHhPk5aHVaX/B9sOXfCY711/xKlfmZCxfhGytfBYCewPY+6srw9Uwil6ZGQCHRYbnN76PS/eBwb7DGSkpvh8o0FKahoy1TOaqfjrJ2bCVPVLHGk1o8ls9atHLRieV1kfIdsZi59etjeW/Ag034eHNWsdOQEq/JEz4xUkEFcExL8vYWHi2x9aOd1G19kTMKEdtXlT+pMWJT+MMpMd9oZTaFPD5zQP4fGnnwS851xdp/GL+hko/vtHkYI76LnS5WOGvxun/eIV9KguAuXr4a/x1PIA5rz4HiwHvoMbjTVYnJeBiUl6LDDWw2wNTyyB3FcelGRdxMqVK5V1ErJegrvZ3S1XnhlfAlT448ufdyeBqCEwrH/Z8SHqqs7CUPep4nMX/3jf383TqMBe1Hyg+sk10GY9jmKY0Nz2medBwbAQ89LuATABU6en9ZvhAxDQzZ6OqQN+nYa/pr8aLdJzC1Fa0wy3+0vY2nbh+z3bkZfz+hDx/P1Xj+Sd+On379+vbFssfnqG2Y2EHstGmsCAf6lI35z3IwESiBUCqg++EKvyZww0w0sXtI8iv1g/cPGecg5o+M2v0HTwAgzLvoc05RfH+zCg+xTnLv1p4EI6pw2WDiAzQw9fw73465UHCN1lWLp9jf0uOLu70DEoxgnQzVmElSVPQmfvwpWeO4OWHOkXapjdpUuXlDA7yYHPMLuRUmT5SBKgwo8kbd6LBGKWwHW0NZuA4kI8Pm1CgF5MQvbSp5FjOoGzXWrGO8+5jG0bsdH0GJbNm97/oKDNwo82Z+P46p9iR6vdo/Sdl1C/Zi1qM8pRvTS9v6x6N+08vLDru2goMqK+U8zzLjitR/Daq3v73QPekMAFxqb+8D6nFaea24HSf0C+YmFQKxzdq4TZrVixAhJmJ356Md8P7QoZ3X14FQmEmgAVfqiJsj4SiEMCLuuvUVM7FeuXPgZ1sd7AbmqQ8q0CFBvOoqruQ2+cvXpOB91dylaLmaXb0XJgPnqMc5AsMfMT/xmW+TtgObYWc7wr7AfeYwKmFVajZd8snMm9H0lJyZi4qg3fXvMCDGpBzUw8u/cg1kw5ipyJyZ51BhOX4OiUVTi2+e8wbQy/eL7pcJcsWaKE2dFPr4LnaywQ4OY5sSAltpEESGBcCcisXuLp9Xq9kseApvtxFQdvPkoCY3jeHeUdeRkJkAAJxBgBmclLljw5Xn755dFnKYyxfrO58UWACj++5MnekAAJhImA7y6EskAvLLsQhqntrJYEhAAVPscBCZAACQRJQM1SGK5dCINsBouRwKgI0Ic/Kmy8iARIgAQA8e2/++67yqskLho2lwGhkcA4EqDCH0f4vDUJkEB8EJCY/HXr1iEnJwcbNmxgmF58iDXuekGTftyJlB0iARKINAHZhVCy7Em2vQcffHAUuxBGusW8XyISoMJPRKmzzyRAAiEnoPr3R7ULYchbwwpJ4G4CNOnfzYRnSIAEAhJwwHpyL/baDNhcErmtZgM2JQZOin9fsvFdvXpVycbHJD0xILQ4byJn+HEuYHaPBEJGwNGGupLX0d4bshrjuiJR8LIL4T/90z8pSXtkN73hth+OayDs3LgToMIfdxGwASRAAvFMwGAwKP79WbNmKf79pqYmyC57PEgg0gSo8CNNnPcjgVgk4DDDODMPtXY7TGUPI1lfCbPjv2E2ZiFpgRF7tpZAL/nwlfMuwGVHe9NWlOiTPPns79qT/prn2vw3YT7/Zn+5BUbsa/duphOLnAZps/j3n3nmGWVXvfPnz2P+/PmQlf08SCCSBKjwI0mb9yKBWCWgzUVN52lU6HQw1H2KXls1crXen4+Wf8fZSeWwyt7zLauQrXWgfdsKPHn0Xjzf/iXcbjfcvf+BTckHkbeqDu1OVz8F02oUvQVvuZuwrEnG3qwV2NZ+o79MHL2TXfVkdz3ZZU/8+7Lrnvj6eZBAJAhQ4UeCMu9BAvFMQPckSn74CFIwAbr0byDFcQGHtvWguGQZsnXerXQ105Dz7DIYWj7CJzafPel1z2NX9QpvOS3SC9djU0UPth264N1xLz7BiX//yJEjkF33ZFOe6upq+vfjU9RR1Ssq/KgSBxtDAnFAQKwBtjbUZF+HuakJ4rNuqjciL6MMJv/uZT6GWepDgfJdClIzZsDecAptDh9LgP91cfJZ9e9rtVosXLhQYUX/fpwINwq7QYUfhUJhk0ggtgk40FlfBv3EDOS98TEU4/wDBXir7R0YcBmWbufw3bN34UqPjyVg+CtitoT491evXq0oe/HvP/XUU/Tvx6w0o7vhfxXdzWPrSIAEYo2Ay/oB1pa1oqDxCvYUfsO7Q5cLDrMJHQBmB9MhXRqmT/W6A4IpHwdlUlNTFf/+xYsXIXn5jx49ih//+Mdg/H4cCDdKusAZfpQIgs0ggfgg4IKzuwsdeBhzZ33dZzvOv+CLG467u9jRhW7fRXxwottyGbrix5GlLgq8+6q4PiMb8Ih/X9L0in+f2/DGtbgj2jkq/Iji5s1IIIYJpOiRkXmfpwO3nBigp/u6pYE263EU686iYe/vYVfc8Hdgb92DytVvwt5XzvvGvhevvnYEVqUycQUYUdTwXex6YR60/mUT7HNhYSG4DW+CCT3M3aXCDzNgVk8CcUNAMwMFxmLckTj8r5biUNcgyWO08/CTYzXI/qgE+mSJw5+DDb+bjJIjh1Gh86ORU4zib1/Ga+nJSEq6H7lnZmFfSzUKpyWWOd+PSt9HCeMT/76E8Yl/f9GiRRCTPw8SGA0B5tIfDTVeQwIkMEYCknhnIfIu/hMsx0uRzqlHUDwlWY/E74tf/4UXXoD4/XmQQLAE+G8WLCmWIwESIIFxJiDb8L7//vuKf19M/vTvj7NAYuz2VPgxJjA2lwRIILEJqNvwin/f4XAoaXpNprsyHCQ2JPY+IAGa9ANi4UkSIAESiA0C3IY3NuQUDa2kwo8GKbANJEACJDBGAuLfX7duHXJycrBhwwbIgj8eJOBLgCZ9Xxp8TwIkQAIxSkD8+2fOnFH8+w8++CD279/PbXhjVJbhajYVfrjIsl4SIAESiDAB1b//+eef49KlS9yGN8L8o/12NOlHu4TYPhIgARIYJQHx71dUVGDKlCkoLy9nmt5RcoyXy6jw40WS7AcJkAAJDEJAVvFXVVUpiXuee+45+vcH4RTvp2nSj3cJs38kQAIJT0DdhlcS9Yh/X7Ys5ja8iTcsqPATT+bsMQmQQAISEP/+M888gz/+8Y9Kml5uw5t4g4Am/cSTOXtMAiRAAkpOftmGV9L0chvexBgQnOEnhpzZSxIgARIYQCDQNrzXr18fUIYf4osAFX58yZO9IQESIIEREZCc/BK/L8fChQvp3x8RvdgqTJN+bMmLrSUBEiCBsBHo7u7Gzp07IeF8Yu4XKwCP+CFAhR8/smRPSIAESCAkBLgNb0gwRl0lNOlHnUjYIBIgARIYXwLchnd8+Yfr7lT44SLLekmABEgghgmoaXplG1455s+fr/j3Y7hLCd90mvQTfggQAAmQAAkMT4Db8A7PKNpLUOFHu4TYPhIgARKIIgLchjeKhDHCptCkP0JgLE4CJEACiUyA2/DGrvSp8GNXdmw5CZAACYwLAdW/L9vwSiif+Pdlgx4e0U2AJv3olg9bRwIkEIcEkpKSxrVXbrc7pPdXt+GVSmtra7kNb0jphq4yKvzQsWRNJEACJJDQBLgNb3SLnyb96JYPW0cCJEACMUMgMtvw3oa1finESqI3muEIEx2XtR75SVkwmq8NfgeHGUa9Hvn1nXANXipqvqHCjxpRsCEkQAIkEPsE1G14xb9//vx5xb8vK/tDdriu4OzBz7B+yyZkNpxCmyM8qlaTXopmdxtqcieHrOnjXREV/nhLgPcnARIggTgkMGnSJMWff+DAAWzZsgUrVqxQcvSPrasuOFr2o6pjPr7/43/AssxDqPnAGhOz67H1OzRXU+GHhiNrIQESIAESCEAgPT0dR44cQUFBAYqKirBr1y6Mfhve62hrNgHFjyPrgRmYt+wxmA5+iK6+Sb7X3J9fD2vfOWmUCw5zJfT6SpgVi4ALTqsZ9cZ8xTWQlKTHAmM9zNZ+B8HdJv07sLc3YWtJpucafQm2Hr+AngF9dsBqrodxgX7QegcUj/AHKvwIA+ftSIAESCARCYRkG17HH9DcABTnPwot7kHavIUwmE7gbNdtL9JA5+QrnwcFLeDsbMDzOWtxZupPYet1w93bjpqpZ1CUsRxb228EEI8LzvY3sTzrF7j6g8P4wu2G27oRMy6cxH67WlzK1GFV0TlkvNUJiYRw9/4HNiUfRN6aD/weQNRrIvtKhR9Z3rwbCZAACSQsAfHvr169WsnJL/79p556CsH792/D+sHbqIUB+VmTFIaatO9hmeEsquo+7Fu85zl3AQ2//gOcKukBDwrX0frLN3Cy4H+heu1c6EQLanTIXvcvOFDRg/LKpgDK+TpaD/0KlgojXiqciRSpN2UmCl8yokKn3uQObJ98hJbMuZiXrvWc1ExDbnUz3M2lSI8CbRsFTVBh8ZUESIAESCARCKSmpir+/VdeeUXx71dUVCgJfIbsu7JY7yx0Ys7XelWXZjrmLZsHu+/iPc0M5K9aCMu2I2hVzPd38NmpJjRkPI2l2ZMARfnbkDn3EY+y77tpClIzZgAdXeh2DvAH9F+Tofcoe/WaFD0yMu/zfpoA/V//T+SYdqPuyO9hbmqB1b8e9bpxeqXCHyfwvC0JkAAJJDqB2bNn4/3338d3v/td3Lp1a0gcrq4PcdBkh702D/cnJXl95Pcio+wwYDehue269/oJmPZ4IYrhPee6jOZfnEBmcQG+laKBq+cKLvaZ4QPc0t6FKz13Bnwx7DVKaQ1S5qzFMctWfOfGv+HVxQuQMTEZSQuMqDdb+60NA2qO7Acq/Mjy5t1IgARIgAR8CKhpemVx3+DHNbTU7YbJUAeL+NzFP973dxWnK4Daml/3m+K1jyK/GGho/gNuKA8Kj2HZvOkQhaeZOh2z+8zwAe6oS8P0qRMGfDHsNX2lNUhJz0FhaQ1+63aj19aGxu/3oCpvOV4dKp6/7/rwvqHCDy9f1k4CJEACJDBWAooZ/kuUrspD2l1aaxKy8g3QDVi85zmHhia823QMJsNCzEu7x9MK5WFAj45z/wn7AMu9E92Wy0BmGlJT/G6iXmOxDZypO22wdAxumdDo5qBwZQmKdTZcvHJt3MMH/Xo1VqnwehIgARIgARIIJQEXHG2n0IAn8fTjDymz9IG1a6DNXoT1ORdw8OwVr1L1nstoQvnGj2FY9j2fB4VJyP7RGjxx/GVU7jjnVfoOdNYbUVQ7FVuqCwMssJuMnBcqUdCwFmvqL3mUvrMTTa/VoLbPPeANCVxQiaa+8D4HrKdOoRWFWJU/I0DbB/Yk3J+o8MNNmPWTAAmQAAmMnoDLig9qDiFj/SJkq4v1/GtLeRR/X/wYTFX70aJm3lPOzQN0/spWg5SZxXizZQfm9/wM+mRZDzAT/2iZiwOW9/DinAf8a1c+a6Ytwo6Wrcg88xQmyhqCiWvx8bdLscWgLtq7B+nP7kDbmkk4mnO/d43B/cg5Oglrjr2ERdMGugkC3iTMJ7l5TpgBs3oSIAESIAESiAYCnOFHgxTYBhIgARIgARIIMwEq/DADZvUkQAIkQAIkEA0EqPCjQQpsAwmQAAmQAAmEmQAVfpgBs3oSIAESIAESiAYCVPjRIAW2gQRIgARIgATCTIAKP8yAWT0JkAAJkAAJRAMBKvxokALbQAIkQAIkQAJhJkCFH2bArJ4ESIAESGCsBFxwWpuxtfK9/nz5Y60yAa+nwk9AobPLJEACJBBbBK6jte4llLffjq1mR1lrqfCjTCBsDgmQAAmQAAmEgwAVfjiosk4SIAESIIEQEbgGs3Eh8mrbAVMZMpKzYDT/NxzmSuiT8mHc8zpK9JIPX85fA3AH9vYmbC3J9OazT/Lbk97lvXYp9phPYntfuXwY97X67aAXoi5ESTVU+FEiCDaDBEiABEggEIHJyK05gdMVcwBDHSy9bajJnewtaELDWR02WnvRazuIldkPwNn+JpY/eRTJz5vQ63bD7f4Stk33oSFvPd5uv+Fzg8NYWXQAUMr14gvLKmDvcizf1jpwC1yfK2L9LRV+rEuQ7ScBEiCBhCUwB8Ul38fMFA00um/imyk30HroV7AUl6AsW+fdjnYCdDnLUGzoxMlPenz2pJ+F0l0/w1qlnAYp6Yvw0qalsGw7glZ1x7044/pXcdYfdocESIAESCBhCYg1oA02OGA1H8WpG70APsfHb7yM2hbAsMwXzMOYO+vrPnvUa5CSmoZM+240t61Hbp8Vwfea2H7PGX5sy4+tJwESIAES6CPggrNzH0r09yMjbzc+vuEC8DXkv9WEOgPQYbEFYa634eKVaz6WgL7KY/4NZ/gxL0J2gARIgARIQCHgsuLQ2o04WdCI7j2FmKZOaR1mGDvswOxgOOkxe/pkn5l/MNfERhkVR2y0lq0kARIgARIggcEIOG2wdACZcx+Bzke7ub64AVm/P/C4DEu30+eUC87uLnToDMjPmuRzPn7e+iCJn06xJyRAAiRAAvFEIAWpGTO8HboNp/MvgTunfRT5xXqYGg6ixX5HKeOyn8OOypdRb/e/pB21r25Dk9UBQFwBDVhTdAwFu1YhRxufqjE+e+UvV34mARIgARKIYQL3IK1gBTbeqUJG8gwsPtQFWY539zEZOT/Zjb3ZHyJP/xUlDj91w0d4qGQ3GiWsb8BhQEXxw7j82lwkJSVjYq4ZmfsasaPwG3FpzpeuJ7ndbvcABvxAAiRAAiRAAnFLQBLvVGFmXhc2W/ajNP2euO2pf8c4w/cnws8kQAIkQAIkEIcEqPDjUKjsEgmQAAmQAAn4E6BJ358IP5MACZAACZBAHBLgDD8OhcoukQAJkAAJkIA/ASp8fyL8TAIkQAIkQAJxSIAKPw6Fyi6RAAmQAAmQgD8BKnx/IvxMAiRAAiRAAnFIgAo/DoXKLpEACZAACZCAPwEqfH8i/EwCJEACJEACcUiACj8OhcoukQAJkAAJkIA/ASp8fyL8TAIkQAIkQAJxSIAKPw6Fyi6RAAmQAAmQgD8BKnx/IvxMAiRAAiRAAnFI4P8HADPL2ZZEExwAAAAASUVORK5CYII="></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that Ayako avoids the trap in this wall.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to pass through a door <strong>in the first wall</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy</strong> the probability tree diagram and write down the relevant probabilities along the branches.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap while attempting to pass through a door in the second wall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>120 contestants attempted this game.</p>
<p>Find the expected number of contestants who fell into a trap while attempting to pass through a door in the third wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in centimetres.</strong></p>
<p>A solid metal ornament is in the shape of a right pyramid, with vertex <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math> and square&nbsp;base <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>ABCD</mtext></math>. The centre of the base is <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>X</mtext></math>. Point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><mn>5</mn><mo>,</mo><mo>&#160;</mo><mn>0</mn><mo>)</mo></math> and point&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math> has coordinates <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><mn>6</mn><mo>)</mo></math>.</p>
<p style="text-align: center;"><img 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RV5+OGHpb6+wTzq9+yzz6mP+Xw+8wgREQViYCfbOHbsmCxYsEDGj79Jrr/+BvOoGKP3i6WmpkYdmzRpiuTmzuASOCKiNjCwk20UFhaqdPtDDz1kHvFLTDxf6urq1PuzZs1Safq8vDxVOU9ERK0xsJMtfPDBB7J69SpZvPgR+cEPfqBG71BS8oSMHDlKpeABhXMlJY/LX/+6XdatW6eOERHRKQzsFHcYeefm3idXXz1cJk6cqNLsaWlD1Hx7VlaWXHbZZerzdPod+zk590lBwYPqgoCIiE5hYKe4w8gbKfhFixap7nIffVStjl9ySara9u7dW22PHDmitpCbm6suBHBBwJQ8EdEpDOwUV2gbi5E3RuCDBg1Sx3bsqFLz6EjJgz6+b98+tQVcAOBCABcE7EpHRHQKAzvFFdalI4hjBK7t2LFDMjPHq/extA3BH6PzyspKdUxDwMecPLvSERGdwsBOcYOgjSK4JUseaXWDF/SIv/nmm9X7WNq2e/duGThwoOzZs0cds5o0aZJaHodlclwCR0TEwE5xgiCMoI116cOHDzeP+mFfp9+19PR0dREQjF4eh451RERex8BOcbFs2TK1xbr0UPTp00dtkZYPhLl4dKpjVzoiIgZ2igPMh2PNOtaoh3pDF10Zf/jwYbUNZO1KFyz4ExF5BQM7xRSWpum2sVijboWmNEuXLm0VmDdt2iwZGRknU/OHDh1S22AwakchHgryuASOiLyKgZ1iCkvTsEQtPz/fPHLK/v37VYW7FQK6HtUHq4y3QgGe7kpXWlpqHiUi8hYGdooZdIlD4MYStcDiONi1a5faBvsYDBs2LGhlvBW60s2ePUeWLFnErnRE5EkM7BQTSI2joYxuGxvMtm3b1Dx5W1JSUtqsjLfKzs5mVzoi8iwGdooJtI1FUMb8t3XNeqDUVH8bWa2goEC2b/cH8wEDBqhtR8Vx1q50mM8nIvISBnaKOqxZ121j9Q1dgnnqqadUwxkrVM/rgrlevXqpbVuV8VZI56PqHl/PrnRE5CUM7BR1aByDavVp06aZR8Kje8e3Vxlvhap7dqUjIq9hYKeoQsMYNI7BUrRQ16y3B4G6vcr4QOxKR0Rew8BOUYN16cXFRaogDg1k2oN582CFbvha3XUOkpOTO6yMt2JXOiLyGgZ2iprCwkJVwJaTk2MeCQ5BffToUfLJJ5+YR05ZvHhxq17yoVbGW7ErHRF5CQM7RQUq2XXbWD033hbcvQ369++vtu0JtTI+ELvSEZFXMLBTxCFwzp79oFpLHtg2NhjMmeNzQ5mD70xlvBW70hGRVzCwU8QhcCIFj7XkocDIftSoUeZe+/Tof+/evWrbGexKR0RewMBOEYUUOQInAmhbrWED4UYvEyZMMPdaS0rqd1rRGyrjq6urzb3OYVc6InI7BnaKGARKzGFjLhsBNFS4AOhoHt4KlfHbtr1l7nUOu9IRkdsxsFPEVFRUqDlszGW31za2q1AZj8Ac7oibXemIyM0Y2Cki0NkNy8mwrKy9trGRoCvjGxoa1DYc7EpHRG7FwE4RodvGzpo1yzzSMQTUW265pd1CNoysBw8ebO756cr4zz6rU9twsSsdEbkRAzt1GdLZ6OyWl5ffqbaxH31UrVL3OlAHg5F1YBGeno9vbDyotuFiVzoiciMGduoStI1FOhtp7VDWrFvV1u5Ro/zOFM5pXamMt2JXOiJyGwZ26pIVK1aoQjad1u6MzZs3S2bmeHOvc4YMGRJ2ZXwgdqUjIjdhYKewYW582bLHZfHiR8IadaMpzY9//GNzLzikyIONpC+44IIuVcZbsSsdEbkJAzuFBQEVTV7Q7GXixInm0c6ZPn16qxu8BIMUue4lb6UL6rpSGW/FrnRE5BYM7BSWdevWnWwbG801620577zz1LarlfFW7EpHRG7AwE6dhtR4QcGDkpNzX8htYyNNV993tTLeil3piMgNGNip03Tb2NzcXPNI52A0jLlzVNR3BarZI1EZb8WudETkdAzs1CkIyCgyQyV5uCn4Tz75RM2dHz161DzSNtwgJiMjw9xrDfdvj1RlvBW70hGRkzGwU8gwwtZtY7H+O1y7du1S21DS+PictpreRLIyPhC70hGRUzGwU8gKCwvVtjNtY4PZtm2bGhF3VaQr462sXelWr15tHiUisj8GdgoJ5psx74z55860jQ0GwXLEiBHmXviiURlvpbvSoVCQXemIyCkY2KlDSHWH2zY2mJqaWsnMzDT32ldQUCDbt28391rTFxhoTRst7EpHRE7DwE4dKikpUXPZ+fn55pGuQdFdqKN+ZAkOHTpk7p0OI+r9+/ebe5Fn7UqH54GIyO4Y2Kld1rax8Vqz3h5UxiP4RxO60uH3x/PArnREZHcM7NQmpJ7RsAWp6HDbxgaKdDoblfHQ1TXxHcHvr7vSRftnERF1BQM7tQltY/0p6Mcj0jYWBWgpKYM6NepFqr1Pnz7m3ul0ZXwoa+K7Ar9/cXGxmpLQqwOIiOyIgZ2CQmMW3TYWqehI0DdzQfo8VIsXL273RjG6Mj7YjWIiDUvg2JWOiOyOgZ2CQmMWpOCnTZtmHum6yspKlc7u6nI5K/29Pv/8c7WNNt2V7s4772BXOiKyJQZ2Og3axmKtOZZ6RTIIo/0r7sEeadGujA+k6w7YlY6I7IiBnVpBYVhxcVGX28YGgwuF66+/3twLDeblOypWS01NjXplvBUudtiVjojsioGdWkFhGArEcnJyzCORgwuFzi6ZGz16lGzdutXcCy4x8Xy1jWW1On4X1B+wKx0R2Q0DO52EanXdNhaFYk5x4YXJahvtyvhAuG0tu9IRkd0wsJOCwIQ12ihuGzt2rHnUGfr166e2saiMt2JXOiKyIwZ2UkpLS1UKHoVhkVizboXq8aeeeipqqXI8XoycY1UZb8WudERkNwzspOaIlyxZJLNnz4lK29jPPvtMff9w0tWYFtBNaNozYsS1Ma2Mt2JXOiKyEwZ2j0OwxRwxRrzZ2dnm0cjCSBbfP5x5e6wbD+ViI9aV8VbsSkdEdsLA7nEVFRURbRsbzObNm9WIOpriURlvxa50RGQXDOwehrnv3NwZas16pNrGtiU9Pd18LzriVRlvxa50RGQHDOwetmzZMpUinzVrlnkkOtauXauCXjjQBS+UdeLxqowPxK50RBRvDOwehXQx0sZ5efkRbRsbacgohBKsdWV8TU2NeSQ+2JWOiOKNgd2DMA+9YMEClTYOdyRtR5jHr6urM/fih13piCieGNg9aMWKFaqC+6GHHjKPRAcq7mMZ2FAZj5GyHbArHRHFCwO7x2DpGZqpoKlKtNvGfvLJJ6rXe6yCu66Mt0PhGqYG2JWOiOKBgd1DrG1j0VQl2nbt2qW2urAtHPX1DSFPF+jK+CNHjqhtvLErHRHFAwO7h6xbt06l4JEejtaadatt27apefxY/CzQFxD79u1TWztgVzoiijUGdo9AOhzFXCjqivaadQ3z3SNGjDD3os8ulfFWeEzsSkdEscTA7hFFRUUq6KGoKxaQ9t+0abOMGjXKPBIbdqmMt2JXOiKKJQZ2D0CTF4yesb46Vmlx/Bz0eO9qgV5BQYFs377d3OsYOtzZpTLeil3piChWGNhdDvO6um0s1lc7DUa5hw4dMvc61qdPH7W1Y/BkVzoiigUGdpfT87rRbhtrF71791Zbu1TGW7ErHRHFAgO7i+m2sZjfjWXbWBTqTZ8+PS6jZn2LVztVxluxKx0RRRsDu0uheA1tY7HUKtZtY9HbHaPSSMznYwpBp9dDhd/ZTpXxgdiVjoiiiYHdpdDtDEusMK8bawiqCK6RyBIsXrxYhg8fbu6FZuDAgbarjLfCBQ+70hFRtDCwuxBSvLptrE5Nx1J5+WsxX+ZmZdfKeCtrV7rOVP0TEXWEgd1lkNpFihep3li0jQ2En5+ZOT5mTXCCsXNlvBX+PlgCN3v2g+xKR0QRw8DuMmgb60/xPh6zNetW+JkPPPBAp9PnbUH2obNBz86V8VZ4rnCHPXalI6JIYmB3EYxQY902Ntpwd7itW7eae6Gxe2W8lbUrHRoJERF1FQO7i6DxCVLw06ZNM494F4r3KisrzT17w6oFVP+jkRC70hFRVzGwuwTWrOu2sbFcs26FlDkehx2WcKEyfs+ePeae/aGBkO5KxyVwRNQVDOwugICKNesoxIpn29iPP/5Y9UK3QyEYKuNRa+AUuBhbsuQRdXGGOgkionAxsLsACq9QgIVCrHj64IMP1LarN36xwh3iMjIyzL3Q6cp4J3V3Q8Ehu9IRUVcxsDscgqluGxvJgBqOzZs3q7niSEIhXDhTC7oy/vDhw2rrFLor3dSpdzElT0RhYWB3MJz4c3PvU4ViY8eONY/GB9LvSH0jBW4HujK+M3eGswMsgVu58hmVgWFXOiIKBwO7g5WWlp5sGxuPNetWGFXv3Plh3C8wrJxUGW+FixJ2pSOicDGwOxTmYJcsWSSzZ8+JS9vYYBDcI32BgbXd4c43Dxs2zFGV8VbsSkdE4WJgdyjdNjY7O9s84k5Y2427xYUjJSXFUZXxVuxKR0ThYmB3IIxiEbCwPCreKXg7GzBggNo6tcKcXemIKBwM7A6DzmQYxaL6PFL92LsKlflJSf1s1zWtV69eauu0yngrdqUjos5iYHeYZcuWqRQ8OpXZxa5du9Q2Xh3v2qKX/zmtMj4Qu9IRUWcwsDsI2rUiLZuXl2+rIFpdXa0KvaIxLVBf36BGreHC43JiZbwV/tbsSkdEoWJgdwhr29iuBLpowMXGiBEjzD17SU5OdmxlvBW70hFRqBjYHWLFihWqQjo/P988Yg9IDaPA66qrrjKP2IuTK+MDsSsdEYWCgd0BUJyGZiVoWmKXNesa0u/IINjtcWlOr4y3wnPNrnRE1BEGdpvDyAyd5dBFDU1LvAbV9l1Z6uWGyngrdqUjoo4wsNsciqWQSkZDGq5Z7zxdGb937161dQN2pSOi9jCw2xjSxyiWQtHUZZddZh61D6yrXr16te2DC4IgKvfdAhd47EpHRG1hYLexoqIiVSyFoik7+uijanXhYXeojN+27S1zzx3YlY6I2sLAblM4WWPd8sMPP2zbFPyOHVVq7j+aa+rRda1Pnz7mXnhQGY/RrdsqydmVjoiCYWC3IaS2ddvY66+/wTxqP+Xlr6k7qEXT4sWLu9w6V1fGNzQ0qK2bsCsdEQViYLchPW+ak5Ojtnak59WHDRuqtnamK+M/+6xObd2EXemIKBADu81gCRPmTTF/qiu67QgB5c03t9o6o6Dp57Gx8aDaug270hGR1Xe+NZjvU5whlTpu3Fg5//xEWbt2rXnU2xCozjvvvC7P40+fPl3OPfdcldp3I/2/A6+/XsGlkUQexhG7jaCbGIq80JCG/EaPHiVbt24198I3ZMgQ11XGW7ErHRFpDOw2gZGpXdvGBsLo0GlV2BdccIErK+Ot2JWOiICB3QYQbNBZDtXNTmgb+/7778s111zlqPncwYMHq60bK+Ot2JWOiBjYbaCiokK1jS0pedwRc6O4KQ3YPbNghXl6cGNlvJW1Kx0uFonIexjY4wwpbb1m3Y5tY4PZvHmzeryxsGnTZsnIyDD3wqeL79xaGW+lu9JhCRy70hF5DwN7nKGxCFLwaDTiBJg2QHYhPT3dPBJdyApEqrMdLkbc1DO+PexKR+RdDOxx9MYbG0+2jY1U8IqFNWvWRmQUHWv9+/d3dWV8IN2VLi8vz9VFg0TUGgN7nKCwacGCBarQyQlNXjTM4aIhipMuRDQvVMZb4W+Eug1kWNiVjsg7GNjjBG1jEWRQ6ERtwxxxpKrvvVIZb4W6Dd2VThc9EpG7MbDHAU6wTmgbaweYI969e7e51zVeqYwPhNv+4i58ubn3MSVP5AEM7DGGEytOsDjRjh3rbwHqFBg5FxQUOHZ9tJ4+qK3do7ZegekTdDNkVzoib2BgjzHMdeIEixOtE9asW2HkjEyD0x63FSrF9+/fb+55h7UrHYo2ici9GNhjyD/ifVDNeTqpuYtWWVmpiv2cHNhRGY+LEy+aNGmS+vuhaJNd6Yjci4E9hnTbWMx5OhEC4ogRI8y92Kivb1BrsiMFlfHg1cDGrnRE7sfAHiOo7sayoyVLHnHkiBeBEGnsiy66yDziTLoy/ujRo2rrNSjWfPbZ59iVjsjFGNhjwNo2FmvAnQiFZ7iXuVMfv6Yr4yNVae9E6JvArnRE7sXAHgPLli1TW6e0jXUzXRn/+eefq61XsSsdkXsxsEcZKpD1mnUndmuLt6SkfhFPGXu1Mt6KXemI3IuBPYowEtJtYyNZABZrmF9HUx23jOxSU1M9Wxlvxa50RO7EwB5FaAaCCuT8/HzziDNVVe2Qm24a75rAnph4vtpyyRe70hG5EQN7lGAEhGYgaArixDXrVjt2VKn5WLdMJVx4YbLaerUy3opd6Yjch4E9CjDywckSI6GJEyeaR52rvPw1ycwcb+7FFmoT9BK1SOnXr5/aerky3opd6YjchYE9ClCMhKIkNAFxcpc2wHIojOaGDRtqHokt1CZEOuOBvwkyEF6vjLdiVzoi92BgjzBr21gUJzkdGpq8/fY7MmLEteYRd8Dv4/XK+EDsSkfkDgzsEVZUVKRGg9OmTTOPOB+Cu9MzD4FYGX86dqUjcgcG9gjCyRAnxYcffphr1iMEGZBopIZZGR8cu9IROR8De4QgQBQXF6mTIk6OFBmjR4+SrVu3mnuRw8r4trErHZGzMbBHSGFhoZqfzMnJMY843/bt2+W66zJcOXJjZXzb2JWOyNkY2CMAAVC3jcU8pVtgLT4uVtz0O2m6Mr6mpsY8QlbsSkfkXAzsXYRU5ezZD6o1605uGxvMhx9+qKYW3AqV8XV1deYeBWJXOiJnYmDvotLSUjWqRUMaN8GJHIWA6enp5pH42LRps2RkZJh7kYXKePyOFBy70hE5EwN7F6Bie8mSRcaIfY7j28YGQmBHN7Irr7zSPBIfeF6jtcJAV8az+rtt7EpH5Dzf+dZgvk+dgMB3++23y8GDjfL66xWuW+ftBbgwQ9X9K6+85opmQtE0ffp0qa7eLevX+7iUk8jmOGIPU0VFhaoaRvUwg7oz6cr4ffv2qS21jV3piJyDgT0MSN2igQcKyzjSi66CggK16iAaWBkfOnalI3IOBvYwLFy4UAUENPJwI1y44ORth0poLCM8dOiQuRd5rIwPHbvSETkDA3snoYDI7W1j3333XXXy9gJU/bMyPnTsSkdkfwzsnYC2sbitJW5v6ea2sZWVlep39ELtQJ8+fdSWI9DQWLvSYaknEdkPA3snrFixQhUQoZDIzZD+HjJkiLnnbr1791bbI0eOqC11DHUlWOKJpZ7sSkdkPwzsIcIJDGt5sabXjS1WNT1ytUtRYH19Q1Q7+un+A6yM75zs7Gx2pSOyKQb2EODEhRMYTmQTJ040j7oTLloQTIcPH24ecT/8XVkZ3znWrnSYniIi+2BgDwHucKXbxnLNuvsMHDiQlfFhQLYDNz7C1A270hHZBwN7B9CdDHe4wp2u3NY2lvxYGR8+TJOg0BKjdhYgEtkDA3sH0GkLy3twpyu3w5QDKv/tJCmpX9QborAyvmt0MSn6OxBR/DGwtwMBBct6sGbdCyn4bdvekrS0IZ4LcKyM7xrUZeA1wq50RPbAwN4GjFx121g3r1m32rGjSmUn3Fz1Hwwr47vO2pUO01dEFD8M7G0oLCxUW7e2jQ2mvPw1ycwcb+55Cyvjuw6jdlwYYvqKS+CI4oeBPQhU+KLSFxW/XrlFJdLvqPwfNmyoecQe8DcYPHiwuRc9qIzfsWOHuUfhwHQVu9IRxR/vxx4AI41x48ZKaupgeeqpp8yj7offG3PsQ4cO8+T9tjE3jDQy1vBT1+B1g650vM89UXxwxB6gpKREjVzz8/PNI96A0RbmSb0Y1EFXxnN+uOvYlY4ovhjYLaxtY7lm3Vt0Zfzhw4fVlsLHrnRE8cXAbsLIAicjFP+4vW2skyBFHotRtL6Qi+a9372EXemI4oeB3YS2sSj6QfGP19rGIlOxdOlS2zWnAcx7796929yLLqSPcctaigx2pSOKDwZ2A046um2sF4t9du3apaYgvDq/rqEyfs+ePeYeRQK70hHFHgO7AScdpOCnTZtmHvGWbdu2qeYiXoee8cjaUOSwKx1R7Hk+sONkg5MOTj5eHLGitgC/P4Ka1w0YMEBtWRkfWexKRxRbng7smFMuLi7yVNvYQHgOMA8aiyYw4di0abNkZGSYe9HVq1cvtWVlfOSxKx1R7Hg6sKNtLJbk5OTkmEe8B6lSNBSx6/I+PK5YZVJ0j3xWxkceu9IRxY5nAzsqwXXbWK/d9ITahuwFK+OjA4Wps2fPUV3p8PojoujwZGBHKhBdsbC8aezYseZRIpHk5GRWxkcRu9IRRZ8nAztSgUjBoyGN19asW2F+HcVMdj7BFhQUyPbtsatUT0lJYWV8FLErHVH0eS6wI5AhFYiUoNfbxm7dulVGjx5l7tkTpktiOefNyvjoY1c6oujyVGDHyBRVuajORUrQ6zCXjLSol7MWgVgZHxvsSkcUPZ4K7BUVFZ5tGxsMRkyjRtl7xB5rrIyPHXalI4oOzwR2jArQIANr1nmP6FOpZrs/F/h76Vuqxgor42ODXemIouM73xrM910NRVjbtr0l69f7PN8TXUNw79evH7MXAXBDnPLy1+TNN7eaRyia8NpE9gjNiLxe90IUCZ4YsaNAByeOvLx8BnULnEQZ1E+HynhUbXM5VmywKx1RZLk+sGNJFwp0kF5FwQ5RR3RlfENDg9pSdOHikl3piCLH9YF9xYoVavSlC3WIOqIr4z/7rE5tKfrYlY4oclwd2HGCwH3GFy9+hG1jLTA1ccstt6hsht0lJfWLeWGV/l9pbDyothQb1q50TvjfJLIr1wZ2zNXptrETJ040jzpQo0+mGsENAe70txQZN+cZ8b1SJY0t5ueHYMeOKjl4sJH1Bu3A1E11dbW5R7GAlLzuSocbNBFReFwb2NetW6dOECjIcXSBWGKWrKzfKasmJxs7WVJSWSf19Q3G216p9C2VsQf/r+TmTJBRd5dJTVNo0X3Hjh2SmTne3KNg0DMeqygottiVjqjrXBnYsYyroOBBycm5zyVr1s+Rf78yzXxfO1MSh2ZJ3tM+WZV9uTRvWCj3r9ghTeZH24IUJ4qUhg0bah6hYFgZHz+6K92dd97BrnREYXBlYC8qKlLLZ3Jzc80jLtatr4yc9WuZnNAs1U+/Iu8d73jUjiKlSy5JNffsDaO3wYMHm3uxo38mK+PjAyl5vIbZlY6o81wX2FFohU5WWBvrmTXaPS6VG25OFmn+i2ysar/oCPPq06dPd0wxIUZv8Whact5556ktK+PjA/+nuivd6tWrzaNEFApXBXakmXXb2Ouvv8E86gXflR69EoztcTn4JVPHkaALC1kZHz94DWM6DdNqvNseUehcFdh1Je2sWbPU1jv+IcePNBvbC2Rw0rn+Q9RluEBkZXx8YTqNXemIOsc1gV23jcWcrOeWcR3/m2x8qU4k4Sq5fOBZ5sHToRAJz5OTTpCYWonXaK1///6sjI8za1e6kpIS8ygRtccVgR2BCm1jsWbdc21jWw7IlsLfS1lzgqTefZNc0aPtP+nmzZtVpbGTag8wtbJ7925zL7YuuOACVsbbAFa2oMkUmk2xKx1Rx1wR2HEljxMwKmnd6Uv5+N2d5vvaP6WxyifFd2fJlNJPJDX7SSm9/0rpbn40mG3btqn0MoWGlfH2gSZT7EpHFBrHB3akaXXbWFfe8lF1nkuTKWWozvZJbnqy2XXuIknPekAqzv+VlKx6Vf48f7QktvPXxKgTFcbp6enmEeoIK+PtA1mm4uJidqUjCoGjAzuCFYpqUFzj6Lax7VGd59BpLthbjby+6C7JGjmo3ZE66FGnvnMZdYyV8faCJZrsSkfUMUcHdrSN9RfVPO6dNethQjajpqZWfvjDH5pHnGHTps2SkZFh7sUeK+PthV3piDrm2MCOF7W72sZGHy5+nHYBhAuSeK5yQGU8RohkH+xKR9Q+xwZ2vKjx4p42bZp5hCjyUBkPLNiyD3alI2qfIwM75td021jPrVkPA2oRuGQrPLoy/ujRo2pL9sCudERtc1xgx8gJa9Yxz+attrHhq6iokJSUQY4cdRYUFMj27dvNvdjTlfHxWktPbWNXOqLgHBfYsdQFS14eeugh8wi1B8H8hRf+pN7funWr44I75rcPHTpk7sWezgh9/vnnakv2gXoRdqUjOp2jAju6Tum2sU65O1m8oLjwqaeekrS0IfL22/4RL7q4BaaU0bIVo2Js49m+1c5QGb9//35zj+yEXemITueYwI5UG7pOofvU2LFjzaMUDE5w11xzlSxZskjde33nzg9Prn3v16+f+Vl+TU1N8sUXX6igjzekNQMtXbpUBX3UNiDwe62QjJXx9saudEStfedbg/m+rWH0iUCFdc2u7DAXYQjEWP/dmeJCXDzhxGjNhmDkn5eXp9KdGjIm1p78CPaYg+7Tp4/07t1bzUtHqqgR2YQbb7xRhg8fbh6JPVzQYN00LpBYrGlP+D/FxSyyK4sXLzaPEnmTIwI7Asfo0aPU6HP69OnmUQIUlj322GOyfPnyqAcdBH2k8gMDNy4iMNq3QnbACp+DrndnnXWWyho4aT29/v/jRaW96f/DZ599joW15GmOCOy33HKLHDzYKK+/XsEOcwaMrFHp/qc//UmNpJGGRNOOeAcdjJq++eYb1Vs98MSK/vZWWKr0wAMPmHv+iwbMYyPw2y144vnGqoLATAXZDy78sRT27bffYR0OeZbtA7u+Cl+zZm1c07F2gkAzbtxYOf/8RJk5c6ZjnhddmIe0PdaHWwO4TndbBZ6c9YVDPAL/dddlyK233saMkc3hAvGnP82S1NTBavqOyItsHdg5b+aHk1VgO1gcc9N8Ly5WcKMaBO59+/apoj4UReGYTv1jvl0Xsfm7Dt5t/G9MUvsQrEYgUvCzgfO39qcvElEtb/3/IPIKWwd2nEy3bXtL1q/3ebJoCRc2L7/8sioa9GoaGCl8/btjxH/48GG1rh3rys8+++xWJ249Fw6Ynhg4cKD8/Oc/j8i9BNC6FF3OAmsHyJ6wkgNL4FgXQV5k28Cur7q9GtCso1MUDSJAefHixhrYO4IROy4Em5qapaamRr766ivJyclpNYLXqyt04E9NTQ1pVMfKeGexTlc9//zzrM0hT7FlYOc8mX/EgYCUmZnp6UDSmcAeCqwiwIi/srJS7e/Zs0fWrl2r3tfwM9Gy+Nxzz1WB/6qrrlLHWRnvLOjncNNN408r1CRyO1sGdq+l0RBsEhISePvZICId2DuCi8ry8nJ1D3Y07kGFNX4+miLpynjQFwbp6elqi49zVGg/egrllVde4+uLPMN2gV1fZbu98AWpQuuSNY4qgsOqiMAK+njRlfFYhfDiiy+q0b5u3BM4946LU0hJSZHu3RPkkktSufwqDvA6u/3229Vy2fBrdVqkqfYt2fDq8zKnuEKa1bHLZfL8X0v2mH9J2fL/JbPmj5Qe6jhR/NkqsOsXIbh9Xkyvt0XKd/LkyVzK5wCoe8AoPnB6KNgKBXyuNfAHXrjpwkjc71137HNa4x6n6Nrqmn9K45ZHJXtKmcjk2fJg9s0ycpARwlsaperlP8mTs4tkw4gnpHJlliSaX0EUdwjsdlFWVvZt//4/+Hbnzp3mEff65JNP1Bs5h/7/7KyGhoZvjx49au754X88I+PH6vvpt8D/h23btn27fv169bn42DfffGN+hDoLzyOe440bN5hHQvGvb7/e8Ydvxxpf9++/Wv/t3/9lHj7J/Phd67/93DxCZAe2uQkMliphLgwjGzfNhWG0gBFe4CgPqWUWYTlLYuL5aou/aWcgBR84osf/+JtvblUpfNSS4K1fwA16Xn31VdWcCVNTKNxbsGCB+RE/ZLgwVYHXjm7+Q8GhRgPZMaxsCP3vd0zeW7dWqiVZbr71Wul72tmym3RPy5J7kv4hX7eYh4hswDapeKSmq6t3u6ZtLE60zz33XKsla+xa1nl2mmPX6+RjXYiFn4vGPc3Nza2mbPTjsQrsk44ghq9Fq16vz/FbV9sUFRV1fJ45vkXmXDVJyuROWfXOPBnZw1F3uSYPs8V/Kk7emG9++OGHXTPHiLapWFONKmqsfWZQDw9GrHgu7UCPqNEZL5ZwUYMLicA6DByvqalVo31cbOB/bejQYeZH/TCPj+CPOWasMEABYCBcICDouR2yJkuWPKLONevWrTOPtuObL+UgKuX+7RzpcRaDOjlH3P9bcULByRuFLU6+I1Ngeg/Ln5B9QArQy+vQ3QQXnWhli+Y3doHHpAN/sP81NDZC4Me9FhD40YY3EAJ/WtoQFfhxwyUsv7TCaxRpfzfAxRGm+zDthwuakPzPl3L8G+bayTniHtgLCwvVFh3CnEbPcWIU9Itf3Nbq5IcTrluyD3TKiBHXSl1dnblnfwj0CPwIaAj8wZaQIvAjhY/AP2xY6xE/bN26Va3hR+BH5gkV/52tM7CT3NxcdYE2depd7V+w9LlErk1LEGn+VOoO/tM8SGR/cQ3sGBlgDhonFKfN/2G9PVpWItuAOTuk+BjI3Q+d6JDKdRMEfmTLEPixJC8w5Z+RkaFeo3hDNz4IfL1ipI/Aj6CPt8BRv53gdbpy5TOyb99e43cqMY8G0W2AjLlznCTIm7L096/LgWCD9pYDsqXkj1LVxBE92Ufciudwpax7OQe29HQCpPFQHHfHHXeoEyN5AwLWrbfewvt9B0DmCnfk0x37kpOTW63bx+sFI2RkPL7//e+rxj24YIjnNJXuStfuLaERuOf9SqaUfiKpk38rORPHy/ihicaICE1rNsmK31fIuXlzJTuF7WnIPuIW2J3UNhYnpXfeecfVnfAoNPhfiEdlvNMhdY9Cvv37959s3BP42sc5ATfu6d+//8nGPW0G3AjA4CI/P1+txmm/K90/pbGqXF54crEUbzhgHusrY/IK5N7bMmVo4pnmMSJ7iEtg1ydHu7eN1aNyvWSNozSCWPev9wqMoDHix2oSpMkDO8UhEGMtvw78AwYMUO93ZdSPC47wu9IR2VPMAztenLp3s53XrOue9SiyycvLj3vakOwD88koMmNv/+gKbNWLILxs2bKTF9oQuG4fUyV79+6V7t27q/4H0FFGENMIqJXhxRq5RcwDu5PutoR7cGNOkEVx8YNCrBtvvDGqKdnOwmMK1jOeYgsZNfQWsL4+dZC2CrxBDz4HEPh14x78TXHBwKwcuUFMA7sd017IIOAua8XFRV24+xNFix3T3jp4BAYMsg+8rhsa/H+fwBE7/qesMCWYmZkpY8bcYAT7S9UNqIicLKbL3RYuXKhS27NmzTKPxA9e+DhBW5esHT161PwodV2TVBWPVSfRVm9pRVJ1wvjwiSopTrN+bKwUVzX5v9TmUNQFTl7L7XYYxSOgB0vD44IM3SBRvLdqVZl8/fXXcs8998ihQwflX//CPyeRs8UssCOtrdvG2mVUjFE6Uu14gSOt2tFcHHVGdxmaVyF1lWtl1pi+/kOp98iq12fI0DOM989Ik2n/9YRMTu0pqZOXiq/yFckb2t3/eTaHW6zCkSNH1JacB4EfrYp/97vfyZIli+S8885Ty95Wr/6j+RlEzhWTVLz15gvxmpfE6AoXFNb5uMDiHIqSlnrx3fszyS0/IAmZT8imJ7Ok7zfvSvHP7pKK9GIpnTdaEtu4xLTjHDsgy8BiK+fBa/7FF19UwRwwLcheFOQ2MQns8SxMsS5ZC6ygpRhqQiCfJMXV35fMxx6VMRsekqf7/Ee7Qd3OWBnvLLiwxzp6HdBxt8Xrr7+eAZ1cKeqBXS8bi8foBn2tkf7nkjV7aDngk3tHz5Dy5gRJzX7SsUEdcLGKRitO7JroJYG9KBDQcWMcngfIzaIa2FGgptvGotI01svGkPZHIwvcaS3WP5uCOSGNvpmSnus7lZJ3aGBnZby9YT17WVkZL+zJk6J6WsU9j9FBatGiRVENrLrCHdkBK4zYkSVgULeHlgOvyrx5TTL5tsuluXyxzH+5Xjq6dQZGXJgXtRtdGY/HR/aBgI5pEvTzR6tYZAp5+2TymqgFdpzw0IgG9z6O1jwWTvjWJWt2vqOU5zXtllVz/0v6PLZYFjw8V/JSv5Ly2YtlVc1x8xOCQ+th3DbUbnRl/OHDh9WW4kdf2OP2yQjogAr3N9/cygt78qSoBfY5c+aoFBjufRwtWHuKgK6XrGGETnb0pVStmC9rBs+U347sK926D5Npi3MktflVmXt/qSNveakvVg8dOqS2FHuBF/ZYdYOAjroHu62iIIqlqAR2vNhw96Zo36McKX5U2qOLHatb7Qi3ttwipXMmyy9rbpNn779S/CvVu0n3oXfL4/OvE6l+VH458wnZVNv+yN2Orr56uFRWVpp7FCsI6KifSUsb0urCHscY0ImiENixrAQvNqwPjdSLzJ/WLzhtDTyCOfs62xU6z/1vSR09SeaWvS/N5TMk8w9V4u/rhY/9Hxk9902117zhUblj9LUy1bdf7TvFwIEDVWU8xQbOAzqgY9kaKtwR0HlhT9RaxKviEYBx28VI9F1HMdzy5ctbVbayIYi34GSOrmB2LHxCZgoXsayMjy78D3DJGlHoIjpiR9tYvPgQgCPxotu3b5/q326tbCVvwUjMridw3A8cEHgo8lAMi7oZFFBisIDzAHq84xiDOlHbIjZi12vWw20bi6/H3ZisKTUcY0Ur2ZW+WyEKtji3GzkI6I899piq09GZOvaiIApdxEbsJSUlas16fn6+eSQ0KITBPdpxUTB16l3mUT++kMnOdH0HK+O7jkvWiCInIoEdc+HLlj2u7mvcmSIWXJmjEAbr3VHZunLlM+ZHiJxh/PibWBnfBVyyRhR5XU7F40r79ttvV+93tm0s5ibfeOMNmTBhAqvbyZGWLl0qO3bsYM/4TkJA513WiKKjy4EdaXSMuF955TW57LLLzKOn00GcTWTITVgZ3zn6PMC7rBFFT5dS8XiR6raxbQV13bsZla1r1rygCo6I3IKV8aHxnysK1HlAr0HXFe4M6kSR1aXAXlRUpKpWp02bZh5pDUFdF8LoJWtMuZOb9OrVS23ZMz44Llkjir2wU/E6Bfnss8/J9dffYB49HV7YLIIhN0tK6qcCFvssnILXPZesEcVHWCN2FL4UFxepghcEdb1kDUtV8L4Vgzq5HSvj/bhkjcgewgrshYWFas36XXfddbJ3s16yhhc3kZckJyerNLNXcckakb10OhWv582RekRqDS/mW2+9jUvWyLP0tFRNTa2nRqVcskZkT50O7EizYbSOufULL0yWs846iwGdPA0Nmm66aby605gXglqwJWu8sCeyj04Fdlyh33PPPaogJhAKZJCK//73vy8pKSnSvXuCCvx2vTMXUaTonvEdFZI6HQI677JGZH9hV8UjyOPOa1jmg17Zn3/+uezfv1/NNWJEH+jqq4er+1f3799fLrjgAunTp4/07t2bgZ9cAZXxaKk8adIk84h7YPqtrKys1e2TWeFOZF9hB/aOYBTzzTffyGef1UlTU7PU1NTIV1991WbgR2XxueeeK6mpqcZov7tq/IE0f79+/XgCIdvDumz8/y5evNg84mwogn3//fdPLlnDhfkvfvELBnQiB4haYO+I7tS1e/dutdXLhXSaLxAKcyA9PV1tBw8erLYs1CE7QM/48vLX1NIuJ0NAr6ioUMtZcQGOgD5z5kxWtxM5SNwCe0cQ+DHi37dvnzHib5Lq6mr54osvVDowGAT+wPl9FvZRrDi9Mh5Ta+Xl5bJixdMqoOP1dOONNzKgEzmQbQN7ezCqaGhoOG1+f8+ePSEV9nF+nyINF6Jom+q0ynguWSNyH0cG9o4EFvZ1NL8fWNjH+X3qLPzPoVGTUyrjcSHy0ksvybJlj6t9Llkjcg9XBvaOtFXY19b8fluFfRzVkJUTKuO5ZI3I/UIM7Edky5wsmbLjFvH9eYYM7d6lm8LZHgv7KBy4LSnYsTKeN2Uh8o6QAnvLAZ/cO3qGlDcny+RVPlk00n+rSi/S8/uhFva11biHhX3ug/smrFnzgm0q47lkjcibQgjs/5Da0nvkPtzjYsMb8tnk1fLOopHSw/9BCtBW4562CvvYuMc97FIZzyVrRN7WcWA/vkXmXLVCBvnmyjnFkyX3zWukZNN/SlbfM81PoM7QgT/Uxj068LNxj/3FuzIe/1tcskZEHQT2FiOuz5OMNUOl/MkJ0n3rPLlqyosyaP7L4stOCe+er9SuwMK+jub3Awv7OL8fP/GqjMfP5ZI1ItLaD+wtNVKada/U5r/on1dXo/dJUjZooWzyZcsgRvaYsxb2hdq4B1DYx/n96ItlZTyXrBFRMO0E9hZpqnpCfjavhzx+Moh/KVXFd0hW8WHPF9HZUVuFfaE27uEd+bouFpXxXLJGRO1pJ7CbS9zK6sz91hJYROc4LOyLPlTGIyVeX99gHokcLlkjolC0Gdhbaksla8JeyX9nnozsYcm5q/T8BJlb+3NZFfgxcjTeka/rdGX8zp0fRuTih0vWiKizggf2pt1SOvMOeWzwcnkvb6icYR72OyGNvpmSnrtRUicvlcdnT5BBLm9YQ36dbdyjA7+XGvdEqjKeS9aIKFynB/YTVVJ8xQQpPmbuj3lCKldmSaLa0UHdp/b8sqSk8jHJSmwd/sl7ENRCbdwDKOxzW+MeXRlfUvKEZGVlmUdDxyVrRNRV7cyxE0VOYGGfm+/Ih8p4FLRNnz7dPNIxLlkjokhhYCdbCCzs6+wd+XTgt8P8fmcq47lkjYgijYGdHMFJd+QLpTLeumQN2Ylbb72NS9aIKCIY2MkVOlvYZ23cA5Es7HvjjY1y5513BK2M55I1Ioo2BnZyvbYa90TrjnyBlfHBlqzdffc09TMY0Iko0hjYyfN04A+1cY8O/G017sH3S0kZJIWFRXLmmWdyyRoRxRQDO1EHdGFfZ+7IhwsCjPjxeUj7Y/78sssuMz+DiCh6GNiJuijYHflOnDghX375pfzmN7/hkjUiiikGdiIiIhdhL1giIiIXYWAnIiJyEQZ2IiIiF2FgJyIichEGdiIiIhdhYCciInIRBnYiIiIXYWAnIiJyETaoIYqa/eKbOl5yNxwz91tLGJMviybdJGNGDpLu5jEioq7iiJ0oavpL1soPpW7TQkmTnjKm5G11j/b6+nqp3vSc3C1rZOaUX8osX720mF9BRNRVDOxEUdbt7HOkj/m+XzfpPugGuf+Be42Af0DKn/2LfMrITkQRwsBOFCfdzk+WHyWYO0REEcLAThQPTTXiW/p7KWvuK5l3/kQu5iuRiCKExXNE0dbok6npM2SDuWuVMHm1vLNopPQw94mIuorjBKKYsBbPNUhd5ctSkjdWpGySXDW1TGqaOMlORJHBwE4UB90Sh0pW3lJ5anKyNG9YKL/5cy0r44koIhjYiYiIXISBnSiqWqTpQL00mHsntTRKVVmxPFJWJ5IwTu4cM4AvRiKKCBbPEUVN+53nRPrKmLzfyKQbx8rIQSyfI6LIYGAnIiJyEWb/iIiIXISBnYiIyEUY2ImIiFyEgZ2IiMg1RP4/IDDHhmQ4gScAAAAASUVORK5CYII="></p>
</div>

<div class="specification">
<p>The volume of the pyramid is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>57</mn><mo>.</mo><mn>2</mn><mo>&#8202;</mo><msup><mtext>cm</mtext><mn>3</mn></msup></math>, correct to three significant figures.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AV</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext><mover><mtext>V</mtext><mo>^</mo></mover><mtext>B</mtext><mo>=</mo><mn>40</mn><mo>°</mo></math>, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>AB</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the pyramid, <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>VX</mtext></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second ornament is in the shape of a cuboid with a rectangular base of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo> </mo><mtext>cm</mtext></math>, width <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mtext>cm</mtext></math> and height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo> </mo><mtext>cm</mtext></math>. The cuboid has the same volume as the pyramid.</p>
<p>The cuboid has a minimum surface area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo> </mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>. Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>160 students attend a dual language school in which the students are taught only in Spanish or taught only in English.</p>
<p>A survey was conducted in order to analyse the number of students studying Biology or Mathematics. The results are shown in the Venn diagram.</p>
<p>&nbsp;</p>
<p style="padding-left: 240px;">Set <em>S</em> represents those students who are <strong>taught</strong> in Spanish.</p>
<p style="padding-left: 240px;">Set <em>B</em> represents those students who <strong>study</strong> Biology.</p>
<p style="padding-left: 240px;">Set <em>M</em> represents those students who <strong>study</strong> Mathematics.</p>
<p style="padding-left: 210px;">&nbsp;</p>
<p style="text-align: center;"><img 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VVDF/l+rzYGGFXlR2Tbsv9bxi65X3K3/g95onPDBnZ4g8IeAdd3OqAEdSTp128IW9hvb968aewkVPw3zB0weySuxtOvr6TI2whA2GKzglhy885UFVK85V/lA9hvDUnWSP62WQtJlR4ycetbMr0fdr1fS3n+e/L23nKRgR0kzUX7rcEh29JtxFFxrMwccVSTwKN/DpWsHV2T6kulB8taHir6Mlq2krpNrFixwkhhxqxRdbHhFfcQwHhE2keMz2gF1ydPnhxC5jMWIqALAhi3SHmLbGexyn8WLQ11VPM1/t5N6Xi7ZG3ohxO3hi5j+lbZp8Kfk5+Ftpb9Z6yqk74XS54FO7Xj7dOhtTmpIVE5NW+XhYrW54ayJDWU9creUFkDMldNWranLUt6CLCCICGgJi3k6Y5VuFiMhQ7vuYUAxi8Wg/UtFt2iy2y7sQRusM/DrciTmV3HyvH5ebJrYte7+vVrkjdzmDy6RCR3/25ZnN2yjq5GqepwA0Z/envWgYgXXEIANjCo5cwepwf1HcwhiMdliJBLTGOzdRBQcywcUL12xm6s4/kCbMOtkoqiffJ2eY399g7X75Vvt/qWiNyUz27WzUmrBsLDDz9MYVvnZ8ILbiIA4dmnTx/Twha0wucAwhk2NKR5ZCECOiCATQw2M/A3gB+CX/wNAixwv5bPzp+R8tT/S/r+XeOaMVZ5Sv799yVRPZSVsMWqi6nwaiDjJ/cRUDvVY8eOxe24p4Ruly5d4nBYcb/PpMDfCCih27x5c/8IXbN6aTufi6Xztqvd25e3hiamSig1d3/ozkFNfwmVFW0M5WalhkR6hMat/ST0ZVjjsNN62a4Q1hV+9BkCBQUFljjuoR78FvGXhQjohICX/GViybMA2nAr5ciyH0v6jPwoy8NUycp9Tf75iR/Jj/ulVsdMhe9sGWMbBTZecg0BtbO1ygaL+jIzM6WgoCDunbJrILDhQCCAdLlQMevuNxPLhhtAgRvf2KSwjQ8vPu0cAlYLW0W5ErpQT+OUFxYioAsCXhC6FLgJjhYK2wSB42u2I6CEIk4FssO72C5hbjswbMD3CCBpCwrS5+pYYgncADtNNcwqeMfBYE81csNY8QnnEEDOboTyQO1rh7BFT5QjFbyXzR5m7xwCbCnICECljILdrtcKBW49HFPMfO211+p5gpeJgPMIQPipNHgQinYWCl070WXdiSKgvJdhz1XzdKJ1Of0ebbhREPeCnSAK2bzkcwRu3Lghw4YNiyvO1gpIcGYpnLJwvi6TvFiBKOuwAgGY/HDKkDr4wIo6ragjlkqZAjcCYRxEMHfuXOMsW04uEeDwq2sIuO1PwEWoa6xnwzEQcFLjE4OMWrcocGvBUf8XOorUjw3vuItAbm6ucW6om/4EoKFZs2ZG0hd30WDrRKAGAQjdtm3bSklJieBge7dLLIFLG+5d7oBp6og9uxxR3B4IbN+bCGB3+cUXXxg5Zd3sAfwZPv30U4GKmYUI6IIA5ms4EI4dO1Z7Bz+qlEWMPJ2DBw+W+fPnS05Oji7jiHQQAdHNxOGWHZlDgQg0hAD8DHbt2uV6YoxYO1wKXBHjMG7kR3ZTXdfQYOL94CGAwwSwarcqi5RVCIIu5F22KwbYKjpZT/AQWLhwody8eVOWLFniWudjCdzAq5SVWzmFrWvjkw1HQQA7SQhbnOSjm4kDdrI9e/YY4Ulw5mIhArogALMgzC+6mj0CvcNVTlIHDhxguIMuvxjSYSCAbDqDBg0yQh50hQSL1YsXL7q6m9AVG9LlHgLKc3nVqlWupCblDjcK75WT1DvvvENhGwUfXnIPAbU6R3yhzgUHg2M3AZU3CxHQBQFohCBsn332WYGmSKcSyB2uimkcPny4oRbTiSGkJdgIHD9+3JgovKJ1UbsJLFx1CMkI9uhh78MRwML14MGDjudc5g43nAsisnbtWiNHMlLksRABXRDAahyrcqzOvZJ0BbsJ2Jlhb6Y9V5eRRDqAgNIQKY2RDqgEbofrtR2EDoOENDiDgBfstvUhQXtufcjwupsIqDA2JzUw3OHe5bgXdxBuDla27RwCyg6qVuXOtWxNS7DnIlwIccMsREAXBFq0aGFojHTRwARqh4vUdD169KhWNegyKEhHsBGAHRSp6bwe16rsubrFDQd7dLH3QADxuSizZ8+2HRDucEWMlTdW4KNHj7YdcDZABMwiALsnUiYirlW3eFuzfVDPgf5Zs2YZ/VHX+JcI6IAA4nO3b98uMCm6WQKR+AKqZJwAhOwjXnFGcXNQsG3nENi8ebPhwOeXlKLKEVGpyJ1Dki0RgfoRwLwPOy6cEt107guESpmq5PoHIu+4h4BSwe7evVtga/JLUSry69ev+6pffuFPkPvhhGo50CplZJOiKjnIPzF9+w5VMlSwfhK2QBuq5a1bt8qiRYv0BZ+UBRIBt1XLvlYpQ3UAgKlKDuRvS+tOK5WrUsFqTWwCxCGpDL2WEwCOr9iKAFTLiHOfN2+eK6plXwtcJLgYOXIkM+DYOoRZebwIwKcAu78ZM2bE+6pnnsfEhoUufCfctJl5BjAS6hgCvXv3NmQC/CecLr614WJ1jdgrr6TIc5rxbM89BGBHgtrVqzG38SCHvjZt2pRHX8YDGp+1HQEseu+//35bQvECacNdunSpYR+jV7LtY5cNxIEAFoIITwhKeNpzzz1nHJWGfrMQAV0QgN8E/AzeeOMNR0nypUoZjlJXr17lwQSODiU2ZgYBeMzPnz8/MOFpmNjgGLZmzRoz8PAZIuAYAsrPwMnYXN8J3HBHKcc4x4aIgAkEkPawVatW4peYWxNdNh6BYxh2uFgIsxABXRCA9hN+FHCgcqr4TuDu2rVLsrKy6Cjl1AhiO6YQwEIQDkR+dpSKBQT6DTMPCxHQCYGBAwcaskJFDdhNm68ErvL+hAqLhQjohEDQF4JOT2w68Z606I3A5MmTjagBJ7zpfSVwN23aZHh++i2RgN7DldQ1hAB+yAgDevHFFxt61Nf3nZzYfA0kO2cpAp07dza0olgU2118Exak3LyZTs7uIcP640UAZ8WiTJ06Nd5Xffc8nMYGDBhAh0bfcdbbHYL8GDZsmCVhpLHCgnwjcDmpeXvA+5V6LgRrc5bx8bXx4Dd9ELBKhvhe4HJS02fQkpLaCFj1I65dq7e/cZfrbf75lXqr5IjvBS4nNb/+BLzdL6t+wN5GoS713OXWxYRX9EAAsgSZ0ZLJAudrgctJTY+BSirqIrBx40apqKig7bYuNMJdbhRQeMl1BCBPkrXl+lrgcnfr+hglAVEQgGfy4MGDxW9n3UbpakKXuMtNCDa+5AACkClpaWkJO/bFErieDgvCpIZdxJgxYxxgA5sgAuYRQIgBTqpiiFp0zFQoxtGjR6M/wKtEwCUEkAkOYXx2xOV6WuByUnNpRLLZBhHAD/bxxx9v8LkgP4CFMrNPBXkE6Nl3OxeDnha42N1yUtNz0AaZKuQM7tWrF9OLNjAIcC4pipPJ4xsgibeJgIGAXYtBzwpcTGpIBI/VCAsR0AmB9evXy4QJE3QiSVtapkyZIsgQx0IEdELArsWgZwXujh07OKnpNEJJi4EAnIFOnDghyB3M0jACgwYNkvz8fIF3KAsR0AkBLAY/+OADS0nyZKapy5cvGx5kBw4cCMy5opZynZXZhkCyHo62EaZxxVbEPmrcPZLmUQTgNNW4cWOJN11wLC9lTwpc/kA9OoJ9TnaiP1Cfw9Jg99QCurCwsMFn+QARcBKBRBbQsQSuJ1XKcJbKzs52Ene2RQQaRODgwYOyYMEChgI1iFTtB9q0aWM4mfGA+tq48Jv7CCBECPLGquI5gas8QPEjZSECOiGwefNmI9mFTjR5hRY4mcEvg4UI6ISAcsq1ypPecwIXdlt6gOo0JEkLEIBaVAtnqcpSydu2SZaNHyoz867VZU5lqfxh2XhJS0mRlJQ0+d7Mt+VI+dd1n3P4St++fY2YXDpPOQw8m2sQAThPFRQUNPicmQc8JXDxY5wzZ47gx8lCBHRCIC8vL6mE55b0papY1v3jXNmw9VcyY+P1ulVWXZAdq/NEfrJCykIhuV22WX7y2RJJH/OWHKmsqvu8g1fuu+8+WbFihRQVFTnYKpsiAg0jkJ6eLi+88IIlmac8JXDxY4SNDD9OFiKgEwLbtm0zUjm6SlOjrjJx5/vyf16dJjlRCKn69LJ8+4mJ8v3OTY27jVIHyktzpklO/r/K+4Xuh+VkZmbKypUro1DOS0TAPQSQnnXGjBliRRpSTwlc2sjcG3RsuX4EoE5G0d2voFHHgZL14DdrdaTRA+2ld2qtS659QbKBsrIyQz3vGhFsmAhEQWDEiBECc2ayxTMCF+pkLWxkySLO932HANTJjz32mHf71XiAfKfLnV2v253AOaTAk4UI6IQAzJgwZyZ7oIFnBC7UyckcCqwT80iLvxCAOtmbYWpVUlGUL8efGyc5ETtftzgEtTLwZCECOiEAMybMmcmqlT0jcKFO7tOnj048IC1EoFr9qbs6OSqrKotk1YaWsvC5dGkS9QHnLyq1Mr2VnceeLcZGAOdbJ6tW9oTAxTZ+zZo19E6ONh5qhXmkSNr41+UPpRXRnuQ1GxDwrjr5phxZvUtavDJB+jXRaxqAJoveyjYMVlaZFALdunVLWq2s1y+tHjiwjad3chRwqi7ItpdGyfhPsiXvy9sSCv1FjoyvkIVZiySvwt0wjyjU+vISskv17NnTY337Wq7s+Dc5OXyaTOyqh+02HEColaHRYiECOiEAb+XJkydLSUlJwmR5QuBiG49YKJbaCFSd2S//su5v5OnxP5Suxi7lm5Ka9aQ8/cgB2VPkfphHbWr990058qmjvLzRw6+lPG+dvP+tH8vT1cK2Qoo3vC35mizSunTpYmi0knVQ8QY/SKWXEBg+fHhSSTA8IXC3b99OgRtlVN4J6SiTwqPnpFLdryyTkrODZWh6C3WFf21C4PTp0+7H3sbVtwop3TZPxjz632X6o23kHiPbFDJOfVu6bfpPSdNEtQwHFaviHuOChw8TgQYQyMjIkH379jXwVP23tRe4OF80LS2NCeGj8bBpX3liel/JnzFJnl93Uiqrrkjesn3ywKYXJKup9qyN1iNPXdNP83JN8mamyz1dJsleOSJLHm0lKUPXSalhXfharmybLVmjfiX5dVBOlZwnvyudNBoyQ4YMkWPHjtWhlBeIgJsIwDkymVhx7Y/nQ4gAOjh16lQ3cda37apyKfz1LBk5faOUy2hZW7JRJna+V196fUQZVru7d+/mYtAGniKZCH7z0G6xEAGdEMCRfTjUACcJRSuePp7v8OHDAicKlnoQaPS30qxdP5m+dLpkyWaZ9LPFkqdBMvp6qPXNZQgEal7sY6faSTA8KBzjCin9w+syPg1mgBRJ+d5M2XCkXOq6R34t5UfelpnfS5OUlEdk/OuHpLzuQ+EV83McCCA8NVEveo2USNF7vHTpUoETBUs0BCqkeN0vZLmMkOkv/0/ZX7ZXXpF/kUc1SEYfjVo/XTt16pRA7cliHwIjR44U2MlZgAA8y9+W38sP5a2ykIRul8mHP/lMXkl/RpYfuRkGUZVUHnlLxrx8ToZuOi+h27tl/NVfyZjlhTV+HmFP82P8CCA8KFHNi9YCF/ZbuGHzsILog6KqdIu8NKlMMnq0FjCyUer3ZeHvtstSeUtmv18aZeUbvR5ejR8BrHCZiCV+3OJ5A5EJtOPeRazqivzHt38iL32/850kJY1SJeOlV2R+zlFZ/v5RqY68ryqV92dvkYyfPy/Zqd8UafSgZM+aLhnLl8n7pV/FAz+frQcBhAdBu6VyqNfzWNTLWgvckydPSq9evaISzotVUnn5jHwSCUSTDtI3o3XkVX63GAGscLHSZbEPge7duyflEWofZS7U3Ohhycpqayysq1tv1FLa906r/ooPVWf+KO/tfVC6tAnLHda0pwx9+oq8V3Cei/BaaCX+Bf4b0HLFW7QWuMXFxdxF1MvRRtI0Y6RMzyqQuc3yJTEAACAASURBVAvek2LjPNMqqSz+vWzY2kd+NrRD7R9nvfXwRrwIqJUtVros9iEAO+6OHTuSThhvH4U61Hy/DP9Ox7upOb+SMwW7ZW9qJ2n/QO1ToUT+Invf+6OcoS3XEqZB+wINbLxFa4HLXUQD7GySIdM3bZdfPbBJun3rHklJuUc6/+qGjP1goTymSTL6BnrgydsXLlzwWPytJ2E2iEY8bjKZfbzbcxOUV3wse44Pkyk5audbKZdLzok80knaaBJTbaIXnnykffv2CWlftBW4yjuRu4jY47FRaoaMX7xHQqGQ8a9sw7TqA8Zjv8m7iSJw9uxZ6dq1a6Kv8704EOjRo4ecO3cujjeC8uhNObLqt9Jq4U+1y4UdBA4gLCgR7Yu2AvfixYuSlZUVBN6xjx5DAL4FEAQs9iOAPNUIDWQJRwCeyP8m77eYLM/1axZ2o4m06dJB5JMzctkwMYXd4kfLEYD25dKlS3HVq63Axap2wIABcXWGDxMBJxBAqFrbtm2daCrwbbRs2VLy8+vmxgoyMFVXdsvqk5ny84k9Io5VvFc6ZQ6TOukYqq7J+eM3tcsm5nUePvTQQ4LFdzxFW4GLVW3r1vS2jYeZfNZ+BOAw1b9/f4aq2Q+10QIcpz766CM6Tt3Fu6o8T379/r3yj08rYQtHyS2yLv+a8USjTt+VJyMPL0F+9U/6ypOZ7elIaeG4hVoZWRDjKdoKXHiAtWvXLp6+8FkiYDsC165do6nDdpRrN5CI6q52DX74ViWVpdvklTFjZfr0RyXtnrvZplLukW91e18k7W4YUKPO8sTCx6Xwl2/dyTiH/OqLlkvh9JflCaZ8tXQgwHHqxIkTcdWprcCFQRqrWxYioBMCNHU4zw2o7s6fP+98wxq1WHVlu7yUNUqW5JfXpSpnmGR2UvnTG0mTfs/LpsUtZUO/v5GUeybKni6/kE3TMyLUz3Wr4ZX4EIBZac2aNXG99I24nnboYZVhyqHm2AwRMI0AYsMHDx5s+nk+mDwCyOrz2WefJV+Rh2to9OBjsrYsJGtN9eGbkprxvGwoe142mHqeDyWCADIgwryEiBqz0TRa7nCvXr0qzZs3TwQDvkMEbEXg5s2b0qpVK1vbYOW1EYBHeLzOKbVr4DciYA8CiKSBmcls0VLgfv755/RQNstBPucoAvRQdhRuo7HGjRsnlNXHeUrZYtAQiHcxqKXAhedXkyZhuUCDxkX2V0sE/vznPxt08TANZ9mjUjw62ypbIwINIwA5VVlZ2fCDd5/QUuAi6QU8wFiIgE4IIMgdHrMsziMwYsSIhE5ncZ5SthgkBDp06BCXuUNLgYtAd6iRWIiATgjcunVLJ3ICRQtiHol/oFjuic7GK6e0FLgIdGdIkCfGW6CIZEiQe+xu1qxZ4EOD3EOfLdeHAEKD4NdhtmgncJWdzGwH+BwRIAL+RwCHRcRjK/M/IuyhDgjE68+hncClnUyHYUQaoiGAGFymG42GjDPXKHCdwZmtxIdAPP4F2gnc+LrKp4mAcwgwBtc5rCNbijf8IvJ9ficCdiEQj3+BdgIXSS9gr2EhAkSACBABIuAnBLQTuEh6wcO9/TTE/NMXJr3wDy/ZEyJgFQLx5PrWTuBaBQLrIQJ2IBCvk4QdNASxzni9QYOIEfvsDgLI9W3Wv4AC1x0esVUiQATiQIALnTjA4qPaIqCdwKUnqLZjhYQRASJABIhAEghoJ3DpCZoEN/mqbQhcvnzZOIrLtgZYMREgAp5FwKxKWcvzcD2LOgn3LQJIK4ijuHQrSBSD2PXwEs9Rdki+Hpm3HGEOLESACJhDACFrZg+ip8A1hymfIgKOI4CDrXHWJkLl4L2PU7RwsMcXX3xR6wceeaACJgCzp22VlpbKvn37qvtWX92qTiRrR/5YN4SySjDAtK/V7OIHjyFAgesxhpFc/yGgdqnYmSqhqvKzQpgiLh2hchByOTk5BgCrV6+2DQhVtxL4aEjtmjdt2lQt8Pv372/s+iGMH3jgAWOnbKcgRt08wMA2trNiBxCgwHUAZDZBBMIRwK4SAgwOgoWFhbJjxw7j2D8ILiVUX3vtNXHbM7dFixaCfyhKkD722GPGdwhlJZDRl6KiItm8ebOx8548ebL06tXLeKd79+48iCSc+fwcaAQocAPNfnbeCQSOHz8uH3/8sSFksXNVAmnw4MEybtw42b59uxNkWN6GEshKGKMBCGIsKM6fP28I4ZUrVxq79pEjR0p6erpQAFvOBlboIQQocD3ELJLqDQTg0Xzq1CnDNqoE7KBBg2TMmDGiw87VbhQhgNVOHW1hJ3z69Gk5duyYKAGMhUafPn2kb9++ru/k7caD9RMBhQAFrkKCf4lAEghgV3f48GHZtm2bsaODQIGTTxAEbEOwYSc8cOBA49/UqVNFLUgOHDggmZmZxo5/9OjRxg5YqbAbqpP3iYAXEaDA9SLXSLMWCEDI7t27VzZu3ChI7wb75ptvvkmbZQPcgZcx/sEBbNq0aVJSUiIFBQUyd+5cw/ZL4dsAgLztWQQocD3LOhLuBgJQj+7cudPYyaJ9CFnsahmqkhg34BjWu3dv4x92v7B3RwpfqOPxHEKWWIiAlxGgwPUy90i7IwggbOfo0aOyZ88eyc/PNxyduJO1B/pw4Xvo0CGB2nno0KGyYsUKwwNahSzZ0zprJQL2IqBdakd7u8vaiYB5BGBrhGCFN/H+/fulXbt2RhgPdmLc0ZrHMdEnYfedPXu2XL9+3VDZox54O0ONj0UQCxHQAQF45OOIPjNFS4HL4HYzrOMzdiGAnVVubq6hLm7atKns3r3bCHf53e9+Z1eTrDcGAnCkUvG/8+bNM8KNkO0KiyGo+FmIgJsIII8yfDjMFO0E7oABA+TcuXNmaOczRMBSBCBosYNCKA88jKHOhLcxPWcthTmpyqByVrteLIaGDRtmLI7gwMZCBHRHgDZc3TlE+mxFAKrJXbt2yaJFi4w0hdhBYVJn0RsBLIKwGIJHM/gHjQRif7FQgiqahQjoiIB2O1wdQSJN/kMAghbexbDPIn72nXfekSVLllDYaspq7GCRoSuywHsZ6mZk64KwhXYCWgpoK1iIgBMImD2aD7RoJ3BxygkSuLMQATsQqE/QhqcnrK9dTPhUXdaHjv3XmzdvHrMR7GwheHHgAwTvM888Q37FRIw3rUAAucSRB91M0U6ljLM5w48LM9MJPkMEzCCAXQ8mYghX7GjNCNnwehua8MOf5Wf3EFBZrZTzG/iMxVK8/HavB2zZrwhoJ3D9CjT75R4C2JVC0OJc2WRttPSgd4eP8YReKAoheJGrGTbesWPHGjZf5LOmE5xCiH+tQCCehCzaqZRbtmxpJBewAgjWEWwEEDKycOFCY7KFcw3Ujck4RNGD3r3xFE/oRTiVysYLj3MUeDXDds843nCU+DkZBNasWWNae6KdwMXq86OPPkqm/3w34AgoO+39999vJKjAZKsObg84NJ7tfrJ+HRC8SFgCYQsnuaeeespII+lZQEi4JxHQTuACxf79+zOg3ZPDyX2ioT7GZIpJ9dKlS4YaEZOtFaV169bGofFW1MU64kPg4sWLph1TYtWMDGHwRodj1bPPPmtoQJg8IxZivBcLgfq85+t7R0uBm5WVJdeuXauPZl4nAnUQwK4WmYdgq5syZYoxqVqdfrFVq1Zy8+bNOm3zgv0IxGMnM0MN7LvQfGCMQM2MdJEsRCARBOJxptRS4DZr1sxwcEmk83wneAjghBnE01ZUVBiTqF3qY/oXuDe24rGTmaUSmg8kz4DH+sqVK43kGdztmkWPzwEBhASZzaOM57UUuF27dpXPP/+cHCUCMRHArhZOUVANrlq1ykj5Z5X6OFrD9C+Ihor91+wWgggXevfddw2VNXe79vPTby2YzaOMfmspcJH8ori42G98YX8sREDZalElVIPJeB/HQxaTX8SDljXPwrwEm6udJdpul57MdiLuj7rhK9KhQwfTndFS4CL5BW1lpnkYuAc3btxo2GoxCSORvZ272khwYa9hLG4kKvZ+TyQGN1GK1G4XakKYKWCuYCEC9SGAhT9OrjJbUkKhUMjsw3Y9l5KSIuFkYGWJToRfs6tt1usdBKBanDlzpkHw4sWLXUlggLASFHVcnHfQ8y6lWGBB6+U05hC2MFcgnAi2XhYiEIlApOzC/WjX1Hta7nCxY2FokGIR/wIBTH6wrw0aNMg4m9atbEEMDXJ+PMaTq9ZK6mCmwFnIBw8eNPIy221LtpJ21mU/Atjd4sCMeIqWAhcdQGgQYu9YiAB2lcoxyu2dBkKDCgsLyRQHEcjPzxd4iLtRsLBbvXq1sdDDgo8qZje4oGebSBWbkZERF3HaClycvsCD6OPipe8ehmkB55wiFy6ErlOOUbGAhI1vx44dsR7hPQsRwK4Smefc0miormCh9/rrrxsLP2VWUPf4N5gInD17VhBRE0/RVuB27NiRnsrxcNJnz16+fFlefPFFQUz2G2+8YSQo0KWL9FR2jhNOeCib7Q2SZUDYwqaMJCv0YjaLnD+fg6kjHg9loKCtwG3Xrh1Vd/4cpw32CrYROMgMHz7ccS/kBokTkV69egk8Z1nsR8At+219PUNmKsTswtyFBSGFbn1I+f86TB3xJL0AItoKXAxsqO44oP0/cMN7iDNMkZ4R6junvVLD6Yj1GWplLApY7EcAcY7QdulU4NSJfMxYeCF0CNoYlmAhoHger6lDW4EL9iHOsqSkJFicDHBvoaqbNm2aobaD+k7Xgjjxffv26Uqer+jCLqJbt25a9gnhQvPnzzcWhlyAacki24i6cOGCjBw5Mu76tRa4OH/0448/jrtTfMF7CMAmhvAL2MisPnTAajSU4xS1L1YjW7s+FYYT7y6idi32fkPebmhjunTpItDOsAQDgWPHjsXtMAVktBa4MEjDhsPiXwQgtJAP+cSJE9o5R8VCndqXWOhYc+/06dMJ7SKsad18LdDG4ChIaGcodM3j5uUnMV8hkibeomWmKdUJTMbMOKXQ8N9f8BeOJyjwRHYyRWOyaGInXllZyQxEyQIZ431oPaBNsOv0pxhNJ3QLdj34HTAzVULweealhuSS5zJNKeQxATMEQ6Hhr79K2MLxBIkFvCRswQmsbqEC17lUXdkmk9KekHWlX0WQ+bWUH3lbZn4vTVJSHpHxrx+S8qqIRzT4Cjt59+7dNaDEHAkwhWAhhoUC/rH4EwH4FSV6mIbWKmWwC6n84KnI4h8EwoUtdgNeLNh54YxW9EXLUnVBtv/iVVlXHkldlVQeeUvGvHxOhm46L6Hbu2X81V/JmOWFUhn5qIvfYb8tKyvT3p4fCZESulA5UuhGouOP7/Argn9RIkV7gduzZ0/tdxKJAB/Ud/wgbBXvsMo9evSo+qrR35tyZPlSOdSyp6RGUlVVKu/P3iIZP39eslO/KdLoQcmeNV0yli+T9+vshCNfdu67V+y30RCB0IWJhEI3GjrevwYtRiL2W/Rce4EL7z+tdxLeHz+O9cBPwhagYZULb0W9CnawG+UNGSvTh7arQ1rVmT/Ke3sflC5tmtTca9pThj59Rd4rOC+6aJZxxnF6enoNjR77BBMJha7HmGaCXKV5gYYrkaK9wMXA1XcnkQjkwXzHb8IWXETicu3icSuL5DdviLz4XLp8q85Q+0rOFOyWvamdpP0D34y4+xfZ+94f5YwmEnf79u2eFrgAVwldlQoyAnB+9SACRUVFSXnOay9wwZMhQ4ZouJPw4GhxiWQlbB9++GHDg9MlMixvVsULq6wzljcQd4U35chvNom8OE76NYn2066UyyXnRB7pJG2i3o+7QVteQBKJtLQ01w8ssKJzELpQQULoMmTICkTdrQMCF9nFEi3RfpWJ1mXbe1AtYcCyeBOBtWvXGoQjTtFvBYtBPY7rgyr532Rrh2kyvV8zT8MMJ0ld03omAqxypGKcbiLo6fMONg5z5sxJKvOZJwQuMs1gxcuzKPUZfGYpgaemSmqB1b7fSmZmpnF8oOv9qiyS1VtT5fmR7WI4ZjSRNl06iHxyRi5XaqI7jgIcdoTZ2dlR7nj3EoWud3mnKEc4EMJUk8l85gmBiw5jxcs0j4r13viLiRM2Tq8ltYgHXZzRiwWFSkMYz7vWPVslFYXbZemvRkqbe1IEgfcpKffItx/9lZTLZpnU5T5JGbpOSqvulU6ZwyQnsuGqa3L++E3JefK70snlGQHqeS+GA0VCGu07hC7SQGKnq48ZIhqlvBYNgYKCAhk9enS0W6avufzzMk2nseLFBM7iDQRgr1q0aJERi+jHnW04F3A4OWw77pVG0jR7oZSFQhKq/ndb/rT/FUmV0bK25M8S2jNROjcSadTpu/LkIwdkT9GNGnIry6Tkk77yZGb7GLvjmsft/JSXl+fr7F1IA6lOwnJ3kWYnF/1ZN8yayXrOe0bgKgcVnsqh/2DG6h2q1nfeecdziQsSQRd93bx5cyKvOv9Oo87yxMLHpfCXb0le+dciVVckb9FyKZz+sjzR+V7n6YloEYtq4OnnAqGLhC8zZ87UN3GKnxmQQN9gzkRWvGTUyWjWMwIXxEKtvHfv3gTg4itOIYBVO/gE9UuisWpO0WpVO3qolc32ppE06fe8bFrcUjb0+xtJuWei7OnyC9k0PUPCInPNVmbpc0qdDDz9XqAVgdf+q6++6veu+qJ/VqiTAYTWhxdEcgo/SEzmeniFRlLH7yr8B+k4MaEEqcA5DI59GJ8siSGgIhGCMnaC/HtJbIS48xb4hEN0rl+/bmqH69nDCyLhhVoZ23p6K0cio8d3hP80b948cMIW6EMNqgSGHtzwHhVYtPjNOzkWF+DbsHjxYsPPgTG6sZBy9x7StyL5UrLqZPTCUyplEAwvsQ8++MBdDrD1OghA1Q+P5Ndee63OvSBcUGpQ+hgkxm0soqEhUL4aidXivbcwicPXgZ7L+vJux44dMmLECEsI9JRKGT2Od3tvCUqsJCYCUPW3bdvWOIQ7aBNmODDY4VZUVPgqm1Z4/+z8vHDhQsMD1Ctn31qNBZzFdu3a5esQOqsxc6I++KQMGzZMkNvbbLSFb1TKABidXrBggcthGE6w2httYAGknKSCLGzBrR/96EeGWhmYsJhHAJMaMvjA9h/Ugt8QzDEIGWLRB4GdO3caJjKzwrYhyj2nUkaHfvCDH8jKlSsb6hvvO4AAJoiRI0cKQh2CXqAezMrK0vTIPn25k5+fbyyirZrU9O1pbMpgjsGhDbTnxsbJybvwK7BS6+JJgavsZXSecnLo1W0Ldlt4jPsxR3Ld3pq7AlvP0qVLzT3MpwwEoIp//PHHA48GFhy05+ozDLDwgZOuleGNnhS4YMmUKVPoPOXi2ITddujQoYHIJBUPzGqnT+cpc6ip3ZyVk5q5lvV8CjjMmjUrsM6HOnEFzlITJkywlCTPClzYe6B+YXo0S8eD6cqg/tq6dWvgvErNAIQ40i1btph5NPDPYFJDyAVLDQIqlpupbGswcfoTNhQwdfTt29fSpj3npRzee+jXUZAmjcU5BJRH5erVq51r1EMt0ZPeHLNUIpt4PEDN1ez9p5R3LFTM3P07z89kEtnE8lL2tMBVg5I/WOcGpJokd+/ebUkguHOUO9sSF4MN453MpNZw7d5/Aj4ScA599913TYekeL/X7vcAcuX+++83nVkqkmLfClx0FPF7Xbt2ZUq9SK7b9P2ZZ54xko9Y6blnE6muVsvFYGz4k53UYtfun7u5ubnSo0ePQGZvc4uLycbTxxK4nrXhKmbAuxHHwDH2USFi319lU6KwbRhjhAjBlotkBix1Edi0aZOsWLGCWpK60NS6AgcqaAKgWWKxHwHIEeA9ZswYWxrztEpZIYJV4IABA7jLVYDY8FftSC5dukRHKZP4wlN57NixcWWpMVm1px9TY8lsMnhPd9YC4ukzYQGIJqsA1sXFxTJ79myTb9R9zNc7XHR38uTJ3OXW5bulV6BFoFdyfJDC2QWJMLjLrY0bd7e18Wjom/Ja5tGkDSGV3H3sbjHP2RkT7nmVMiDmxJbcQGvobcRKYrc2fPjwhh7l/QgEuBisDQh2ty+88IJtKrvarfnnG0Kn5s6dS9OZjSzFwhgLZDu9wn2hUgYPqL6zZyRi1Td48GBZtWqVqAxf9rTk31pp8qjhLb23a7CI9xOxixcx88+rec6KMKxYKmXfCFxAy4nN/AAz+yRsGocPH5YlS5aYfYXPRSCgQqmCHr5G223EwIjzq5VCIc6mff94sp7J4QAFRuBylxvO9uQ/c4JMHkNVA3cnYnh/Ag8mqlGjIv6/XADHj1lDb1g9zwVG4AJYTmwNDS/z9xHjjCP3EN7CkhwCVv+ok6PG+be5GLYOc5zOBZuuytttXc3BrMlqmREogRv0ic2qnwwnSKuQrKkHaiuol5MJOaipzVufaO6xjl9wYsSJVMglz5IcAnbMc7EEri+8lMMhR8IBhK/AvZslcQTWrFljnFoS9DNKE0ew7pujR482Jkn8yINUcIwm+kwvd2u4jp0tPGmhXmZJDgGn5znfCVzAjx82TnoI2sSW3NCreRu4cYKswcOqT1i8zJ8/33Dus6pO3euBo8+8efMMFSgXb9Zxi+FmyWOpwh1VnHPyNTZcgy8FLn7Yr7/+eqAmtoZZbf4JrPpgI+IEaR4zs08iLWarVq0kKEkMENuI3RjtjWZHiLnnmHvAHE71PYWF4LRp04zFYH3P2HHdlwIXQFHtkthwUbtbTpCJ4WfmLZXEAP4Gfi7o36hRo+TFF1/0czdd6xt3uYlDv3nzZiPJhdO5BXwVhxsJPxxU2rZtm/AxS5H1BeE7nFtGjBjBHYnNzIZnZEVFha8dqDCWeNKNvQOJzmjx46vi4u06YjRQTlPh8COkhQ5U4YjE/szdbWx8rLw7adIkw4EKDkV+LMo+BkcxFvsQ4C43fmxfe+01wyEUDrZOF9+qlBWQcKCCIAmKzUz1O5G/sN1OmTIlkVf5TpwIwD6OdJlwKII9yU9F2ceQnYx+APZyVtlyDx48aG9DPqldeXY76SgVDp3vBS5+8PjhI/G3321m4YyN9zMWJfDsHjRoULyv8vkEEYD9KCMjQ2BP8lOBwyKSM0AYsNiPAHa5K1eutL8hj7eA+R/hoq+++qprPfG9wAWy+OEjnRxjc+sfZ9AA4LBr7kjqx8iOO88995yRHQ0LHj8UqMiRkAEeoCzOIKAWNlDjs9SPwMyZM405DqZGt0ogBC7AhS2JquXowwwrPxyZxsQE0fGx8yrsSFAt46B6r6uWQf+zzz5r9IcLNztHTd264fm+fv36ujd4xUDAbVWyYoOvvZRVJ9VfCFxMbADfzVWOokeXv1aelKFLn7xGB/JWo3g57SM8Zh966CEeTuDS4IN5worj5Vwi37ZmVbTKpUuXHJn3A+ulHMlBqF6gNoWXGssdBLArQYgKbG4s7iEAFSxUsV5VC8IkgQUtvK9Z3EEAcxudQ2tjj/kN8/2ePXscEba1W6/7LTAqZdV15Z2GXR2LyNGjR40AcO743R0NUMFidwLBixW5lwroHTp0qLFwoyrZPc5lZWUZpiE6h9bwYO3atdK8eXNBhjcdSuAELkBfvHixMTn4NQYynoEFuw8SXbC4j0C4BsYr9lzQCYdEXXYQ7nPRPQrgD7BgwQIj2sA9KvRpGdoibKx00mgGUuAqRxU4eAR5NYidyYkTJ5hVSp85QpQGBitzLxSEAMF2qMsOwguY2UnjD37wA0PI2NmGF+rG3AZtEbRGOmldAilwMWAQA4mVOVzFg1ry8vJ84OBSJZWl+bJtyzIZ32m25FVURWVnVXmhbJg5VODQkDb+LSks/zrqczpcfOONN4xJU3d7LuyFhYWFHgkBqpDSP7wu49NSjDGQ8r2ZsuFIudQZLZWl8odl4yUt5c5zaeNflz+UVugwLEzRoHID+yXMzFSnIx5SdlvYtFXIVMQjrn0NrMAF4uPGjTOAh9NQEAv6nZ2d7emuV5Wul3987f/I1hdnyMZb9XSlslCWj/kfUjJ0ndwO/UWOjL8mM8e8JUcq60y39VTg7GUv2HO9Zbf9Wq7seFt+Lz+Ut8pCErpdJh/+5DN5Jf0ZWX7kZg1zqy7ItpdGyfhPsiXvy9sSMsZKhSzMWlTvQq7mZX0+YV4LsvOUstsqbZE+nBGRkAbFTTJu3boV6t+/f6igoEADJJwj4dixY6HJkyc716CtLf05VLJ2dEhSXwnt/9PtiJbu3EvN3R/6U/Wdq6H9ud8N5aw9HYp8uvoRDT7s2bMnNGLEiBDGqE7Fc7+Z2+dC//7vF2vz+vbp0Nqc1FD4uLhdsjaUI/1Cufuv1sBtPPfd2tdq7mr56fr168acptu4cQIsHX4zseRZoHe4WPlgN4G43MzMTCOsQavVkI3EfPDBB0YyEBub0KPqqvNS8N5ReaRLmjSppqiFpA8dLJ+890c5o+cm16AUdtEhQ4Zodbwd1HU4bg+7KM8c4djoYcnKaiu1JrtGLaV977TqEYEPjR5oL71Ty6Tw6DmpVHcqy6Tk7GAZmu58ontFQrx/4aPSq1cvIwIh3ne9/DycYJHCF5o7ney24ZjWGoPhN4L0GSExBQUFRlIMqMr8XjBpzpkzR9LT0/3eVak680d5b28z6d2+Ze0JFz3fu1sKznylNQYqrlUXs4dS18H/wfvlfhn+nY41C7GmfeWJ6X0lf8YkeX7dSamsuiJ5y/bJA5tekKym3poqkVnvwIED3meRyR5g3lZZznQOcfTWKDIJfiKPYbWOSQQu5BBIfi6IvUXCc6yE/V2qpPLyGflEOkiXNjX7Wy/1GSt15UTltl0OIRbwatcpzCJhXlZ8LHuOD5MpOeE732bSb/pq+XB5X/nDpEfkW/dMk/NjfyHTMlLrLtYSbtiZF3EICRbVfp/LgCb6iLl7/vz5hjOsMwgn1goFbhhuUJNBFQOVmZ8LVr48p9Q7HFZmD6jLKzk08AAAIABJREFU3PJcRrvYZeOkFV3VdeY5elOOrPqttFr4U+nXJGIKbPS30qxdP5m+dLpkyWaZ9LPFkqexR3t9fQaPEJOLxbWfC4Qt5muYXrwQmhYx2vzMGnN9002FZ45q809hgAZFnSzSSJq06SSPyDkpuVxtlTMPlkZPQk2GmEL4Gjht9oBtDDGN/shBXiWVR/5N3m8xWZ7r1yyCwxVSvO4XslxGyPSX/6fsL9srr8i/yKMae7RHdKDWV5iM/K5WRhw4Mkl5xcRBgVtriN5xooIKD6ozXexmESQm9bWkpCQg6uQ7MDXq9F15MudvIjD7Wj47f0bKc4ZJZqd7I+7p+xUxhfA1QLiDU0JX2cYwselsGzPLtaoru2X1yUz5+cQeNbbbuy9XlW6RlyaVSUaP1oYKuVHq92Xh77bLUnlLZr9fWjdm12yjLj0HgYvFtV8L5udPP/3UUyYOCtwoozHcbqaOdYrymCcvYcIOlDq5UXvJfPJBeXvPx1KTvqBSLpdckZwnvyudPPYLgK8BhJ8TQhfCFu2gPc94JMf4VVaV58mv379X/vFpJWyrpLJ4i6zLvyYiyt4fUUGTDtI3o3XERW98hY8GfDX8mMIWwhabImyOPGXicCI2qqE2YsUtNfSunfcvXbrkuxhdxByjX/4qseJwQ6HQlx+Glmb9MPTK/suh26G/hMr2zwtlZS0PFX2pcxRubA5t2LDB1lhLf43926EvS7aGcrNSQ5hrav8bHVpb8uc7YBvjJDWUOm596LQxNm6Hvjy9PjSu4/OhrZf/Epshmt7dunVraMWKFZpSlxhZdo/9xKiqeSuWPAt84osamKJ/8tPEg74gkYKvyp/2h3JTwyfR1KgJLW6XFYSWj+sREkkNZeVuDBWVeXMCDecdJlIkL7E6wYEa85jY/FBuX94amlhrjISNl5y1oZKwddftsg9D63NzqoVy6rjlob0lNSlTvIaH337zSFCk+6YhlsAN1AH0iSqC/KJag3q8rKzMMw4GifIrSO9ZrVpTYx0e+15xRAkSvxPpKw6X8IPDGzzlveC8xwPoExmlYe/AWQQDFsx2KywjjJyEPx4+fNjwck24Ar6oHQIQiiqULdmYSwpb7dhrCUFYPJ06dcqSutyqxCvCtiF8POYy0lB37LvvB6G7dOlS6dKli30gsWZXELBC6FLYusI6Rxrt06ePFBUVOdKWHY2ozY4fdukUuHGMkHCh63bWnzjINh7FcV3wWPSUR1+8nQzw80roDh48OO6QISVscZwZ1cj+G0TdunWT7du3e7JjMJksWrTIFypxMOAbnuSCi0QroYtwCQgxr0xQJ0+eFKR7Y/EvAhiLTZs2NUJ5zO4GlLD1S+iPf7mbeM8QHpSWlmYsxDB/eaUo/wSzY9kL/eIONwEuYdDu3r3bU8kxYL/t2bNnAr3lK15CAPY6Fafb0CHksIv5Kc7WS3xymlakPvSKHRe+CErYIs7WS4uEhvhKL+WGEIpxX+XxRGoxJHTXWV0Lz7nr168H4MCCGAwL0C0IU6SBRKKTaEkrlBMKd7bBGBQwgcGOO3v2bK07rOZUEOm5pBZ3kaWXsk1DTGWkatasmZFAO1kvUZvINFRJI0aMoLC1C2AN64WQRRpPFUYRTiJO/VHXownj8Gf52R8IdO/eXQoLC7XuDMwbOIgAXverV6/WegOTKJBUKSeK3N33IHSxasQgScRhJcnmTb0OVRJi8ViChQByL8P+BQELFZ1S1R08eNA3TijB4mjivYVadseOHdoe16d8CeBn4hW/mES4QYGbCGpR3sEgUbYzqOt0KrDlde3aVSeSSItDCGCifffdd43dDcJDzp07Z6jq/GQXcwhKzzczY8YMuXTpknb9wHzZtm1bY/6ED4KfCwWuhdyFeg5HqEFdh12FLuXixYvSo0cPXcghHQ4jgEm2uLjYcJqDTRe2fJbgIYA5ANEKOhVoXjBfYowGwbxBgWvx6IMaDx7MUNvl5uZqocJBwgusIFmChwCcZcaOHWvsHt5//32ZP3++MRZ008IEjzPO97hjx47Gwsv5luu2CPPGM888Y0R64MzeoGhcKHDrjoWkryDuDR52Dz30kOt2XdhG4DClswd10oCzgjoIYEJbuHChrFy50rDXqt1DTk6OsZvArkLZdeu8zAu+RKBVq1ZaOE7BxAV/Fz87R9U3gChw60MmyesQcMqui90lnFfcKNeuXRPsulmCgwAWWU899ZTRYdhvI3cP+I5dBUwN8ArF8yz+RwDzAByn3CyYB5XGxc/OUfVhTIFbHzIWXcfOAvaJXbt2uaJihpPMgAEDLOoNq9EdAaiQscCbMmWK4T1fn2YD15csWSLDhw83kl94LVWp7nzQlT5ouxpKiGIH7Tdu3DDmP8yDELpK42JHWzrXSYHrAHewowhXMR8/ftyBVu80AWeZ1q1bO9YeG3IHATWhQYWMBR5Ux2YKMk3B0Q/vQQWtayy5mb7wmYYRwC731q1bDT9o4ROY74YNG2Y4biK+NlLjYmFT2ldFgesQi5SKedWqVfLss886Zj+7efOmwHbD4l8Ewie0aCrkhnqOSRjvocC25uSCsCHaeN9aBKDtgtbLiaL8CDDfYVHn95AfM5hS4JpBycJnevfubdjPKioqDDub3eodeihbyDzNqlIT2rx586ontPpUyA2RjveQwEUtCLnbbQgxb95v0qSJlJWV2U48Fm1YvKHAX4B+JHcgp8C1fejVbUBNbpgo4UBg9+SW6CRcl3Je0QUB2FwxoUE9h92pVROaWhCin9zt6sJt6+ho37694SxnXY21a1KLQOxqsXjDIo7zTw1GFLg1WDj+KXJyszo2ErtnnIHL4h8Ewm21Sk1n9YSmFoSYMLEoRDw52mXxPgKNGze2zWlKLQJxRCR2tZjfWGojwNOCauPh2jcIR0xs2KkgVMMKxwLUuWbNGsMb1bWOsWFLEMDOAR6eo0aNkq1btxrexVYL2miEot3NmzcbPgc4oB5OVizeRiDWaTaJ9AzzDExXV69eNeYaq7QtidCiwzux8OUOVwcOiRiCFqpBODUgrAOpITHZJVOQxo0pHZNBUI93oflAXC3ONEZaRgg9J4Qteo924OyCUA60P3LkSDpV6TEskqIi2bkFjaMOJE+BWQzhZdu3b7fMtJFU5zR+mQJXI+ZgcsNkikkVyQhgQ0s2PhJOEizeREBpPbB7gGoXcbPIYuZGgcYF7SMBvlIzM2GGG5xIvs1kDzGAoMUCTDlFIZUtNR/m+EKBaw4nR5/CpApnA9jo9u3bZ+wqErHvwhuRAtdR1lnSGOylcKTDzgEaD+wcdLGHIWGB0sRgksUOh/ZdS9juiUrCtS2Yn5Atyq1FoCcAiyCSAjcCEJ2+whaidhXY5SDZN3Y9ZgtS98ErkcUbCEBwQYDdf//9hg0fjic67hyUJgb0oYBeCl5vjDFQ2axZMzl//nxcBEPQwpwQrm0Juq02LgDvPkyBmwhqDr+DXQV2ORMmTDAcq+BcFY/gdZhcNhcnAuGCFq/CpAC7qVN22jjJrX4c9GGHo477o+CthkbrDzgbu7Ky0hSN4YIWqmidtC2mOqDZQxS4mjEkFjlK8CIfKoQudryxVM1ffPFFrOp4z2UEoglaL6rooFKk4HV5MFncfDRBG9T8x1ZCy7AgK9F0uC78KKDiQcHqs2/fvrV2RXBPR95U3XdKDsPmenPQTmzZssXYLWAnO2bMGF/ZwbCQ2LRpk7zwwguyYsUKQxVpRZib64zzCQFweEKJNFfAGQrneCOvNgrmFApZA4q4/osVFkSBGxeUej4MwYtjt/Lz8wWxkllZWcYEHovxevbE31SBT+vXrzcO3QafEErh58UQBC/G5KJFi4wxCc0MJ3D3xzjSLmJBBP8QFPBp586dhh0ecwcWgLo46bmPVvwUxJp3KXDjx1PbN7BzQhgRdhYLFiyQOXPmSCgU0pbeIBAWLnRw4Dbs8EETOtg5HT16tFobg129WhQGYQzo1kfME0iIA8H6wQcfGPMENRHWcYkC1zosPVETJjiVlQi7Ck5wzrNNaR2g8sdkhuPy6NUphrNf+KLwBz/4AXdTDg5Ppe7/9a9/LX//939vnJs8aNAgX2taHITXaIoC12nENWkPjC8pKane9cImAwEcaevVhFzPk6E0DMgSpnazxDo6W5W9EGkjT5w4YSwKEXZCW290vJK5qjQMypyBs2nLy8sFZ9OyWI8ABa71mHqixnDGqx8dYiehaobKGZliKBCSYyWyLeXl5RmZd1ATHFF+9KMf+coJKjmEGn47GobZ2dkUvg1DV+8TsX7vly5dYo71epFL/kb4vBtZG224kYj45Dt2WwgdQtxcZIFaqaioyMhiBZUnhG96errxj1ljItGq+x1OJwUFBUa+67S0NEPIUkDUxSmRK5HCd8iQIZKZmUm1swkwo/2uoy2qlQ1XOU2ZqJqPxIEABW4cYPnlUbM/qvCVMISzEiA9e/aULl260LYjYuS1PnXqVPUCBUcewsM4IyODuzAbfzBK+CJUBU4+amHYvXt34n738ACYjD7++GNDw4JUrlDLRxOy4WwyOzeEv8PP5hGgwDWPlW+eTPRHhfdwKoya5GD3RT7fDh06BEYAY6KHgIUWQC1CsNPq06cPVfAu/UKwezt9+rQcO3bM0CyADAgXaGaCIoCxOFYCVv0+1eIPp4KZdcpLdG5wifWea5YC13MsS55gK35U4T9wHPUH9TN+4HAIwo8beZrN/siT75E9NUC4XrhwQc6ePSuqj3AsUwK2Xbt23E3ZA31StYYvigoLC4049PDF4UMPPeRpOzp+e7C1Iucxfss4xASx9uF9TFQDZcXckBTzfP4yBa7PGRyte5iQkG4vmg032vNmr+HHqiYBeJdC1QcBBcGLnXDr1q2lVatWxpm+OiV1AB7IugWhCtUbDnbAAqJ///5GTGjQdvFm+e2V57ADBk/PnTtnaGiQcOOjjz4yBBSEL0wl2AU2btxYqwWUEqw4vP3zzz83aMdvDMLVrsUtBa69o5oC1158ta09FuOtJFrtEjFhFBcXy82bN6uTHGDSaN68uTHZqaMCMfGp0rZt26TsxJg8VFGTFr5DLY6iJl61KEDbDzzwgLE7T7Zt1S7/6omAEmZYIH722WfGYksJM7XQAuVYbKGoxaLqTTLaGywArl27pqoy2sYXtdhDnnMsVlGwa8UJPjhUAKabli1b2roooMCtZostH2LNu/RStgVyPSqNxXgnKFQTHtrCzhIFp5Soz/iOXWYyRQl01KEmLXzGxIXdDCYvel4ng7A/31UCMXyRphaL6HG4QEwEgXCBjvex0ItccCYj0BOhSb1DgauQsOdvrHmXAtcezLWoNRbjtSCQRBABIuA4AhS49kIea97l8Xz2Ys/aiQARIAJEgAgYCFDgciAQASJABAKEAJwHWdxBgALXHdwdaxV2VBYiQASIgEIAntzKUUxd419nEKDAdQZnV1qB9yNi+ViIABEgAkTAfQQocN3nASkgAkSACBCBACBAgRsAJrOLRIAIEAGFAMKfVIiSusa/ziBAgesMzq60ggw74TGvrhDBRokAEdAKASSmQVpWFucRoMB1HnPHWkQ6OxYiQASIABHQAwEKXD34YBsVyOzEQgSIABFQCCC7G9KasjiPAAWu85g71iLSyVGl7BjcbIgIeAYBnQ4W8QxoFhBKgWsBiDpXgZywLESACBABIICDRnCQB4s7CFDguoO7I60iObo6kcSRBtkIESACWiOALFNuHZqgNTAOEUeB6xDQbjbDbFNuos+2iYA+COCoQkQvsLiDAAWuO7g71iqzTTkGNRsiAtojACdKRi+4xyYKXPewd6RlnBGLMz9ZiAARIAKHDx82zoomEu4gQIHrDu6Otdq1a1f5/PPPHWuPDREBIqAvAjgLt2XLlvoS6HPKKHB9zuAOHToIVrUsRIAIEIEdO3ZImzZtCIRLCFDgugS8U81iNYtVLQsRIALBRgDzwOTJk4MNgsu9p8B1mQF2N4/VLFa19FS2G2nWTwT0RgC+HA8//LDeRPqcOgpcnzMY3aOncgCYzC4SgQYQOHv2rMCng8U9BChw3cPesZZ5apBjULMhIqAtAkjzinSvLO4hQIHrHvaOtdynTx/BGZgsRIAIBBcBHlrgPu8pcN3nge0UtGvXTgoLC21vhw0QASKgJwIqhzIPLXCXPxS47uLvSOvKcerGjRuOtMdGiAAR0AuBU6dOSUZGhl5EBZAaCtyAMB2OUxcvXgxIb9lNIkAEwhFASFB6enr4JX52AQEKXBdAd6PJAQMGyMcff+xG02yTCBABlxHYt2+fdO/e3WUq2DwFbkDGALwTDx48GJDesptEgAgoBGBKKisrY4YpBYiLfylwXQTfyabV2bhMgOEk6myLCLiPwOnTp2XkyJHuE0IKhAI3QIMAdtyjR48GqMfsKhEgAgcOHKD9VpNhQIGrCSOcIAN23GPHjjnRFNsgAkRAEwS2b99O+60mvKDA1YQRTpCBsAA4T7AQASIQDAQQf4sD53lCkB78psDVgw+OUIEfHZwn8CNkIQJEwP8IIOHNkCFD/N9Rj/SQAtcjjLKKzHHjxjHrlFVgsh4ioDkCu3btkszMTM2pDA55FLjB4bXRU/z48CNkIQJEwN8IIBxozZo10rt3b3931EO9SwmFQiG36U1JSRENyHAbBsfaB97Xr1+XFi1aONYmGyICRMBZBPbu3StFRUUye/ZsZxsOeGux5Bl3uAEcHAsWLDB+iAHsOrtMBAKDwObNm2Xw4MEa9rdKKkv3yLLxjwiEU0rKUJm5oVDKq6KQWpEnM9PwjPr3hKwr/SrKg964RIHrDT5ZSiV+hPgxshABIuBPBJQ6uW/fvtp1sOrKbln9e5GfvHVCQqG/SNmHP5HPXhkpY5YXSmUtar+WK/u2ydvlYRdzhklmp3vDLnjrI1XK3uKXJdQi21Tjxo2pVrYETVZCBPRDQF918ldyNv+43PsPA+TB6u3eV1K6bpx0mdtJ9hfPl+ymd29UFsqyUTul7+Z5Ndf0g7oORVQp14Ek2BdwJuaKFSuoVg72MGDvfYyAvurke6VjVriwBRO+KQ+07ySptfhRJRWF22X53jXyywVrZVteacTut9bDnvlSvcbwDMUk1BIE4K28cuVKS+piJUSACOiDANTJJ06cEB3VybFQajw8Xbo0uSuSqkply+L1Ui7lkr/kWRn1aJb8eOY2Ka2MZuiNVate9yhw9eKHY9QgVIBJMByDmw0RAccQ2LlzpyDeHposb5QbUrTnijw3JbtGzdyoq0zcUyah22VStH2V5GaJ5C+ZKj/7TZGnd7oUuN4YkbZQOXXqVEGeVRYiQAT8g8C2bdskJyfHIx2qksojm2RDq+fluX7N6tLcKFX6jXhGFu//SPa/8ojkL98uhRXe3eVS4NZlcWCuZGdny8aNGwPTX3aUCPgdgePHjxtdxHGcniiVRbL6/ebyynPp0iQWwY0elOxZMyVX9sqeohuxntT6HgWu1uyxlzjkVu7Vq5ccOnTI3oZYOxEgAo4g8MEHH8iUKVMcaSvpRqouyI7Vn8rwn/+TdFW221iVNkmTLo90kS5tYormWDW4fo8C13UWuEvAhAkTZP369e4SwdaJABFIGgE4S82ZM0cGDRqUdF22V1B1RfJ+vUu+9Y//rUbYVp6UDesOSUV9jVeWyZl+k+Txzt6Nw6XArY+5Abk+cOBAw6ORJwj5heEVUpq3Q7YsGy+dZuZFmbyuSd7M9LDMPSqDT4qkDF0npd41j/mFgQn3Iz8/3wj3095ZqrJYtr0yUR6d/t/l0bS/qRmL38qRTXK/oVquKj8iO3Ycqc4+VVV+SF5fcFSGvJApTRNGyP0XKXDd54HrFNB5ynUWWEQAEghMk9c2rJcXZ2yUW9FqrfhY9rx9JMqdVMl58rvSiTNCFGy8cWnRokX6O0tVXZBtL42WUUv2RgE1U57MbC93huAN+fB//VjS7kmRlLTxsvzQf8oPfz5dslO/GeU971xipinv8Mo2SqGKuv/++5l5yjaEHa64qljWDc+Wub3fkeLF2WE7giqpyHtTlskomZf94N2JDbRh1ztXzk/6XzLRw+o6h1HWqjn4YcA0tHr1aq3oCiIxzDQVRK7H0WecGoTMU1BJsfgZgb/K/9dmhOTWErYiVaW/lcXHMzydo9bPXDPTt6VLlwr8MVj0RoAKJL354xh1iNuDSgp5lln8isA3JbVzu4jwi6/kTMEhafOzR6lO9ijbS0tLDcrhj8GiNwIUuHrzxzHqELeXlZUlBw8edKxNNqQBAlXnpWDbg/JPQ9qGqZg1oIskmEYAh8zPmDHD9PN80D0EKHDdw167lidPnsz8ytpxxV6Cqs78Ubb9fZakqxNa7G2OtVuMAHa3MAV5LW+yxTB4pjoKXM+wyn5CscvFPybCsB9rPVqAOrlQ/n5ozzDHKj0oIxXmEMDudtasWR7Km2yuX359igLXr5xNsF/Y5cIBgyUACBjq5P8qQ9NbBKCz/uui2t0OHz7cf53zaY8ocH3K2ES7xV1uosh57z2qk73Hs3CKubsNR8MbnylwvcEnR6nELnfatGn0WHYUdacbozrZacStbI+7WyvRdK4uClznsPZMS8pjedeuXZ6hmYQCASS2mC1p93STSXvLpXzJo/LtlCdkXelXdeGBOvlQd3kig+rkuuDofwW72/nz59N2qz+ralHITFO14OAXhQBW0GPHjpUDBw7wR61A4V8ioAECcGqEnwXPstaAGVFIYKapKKDwUmwEsMsdN26crF27NvaDvEsEiICjCEDYMu7WUcgta4w7XMug9F9FzLHsP56yR95GYNu2bXL48GFZsmSJtzviY+q5w/Uxc+3sGnIsb9261Uj5aGc7rJsIEIGGEUDaVaRfhVMjizcRoNOUN/nmGNWI8YM99/jx4461yYaIABGoiwDMOzDzwNzD4k0EqFL2Jt8cpRrCdt68efLuu+/SgcpR5NkYEbiDAJ0YvTMSqFL2Dq+0pLR3797GqpphQlqyh0QFAIHc3FyGAfmAz9zh+oCJTnRBOVBdunRJ2rRp40STbIMIEAERgaMUFrs8XN4bwyHWDpcC1xs81IJK/vC1YAOJCBACXOh6j9mxBC6dprzHT9cofuyxx4y2IXhZiAARsB8BeCUjUoBaJfuxdqIF7nCdQNlHbVy+fFnatm0rVC37iKnsipYI7N27VzZv3kxVspbcqZ+oWDtcCtz6ceOdehCgarkeYHiZCFiEABe2FgHpQjWxBC5Vyi4wxOtNUrXsdQ6Sft0ReO2116hK1p1JCdBHgZsAaHxF5NVXXzWy3iA+kIUIEAHrEFA+Empha13NrMltBKhSdpsDHm4fNqaVK1cyIYaHeUjS9UJAJbjYvXu3ILUqi/cQoErZezzzBMU5OTmSkZEhr7/+uifoJZFEQGcEkCsZR2Li90RhqzOnEqeNKuXEseObIjJt2jQpLCwU7HZZiAARSBwBmGmQK3ngwIGJV8I3tUaAKmWt2eMN4uhR6Q0+kUp9EVCe/2+88QbzlevLJlOUUaVsCiY+lCgCCMrfs2ePTJ06VaAWYyECRMA8AjgcBAkusMO97777zL/IJz2HAHe4nmOZvgS/+eabcvHiRR6OrS+LSJlmCEA7BG/kVatWCQ4JYfE+Atzhep+HnujBpEmT5IsvvhAIXhYiQARiIwBtEOJtZ82aRWEbGyrf3KXTlG9Y6X5HoA5bvHixbNy4UQ4dOuQ+QaSACGiMALyRH374YWOHqzGZJM1CBChwLQSTVYkRzgAHEHgvMykGRwQRiI4AtECffvqp8TuJ/gSv+hEBClw/ctXlPsGJCqt3xBTCRsVCBIhADQLQ/kALBG0QnaRqcAnCJwrcIHDZhT4ilnD+/PmGuoyeyy4wgE1qiQCELbQ/0AIxuYWWLLKVKHop2wovK4fq7MSJE8L4Qo6FoCOg4tWPHTtGJykfDwZ6KfuYubp3DbG5vXr1khdffJExurozi/TZhoAK/ykoKKCwtQ1l/SvmDld/HvmCwtzcXKMfS5Ys8UV/2AkiYBYBJWzh18C0jWZR8+5z3OF6l3e+oRzxhozR9Q072RGTCChhi1hbCluToPn4MTpN+Zi5OnUN3piw48Key8QYOnGGtNiFgBK2OJCAZ9vahbK36qXA9Ra/PE0tha6n2Ufi40AgXNjCj4GFCAABClyOA0cRoNB1FG425gICFLYugO6RJuk05RFG+Y1MxObCcxmp7RCXyAQAfuNwMPtDYRtMvof3OpbTFAVuOFL87CgCSuiiUcbpOgo9G7MBASVskfAlJyfHhhZYpRcQoMD1ApcCSiOE7tq1a5kcI6D890u3kTccqUwZ+uMXjibej1gClzbcxHHlmxYgAFWySo7x1FNPMfeyBZiyCmcRQLrGLl26UNg6C7snW/uGJ6km0b5DAEI3LS3NCJ9AnlkcgMBCBHRHYO/evTJ37ly5dOkSx6zuzNKAPgpcDZhAEu4ggFjF1q1bS9u2bQUp8JgogCNDZwQQT75v3z7jIAIuEHXmlD600WlKH16QkrsIKHsYdr1IGsBCBHRCgM5+OnFDP1pow9WPJ6QoBgKdO3c2dg0HDx6UhQsX8tCDGFjxlrMIwBMZvgY4kGP16tUMZ3MWfs+3Rqcpz7PQnx2Aig6hQiiI18VEx0IE3EQAzlEwe0yZMsVw9HOTFrbtTQSoUvYm3wJFNZyoFi1aRC/QQHFdr87CXrtx40Z55513BBoYFiJQHwKxVMoUuPWhxutaIRBu1x09ejRVeVpxx7/E3LhxQ2bOnGl0cPHixdKiRQv/dpY9swSBWAKXKmVLIGYldRCoKpcjG2bK91JSBAMw5XszZV1eqVSUvi2zt12q83hDF7Cr2L17t5w8eZIq5obA4n1LEDh+/LgMGzZMBg0aZNhrKWwtgTXQlVDgBpr9dnX+phxZ/oykr79HXij5k4RCIbm9aZTcs+cF+XZw+qJ/AAAG2klEQVSX30mnHq0SahgTHg6wHz58uGFLQwwkCxGwGgF4IUOF/OyzzxoqZHrKW41wcOujwA0u7+3r+V/Pyr//5vfS8Yej5CedmxrtNErNkPFzZkpujwzp1eHepNqG4wpsaStXrpTc3Fx6MSeFJl8ORwCmC3ghV1RUyIEDB2ivDQeHn5NGgAI3aQhZQX0I3Dp9QT6vCrvb+NvywH/rK39nQboVqJjfffdd6dGjhwwePFig/mMhAokigF0tnKKQDxleyLNnz6afQKJg8r16EaDTVL3Q8EbiCNyUI8vGSvqMo5KV+6b8y89HSucm9q3tIGznzZsnGRkZ8txzz9GxJXHGBfJN7GqhKcEibtasWRw/gRwF1nWaTlPWYcmaTCHQTPpNXy0fLv++lCwZJVnP/28pLP/a1JuJPNS7d29jt4vYXTi50LabCIrBe0fZatWuFv4BdIwK3jhwssf2bTuc7AXb0g+BRqmSMW2F5K2dKLJxqnxnzK8kz0ahi1OH4NyibLvPPPMMk2XoNyq0oQhJLGCKULZanl+rDWt8TQhVyr5mrw6dq5DiddMke9I6kdz9Urw4W+64UdlLm0qWASE8adIk2uPshdsztUN9vGbNGsFf7GiZxMIzrPMMoVQpe4ZVXie0SiryVsuG0q/COtJUuj7+T/J0qkj51qPyH38Nu2XjR3gyI24XOxjsZKhmthFsD1SNBBYI9YH6eMCAAbJ9+3YKWw/wzW8kUqXsN4662p8bUrRnh5y6XBmVitRR1ngoR608ykXY4+BtCjXz5s2bZeTIkQJVIktwEICdFtoO2PZRsAjDYoyFCLiBAFXKbqDu1zarimXd8GyZ9PXTsn7ZP8vT/VKlUWWxbPvlSzJqyX+RpUXvyMv9mrnWewjbpUuXGjubyZMnc4fjGiecaVgdDp+VlWVkJ+OZtc7gHvRWYqmULYiIDDq87L9CoOrMUTn/s0Pypx6fypa1E+Se9DuZoFLHLZe9JZPk+3eTYKjnnf6LA+3xDxMxVIuYiCl4neaC/e2FL6x42ID9eLMF8whwh2seKz7pIwSgaty1a5dxChEFr/cZC34ePXqUGgzvs9LzPYi1w6XA9Tx72YFkEFCCF1mGWrVqJRMmTDB2wcnUyXedQ0DxD8c3cuHkHO5sqX4EKHDrx4Z3iEA1AkoViQtI74dTYhDfy6IfAvA63rRpk5GOEc5wjz/+OG3y+rEpkBRR4AaS7ex0ogggVSQm8/z8fCOZBiZ0Otwkiqa170XyZsyYMcwOZS3ErC1JBChwkwSQrwcTAeyidu7cacRv9urVy1A39+3bl7teh4cD+IDFD9T+KNQ+OMwANhcXAhS4ccHFh4lAbQSUQ86OHTuqd72ZmZmCHM4s9iAQjjlCuVasWCFIv8jMUPbgzVqtQ4AC1zosWVPAEVC7XiRTQEEShezsbKqcLRoXUBkXFBTICy+8YIRswYmNWgWLwGU1jiBAgesIzGwkaAhcvnxZ8vLyjExG6DuEb8+ePbnzjWMgqJ0sDntHukWo7kePHi3p6em0zcaBIx/VBwEKXH14QUp8ikC48C0rKzPSSCKHc7du3Sg4IngOrE6dOiX79u0z4mZnzJghQ4YMoZCNwIlfvYkABa43+UaqPYoA1M5FRUXGvzlz5hiqUYQYYffbpUuXwDldKQELTLCLTUtLMwRsnz59qC726Bgn2fUjQIFbPza8QwRsRwBHwZ08eVIOHz5s7OhGjBhhCBw4AHXv3t1X9l+oiC9dumT0t7i42BCwABihVVAT+62/tg8eNuA5BChwPccyEuxnBCCAz58/b+yACwsLBd7PyOkM+yV2fz169JCWLVtqr4rGzvXatWty7tw5gXAN7wt29B07dqRK3c8DmX2LigAFblRYeJEI6IGA2hVCCEMYX7x40Qg/+uijjwT2TRSc4YoCYYzStm1b21XTEKi3bt0y/kGoVlZWGjtX0IhFAnbq2KWDttatW0u7du18tVs3gOZ/RCBOBChw4wSMjxMBHRBQghhCL1zggTbEpqqC3XHz5s3VV+OvEtC1LkZ8UQI0/DISTEDQoyiBis+qPiXwGQ8bjho/E4EaBChwa7DgJyLgOwSw4wwvV69elc8//zz8Ur2flQBVD3hBla1o5V8ioCMCFLg6coU0EQEiQASIgO8QiCVwtTmAHkSyEAEiQASIABHwKwJaCNxQKORXfNkvIkAEiAARIAIGAo2IAxEgAkSACBABImA/AhS49mPMFogAESACRIAICAUuBwERIAJEgAgQAQcQoMB1AGQ2QQSIABEgAkSAApdjgAgQASJABIiAAwhQ4DoAMpsgAkSACBABIkCByzFABIgAESACRMABBP5/tU6BvSHlI44AAAAASUVORK5CYII="></p>
</div>

<div class="specification">
<p>A student from the school is chosen at random.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that&nbsp;are taught in Spanish.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study Mathematics in English.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study both Biology and Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {S \cap \left( {M \cup B} \right)} \right)">
  <mi>n</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>S</mi>
      <mo>∩</mo>
      <mrow>
        <mo>(</mo>
        <mrow>
          <mi>M</mi>
          <mo>∪</mo>
          <mi>B</mi>
        </mrow>
        <mo>)</mo>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {B \cap M \cap S'} \right)">
  <mi>n</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>B</mi>
      <mo>∩</mo>
      <mi>M</mi>
      <mo>∩</mo>
      <msup>
        <mi>S</mi>
        <mo>′</mo>
      </msup>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies neither Biology nor Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student is taught in Spanish, given that the student studies Biology.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = 6 - \ln ({x^2} + 2)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>6</mn>
  <mo>−<!-- − --></mo>
  <mi>ln</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mo stretchy="false">(</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
  <mi>x</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>. The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> passes through the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(p,{\text{ }}4)">
  <mo stretchy="false">(</mo>
  <mi>p</mi>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mn>4</mn>
  <mo stretchy="false">)</mo>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p > 0">
  <mi>p</mi>
  <mo>&gt;</mo>
  <mn>0</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
<p><img src="images/Schermafbeelding_2018-02-12_om_13.30.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/05.b"></p>
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis and the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x =  - p"> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>p</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p"> <mi>x</mi> <mo>=</mo> <mi>p</mi> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>On one day 180 flights arrived at a particular airport. The distance travelled and the arrival status for each incoming flight was recorded. The flight was then classified as on time, slightly delayed, or heavily delayed.</p>
<p>The results are shown in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A <em>χ</em><sup>2</sup> test is carried out at the 10 % significance level to determine whether the arrival status of incoming flights is independent of the distance travelled.</p>
</div>

<div class="specification">
<p>The critical value for this test is 7.779.</p>
</div>

<div class="specification">
<p>A flight is chosen at random from the 180 recorded flights.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down&nbsp;the <em>χ</em><sup>2</sup> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down&nbsp;the associated <em>p</em>-value.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, with a reason, whether you would reject the null hypothesis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that this flight arrived on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two flights are chosen at random from those which were slightly delayed.</p>
<p>Find the probability that each of these flights travelled at least 5000 km.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}{{\text{e}}^{3x}}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mn>3</mn>
        <mi>x</mi>
      </mrow>
    </msup>
  </mrow>
</math></span>,&nbsp;&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
  <mi>x</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>.</p>
</div>

<div class="question">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> has a horizontal tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>Sila High School has 110 students. They each take exactly one language class from a choice of English, Spanish or Chinese. The following table shows the number of female and male students in the three different language classes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ<!-- χ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>&nbsp;test was carried out at the 5 % significance level to analyse the relationship between gender and student choice of language class.</p>
</div>

<div class="specification">
<p>Use your graphic display calculator to write down</p>
</div>

<div class="specification">
<p>The critical value at the 5 % significance level for this test is 5.99.</p>
</div>

<div class="specification">
<p>One student is chosen at random from this school.</p>
</div>

<div class="specification">
<p>Another student is chosen at random from this school.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis, H<sub>0&nbsp;</sub>, for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the expected frequency of female students who chose to take the Chinese class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether or not H<sub>0</sub> should be rejected. Justify your statement.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student does not take the Spanish class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that neither of the two students take the Spanish class.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of the two students is female.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img 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wicaB8OieULH8LkqpiATIB1Y5kEv3pKgI2yp8S4PBMYgwDrxmPA4UNuEWD5wi1MXIgJjE1AqRsvWLAArBuPzYuPuibAV8qu2fARJuAWAUrF9MorryAjI0PSjadOnerWeVyICTgjwEbZGRXexwTcIEC6cXl5Oa5fv87+xm7w4iLuEWCj7B4nLsUEhgiQbvzmm2/i1KlT2L17NzQazdAxfsMEJkqANeWJEuTzo4YA6cYUUpP8jSlbNOnGbJCjZvoDNlC+Ug4Yam4onAmwbhzOsxdefWejHF7zxb0NMAHWjQMMnJsDG2X+EjABJwRYN3YChXcFhABrygHBzI2ECwFZN16xYgUSEhJYNw6XiYugfvKVcgRNJg9lYgRINyYXt7lz50oP9OhhHm9MINAE2CgHmji3F3IESDd+++23Qa+7du3CwoULQ66P3KHoIcDyRfTMNY/UgQDpxlVVVVi/fr0UUpP8jtkgO0DijwEnwEY54Mi5wWATUOrG1BfyN6ZUTLwxgVAgwPJFKMwC9yFgBFg3DhhqbshLAmyUvQTHp4UXAdaNw2u+orm3LF9E8+xHwdhJqlDqxseOHWPdOArmPZyHyEY5nGeP+z4mAYpTkZ6eLpU5e/Ysp2IakxYfDBUCLF+EykxwP3xGoLu7W3JtI3/jo0ePSn7HPqucK2ICfibARtnPgLn6wBHgVEyBY80t+Y8Ayxf+Y8s1B5gAZfz4zne+I7VKbm5kpHljAuFGgI1yuM2YR/01Qf/efhQfuQKrR+e5KmyCvrEYS2NiEBOjRmbNH2DSN0K7VI0Y2pe5H41vrUWMuhitJt+06KonrvaTvzEZZFoiTXGPSVemh328MYFwIcBGOVxmypt+mjpRnbsXXRZvTh59jlX/Dl5afRpzGvpgEQY0bYjFOy9tRt2cKvRbBETTy1j1gxMQhhIsSwjeV+uBBx5ATk6OlC/vww8/lB72kX8yb0wgHAgE7z8nHOhwH50QuA/TpzyIEV+c6VMwecQOJ6cFYRfJGWVlZdLDPgo0tHHjRim+RRC6wk0yAfcJCN4ik8BAiyhUQQD2P1WRaBn4VLQUpghkFIq3ynOEio5J+y1CWAyis6Fc5AydoxIZhdWiRTcghLgtdNVrhuuS6xzxmiIKW/5sKyfXKZG9KwydtaIwQ2U7X5Ujypt1YjAI1JuamsSiRYvE66+/Lm7cuBGEHnCTTGB8AiF4feP+DwqXHINAwjKUXmlBoUoFTfVlWJSSQtsv0D61AHpxF4a255CWYEJX5UY88e4D2NR1F0IICMtvsTPuOJY/V40u8yTMzTsBi64aGqSgsOW6vcxlVGtUUBW2YEB0onTZDIcO3cPVxq1IST0KvNSKQWHBYOsy9OSuxpbGP/lI53ZocoyPlE+P9eYxAPGhkCDARjkkpiHAnVA9gdynv4F4TIJq7sOIN13EicpryM7NQppqkq0zsTORsSELmrYP8JHhnncdtH6Mpp81AoVa/GjVPMQjFvHzHkdu9n2o+VkLeoPwLJD1Zu+mks8KHAH2Uw4c69Btia6qDZ2AWY/Wxl/hFvX01gUcyC9DG9Ygy8ueW3t/g+PNQHKWGvFDdUzHstJOSVMZ2hWEN7LeTDExCgsLcfjwYRQUFPBCkyDMBTc5kgBfKY/kEaWfTLhSkw/15CQsP3DBZpSnrMRPO9+CBh9D12+OWC606o/iKK9Zs0aKq1xSUsL+zRE72+ExMDbK4TFPfu0lubptye/ASnJ1+2Up8latwqpV/wD1wH+gx68th07lrDeHzlxEe0/YKEf7NwBWmPt70YP5WLzgywpXty8weMs0ITqxiY8iSwP06AwYvta+A33NWsTErEWN/s6E6vf1yc705ubmZl83w/UxgTEJsFEeE0+YH4xXIyn5r2yD+NwMs9MHa7FISH0M2ap21B3+NYxSmXswdhxC8eaDME4EQewcrNQ+h6SyUuxtvSp5W1iNv8bhuovIKN+GtXPvn0jtfjtX1pspmNFPfvITPPXUU+zf7DfaXLEjATbKjkQi6bNkFLNxL38+4h7Mw4leF8uNE5bgh6dLkfZBLtRxtIQ6Bdt/NR25p06iUDURIJOgWlaE+s71sLy2CHExMYhTV8CyoR71W9MUD/8m0ob/zpX15hdffFHSm+mBIMfT8B9vrtlGIIZcmRkGE2ACYxOg+BlnzpzB6tWrceTIEenBIMkdvDEBXxPgK2VfE+X6IpIAGWAKdnTjxg309/dL8TRYb47IqQ76oPhKOehTwB0IRwLk30zxNK5fvy7F1yCpgzcm4AsCbJR9QZHriFoCFH3ulVdeQUZGBrZv3w56SMgbE5gIAZYvJkKPz416AosXL5biaVBwfYrfXFtby/Gbo/5bMTEAbJQnxo/PZgJgvZm/BL4kwPKFL2lyXUwAkHyaWW/mr4K3BNgoe0uOz2MC4xBgvXkcQHzYKQGWL5xi4Z1MYOIEWG+eOMNorIGNcjTOOo85YASc6c2UzJU3JuCKAMsXrsjwfibgBwJK/+Zdu3Zh4cKFfmiFqwxnAmyUw3n2uO9hS0CpN7/88suYNWtW2I6FO+5bAixf+JYn18YE3CKg1Jtp+XZVVRX7N7tFLvILsVEOgzmmqyoKiMNbZBGQ9eazZ89KA0tPTwfrzZE1x96MhuULb6gF6Byl/lhWVsb54wLEPVjN0Hy//fbbkp8z683BmoXgt8tGOfhzMKoHFLO3vr5eWrJL8RTo9pa36CFAd0a0+ISCHLHeHD3zLo+U5QuZRAi8kkRBt68rVqyQenPu3Dk2yCEwL4HuAunNx44dA8XTYL050PSD3x4b5eDPgdQDujp65pln8OGHH0qGefPmzVJMhRDpHncjwARYbw4w8BBqjuWLIE8G64hBnoAwaZ6/J2EyUT7oZgheKd+DsasO2qVqxMQkI3ffeXsyz7FGa4VZ34SK3GTExFCOuUxoj3Q4P8/UCq2aysh/wcmqTLoxuUGtX79euk09deoULyQYa4qj/Bjpy/Swt6CgAPQQkPIFUgYU3iKPQIgZZSvMXQexbtvHyKzvg7CcRe71PVhX2aFIUT96EqxXz+LQvwH/dPAjCHEXhgv/hGtFTzk57x6uvt+IOmWKZs0KLEkMXFZl1o1Hzx/vcZ8A683uswrbkpQ4NWQ2y2VRrXlUFLZcH+7SQIsoVK0R1brbw/tGvLsten/5gei3KHfeFrrqNQKqItEyoDgweEGUa3aO3Kc8zc/v29vbxZNPPikKCgrEJ5984ufWuPpIJ3Djxg1x4MABsWjRItHQ0BDpw/VgfBYxqDsryot+LnSKf/+RFdhthKZ6jDIjz5A+DepEc/lucdilPXJyjoe7QupK2dr7GxxvnomkWfHDP3IJ30Rm9lUcb++DdXiv4t39+FrGdzBzxEgm4aHZiVApSgFWmDpOobL5bbz2ejUaW/VjXn2POHWCH+g2k243yc2Jbj/pNpSX1U4QKp8upZ6iB8JHjx6VHhA/9dRToAfGvN1ER/WPUNB1x8coyIYcRm7BR7D4uGZldSNMmfJA4N/fQW/7WTSrEjH7oUkOzd9F8/HfoNe5VXYoO/zxr1amIinePkSrHu+UHoYRRrSV/QCrl2fgCW0j9GYPKx2uftx3JFWQbkxuTeTeRG5OdPvJGxPwJQGl3kw//HQBQA8GeQtPAiFklM3o130MJCdilmxIvWZ6E51NV/H8i8uGr6Bj5yGvyQBhMaDz1FsozADayjbjuTc7/XLFTP7GtGyWNlpGS4aZ3Jx4YwL+IqDUm+kBMl0Q0APl8Ng+Q6s2FTGZB9HaIT/oj0GMOhcV7znc1Zr1aK3RYqn8sH6pFjVDd75UzwosL+sCmvORFJcKbetn7iGwGtHVWIHcIUcANZZqa9CqN0G6027dgXnL98CIk8hPegBqbSvoCKB0TrA7GtS0en3BF0JG2T1u45eih4X1ODJjE55PmTK6eKwKKU9uRGnLb9FSlIy2ylPoMPnuarm7uxt0G0n+xnRbSbeXnOF49DTwHv8QcPRvpoVIdIEQNrFTml/Haw0PIv90v+2h/dE5+DfNVrzZdcsGzHwJNZtWY/25r6LUcNdWpvSrOLc+A09UkEPAdCwrPYuWwhRAUw2dpROly6a7AfsWuio34ol3H8CmLqpXQFh+i51xx7H8uWp0mYGEZbtxpaUIKqxBte42DKXLkIB7uNq4FSlPvI+HSrtgofMG/wVJ57YgY8spXPXCtISQUY7HrKQ5QE8v+iciKZg7cejE36Do+VQolOnRkxI7E8u2a1GIZjR1TvxqQtaNyV1J1o3ptpI3JhAMAnQhQBcEZJDpAoEWJoWF3qzagJ0/egpzpbvlSVCl/j3SVBfx3kfXYJWeC9Vjx3vpqCrZiDQVyZyToEp7AQeOboCuoAIn9F7qyKaLOFF5Ddm5WfZ6AcTORMaGLGjaPsBHhnvOp9HUjv2bG5G8uwhb0lSQDGr8AuQdeAPZZ0qwv83Nq3RF7SFklO9H4pIV0Cg6J721foa+7lvQZD2KxPF6a/0T3j30H1i583uY544EEq9GUnLSyAeLju2P85l143EA8eGgEqAHyvRgmS4WwlJvlv5HgR6dAWaQLNkMY/IjWCAZZBltLOJnJSIZH0PXb5Z3evaasAylhk6Upt1Ea2Oj9GPWWKPF8qR8NLusyQpT5/uoM6qxcPZ0m0GWy0r9NqCu6fd2iUM+MP7reGZu/Bp8WCI28VFkJZ8beeVqNkDX8wiylsweOWjHdq1X0frGGUz+H/992CCbL+FIzXnXUMwG9Kbk4+m53vkps27sOAn8OVQJUIYTWqBED5zDT2+2U5Uu0AxjIDagu+8zF15aY5wmHTLhSk0+1JOTsPzABUhiyZSV+GnnW9CMa+y7ULZ8hmJBWgxi4uYjv1m5IGK89oePh5RRRuxcrC15Gh2vHUSr8R5AhnZvJTq2bsPaIcNJGs5mqJfuQ5csc5ivoLEoD8u3voDl6vuG4UzWoB7TJBnDauzCu+92Da3ysxrPY9/rF/HYS0uQMMzDrXeybnzmzBnWjd0ixoVChQA9cKZAV7SFnd4cOx2zF6rHQOnkinWM0spDVv072JLfgZUNfbD8shR5q1Zh1ap/gHrgP9CjLOj0vU1jlnRo0pQVfzbd2elJLneGllFGLOJTNqG+dDqOpNyHmLg8NCW9ivqtaa71Yeuf0LhlDVaXObvJWKK4wr6JC//zCajjbE90K8//Fx7fuRXLRtwGueQkHaAn2eRu9IMf/EDSjQ8dOsQxjsdGxke9JWDW472KXKjJw2DpZmgphEBiBbq+8LbC4fPoYWBY6s2YitRMDVQ9F3GJLtqGNivM/b3owRwvpUj5/PlYvODLijvyLzB4y+ZfMdTUiDexSEh9DNmqyzh/6dORV+jmDlQsTURmzZWR+0ec7+KDh4tNorL4559/Lo4cOSIASCun6DNvTMBfBCyGZlGU8TWRUdggdIP/JQZaioQKEKrCFjHgh0Z/97vfDa001el0fmjBnSqvi5bClNGrcKVVvqrhsQ/2iOqcBUKVUyUuGO4KISxi8PJhkaNSiYzyC2JQakq5Wu+2GBz8LycdUJYRQkgrh1Uio6hZGKRVgHeF4UKVyFFBAClDq4wtumqhAa0w/k/xn4P/KSziruhv2CRUqhxRecEgpFMHL4uGQo1ARqXoHHS5pNBJn2y7QuxK2cUvRxB3Nzc3S/7G5F1x48YN9jcO4lxERdPWP+HUjq04PKcMR/eswtz4LyFhfiq+CxWSk9Su7xgnACes9GbybDjYgKPpf4ZWkirjMPmFPyD9aBtOb5PvqO9H4sqNKLq3A0lxc7D6RO/4V6sJS/DD06VI+yDXdjcdk4Ltv5qO3FMnUahYGhybmAlt0QDykx7Eg6v/Fb3WSZi5qgRtR9NxTZuCOLqzmbwG7854Dp31m5DijsOBw9xx6E4HIPJHWhFFUsWMGTMkqYLd22Qy/Oo/Ajaf10Wr/z/s1tUiz/4c5YuuCsxL7UCxYp+/+kDeRNXV1UNZb1auXMmLnvwF20W9fKXsAEbWjekJNfkbs27sAACen3QAACAASURBVIg/+o+A9WM0/awRKHxe4RF0Cx/9sg1/dBp+wPddCV+92fcsglUjG2U7ebpCqK2txbRp0yS3IXpCzXEqgvW1jNJ2JfdPKGQKWp36v7Ct4N+A76ZifkLg/l0d/Zs3btzI8TQC9LUM3CwHaEDeNMO6sTfU+Bz/EDCi5/wfYLTeg7HjMN5s+CMAFTRLJsPwO+P42qiPOyXrzSRj0N1jSUlJGMXT8DGMAFUX1UaZdGO6AvjJT34i+RsXFxdznIoAffG4GScEElLx/d15QM1qzJq1ET8fWILnX1qGr8KI5vrfYOChaQp3LSfn+3GX7N+ckJAg3U2GVTwNP3LxR9VR+aCPdOM333xTWuG0e/duaDSjFnf7gzXXyQQiggD9/+zduxdtbW3Yt28fy3w+ntWoMsqkG9MqvNWrV+PIkSNYs2YNP1n28ReKq4seAuyh5J+5jhr5giJkUXxjiphF/sY5OTlskP3zneJao4QAuYlSPA26uGG92XeTHvFGWdaNKUIWxTemiFkc39h3XyCuiQmQ/EfeSuSxQd5L3uvNJugbi+3B69XeLVEOkemw6muQGeNBgH1FvyPWKJPuRU+K6RecfsnpF50XgChmnt8yAR8SIP9muvuku1C6G6W7Uk/jN1NQoJdWn8YcCgokDGjKmxe0B5s+RONxVRFnlEk3pl9q+sWmX276BecHeR5/L/gEJuAVAboLpbtRuiulu1PP/Zvvw/QpD0alMZaBR5RRVurGn3zyCevG8izzKxMIMAHP9OY70NesRZwUUN4em1hdjFYpTZsJ+tYaaJeq7SF5M6Edkf/OnttvqRaH5Kh6Q+cOD9qpnGBqhVYdo8i1R+Vt9Q3l3xszHyAAqQ7K5bcfFRTJL8ZW38Bw0/Z39njN6lzs6xjH39xlqKIwOkCRrQoKCqRIVxTxijcmwARCh4AyyuJY/5+2CGzDEdmEGBCXq/NGRGCzGNpFZc4CRQQ2e3Q5LBA51T1iUNwVBl2fPVqcgoFjtDlhGYq+B0210MnB3KRocfY+jIpIJ0eOU0Skk8pDQJUnqi8PCGH5VOh6B8TIscjjsJdRdMvZWwrIHLbbjRs3xIEDB8SiRYukkJphOxDuOBOIAgL0/zpW2NuRhkwOp7lA5DX02UJiyozsYTY11ZeFRbgI+SmXHXp1CNUpbJ9V63LEOhWF4rwthQGVwqSqikTLgD1kqmqTaOinEKHyJhtz+zl2o+wYVnV4LL32Hxb3DDK1EpbyhawbU+YE2kg3phVHvDEBJhC6BEhvpgeC7m1y/jvHwPMARuTtc682wJ4DtPks2nvvANY+tB+/iuwN38fy5Kv23H62HIDIfgypCbd8kA/wLq417cML+WeQvLsAG+a5l+Mo7Iwy6caUmZee8NIDPcqg4P5EuzuBXI4JMIHgEriHa329GCvLnbG7D9es7vdSygGquYjj7X2wUvCnP6Yj89tpWJI105bgVMoBeB+yM7+JBJ/kA7yE2rJ/xyOFS9Gzowqnriqzpbju95dcHwqtI+Rv/Pbbb0uRqigzLwVK4Y0JMIFIJTAJD81OhAq9LgeoWjgbD8UC/S5LOByInY0lWY9gh+4TXO38Jeq+loj8+PuldnC8DwZ9H473pEObOhXk/iHlA+x2qGPoo5wPcKxErikobPk5SjM+w991L8PmV5fh24dWYeY4l8LjHB7qQdDekL9xVVWV5G9MmXjJ35gNctCmgxtmAgEiMFb+O8pwrwxx6m6XbIYedT/BjupmJGc9isRYezs9ddizpw49knRBZtGH+QClhNAFSKopwf62z8btbMgaZdaNx507LsAEIpuAFDUvDWc2v4o3ZDcy8yXUvLQFZUkFKFk710N/ZrsBxinU1gMLZ0+3nS9p1DrU1g7apAuJaiwS0tZh93fPYXPxIXRIiVqtMF+pw0vrDyOpfBvW2jPDjD8JlBD6+6gofwhlr9Whyzy25hKSRrm7u3tINyYndNaNx592LsEEIo9AAubl7XPIf/fP0KW/Ad3pLV7lv0PCN5GZnQKoNMgkmYI2SdZYAjhmw3YrH6C71KfgW8/kIU9Xjm1vdsI8xmkhFSWOkpPu379f0o0pFRNn/hhj5vgQE2ACEUkgJK6USaog3Zjc2kg3PnbsGBvkiPy68aCYABMYj0DQjTK5tVHwEtrOnj0rGWZ2cRtv2vg4E2ACkUogaC5xpBuTaxutkSfdmCO4RepXjMfFBJiAJwQCbpRZN/ZkergsE2AC0UYgYPIF68bR9tXi8TIBJuANgYAYZVk3NplMrBt7M0t8DhNgAlFDwK/yhTKxIuvGUfOd4oEyASYwAQJ+McqcgnwCM8KnMgEmENUEfCpfkG5cW1srpWIif2MKqckLQKL6+8WDZwJMwEMCPjPKzc3Nkr8xeVdQ8kRaCML+xh7OBhdnAkwg6glMWL5g3Tjqv0MMgAkwAR8S8Noos27sw1ngqpgAE2ACdgIeyxesG/N3hwkwASbgPwIeGWVZN7506RLrxv6bE66ZCTCBKCbglnxBunF5eTmuX7/OcSqi+MvCQ2cCTMD/BMY0yqQbv/nmm1IKpt27d0Oj0fi/R9wCE2ACTCCKCTiVL0g3pqXR06ZNw6xZsyR/YzbIUfwt4aEzASYQMAKjrpTPnz+PV155BRkZGZJuPHWqPWVKwLrEDTEBJsAEopfAkFFm3Th6vwQ8cibABEKHgCRfUMD5pKQkqVeUiokDzofOBHFPmAATiC4CklFeuHChJFX8zd/8jbRUmlzfeGMCTIAJMIHAExiVzVpeNk1dKSsr46vmwM8Jt8gEmEAUExhllGUWygd+27dvBz/wk8nwKxNgAkzAfwScusRRcxRyk0JvUghOco2jkJzkKscbE2ACTIAJ+I+AS6NMTVLoTQrBSaE4KSRneno6WG/232RwzUyACTABl/KFMzRKtznWm50R4n1MgAkwgYkRGPNK2bFqcpU7dOgQCgoKsH79ehQWFoKWYvPGBJgAE5gYgTvQ16xFTGYN9FYPajLr8V7F6ziiv+PBSS6Kmq+gUZuJmJgYxMSsRY0v6nTR1Fi7PTLKckWsN8sk+JUJMIHgEbDC1HEYuQUfwTLhTtyB/sSrWF33dTT034UQJ5A39/4J1+pNBV4ZZWqI9WZvcPM5TIAJhDaBBEyZPLTQOShd9dooy70lV7ni4mIppOfJkyfx1FNPgbRn3pgAE2ACEyJgNaKrsQK5apIT6E+NpdoatOpNAKwwte7AvOV7YMRJ5Cc9ALW2FXQEuAdjVx20S9X28zKhrWmF3uxCF7FeQU3mHCTlnwSMe7D8r+OG6zLr0VqjxVKp/RjELNWiplUPszwwUyu0aurXflTkJkvtDfdDLuThq/Dx1t7eLhYtWiQKCgrEjRs3fFw7V8cEmEBkErgtdNVrBDTVQmehEf5FdJY/LlQ5VeKC4a5tyJZ+0VKkEcioFJ2DVMgiBlqKhAprRLXuth3LXdHfsEmoVDmi8oJBSFUN9ojqnAVCldcg+qUdzgja21cViZYBeyH5vKE+3BWGC1UiR6USGeUXxCBVM9AiClUQUOWJ6ssDQlg+FbreAWcNuL1vwlfKjr8BjnpzVVUV+zc7QuLPTIAJjE3AdBEnKq8hOzcLaapJtrKxM5GxIQuatg/wkeGe8/NN7di/uRHJu4uwJU0FycDFL0DegTeQfaYE+9s+c37eqL2kV9djx3vpqCrZaO/DJKjSXsCBoxugK6jACcWDQFX29/D0vAQg9m8x92sJo2rzZIfPjTI1rtSbTSaT5N9M8Zl5YwJMgAm4RSBhGUoNnShNu4nWxkYpvntjjRbLk/LhOjKPFabO91FnVGPh7Ok2gyw3Fq9GUrIBdU2/t0sc8gFXrzfR2dQMY/IjWCD/KEhFYxE/KxHJ+Bi6/iERw1UlXu33i1GWe6LUm8+cOSPpzRSRjjcmwASYwNgETLhSkw/15CQsP3ABt6jwlJX4aedb0IxrELtQtnyGXU+269Fx85HfbBy7SeVR62fo6zYo9zi8N6C77zO4UKkdynr2MSCPGWX/ZoqnsWvXLinI0csvvyxlNfGsu1yaCTCBaCBg1b+DLfkdWNnQh0OrHrZf9dLDvWb0AFg4JoQ1qNbVTsylLXY6Zi9UAy6vIeWr8bEM95iddHnQr1fKjq2S3kzxmimeBi3fZr3ZkRB/ZgJMgDwrzP296MF8LF7wZYUM8QUGb9n8K5xTikVC6mPIVl3G+UufjryKNXegYmkiMmuujNzvvCIAU5GaqYGq5yIuGZX6tdy3OUiaFe/y7IkcCKhRpo7KevPZs2elflM8DdabJzKFfC4TCA8CFD/HvRXAsnFtR93hX8MoaQT3YOw4hOLNBzEsQsj6Lo3fis/Nn8OasAQvV6XjzOZX8UaH0WaAaaXeaztRgE0oWTtXYeTH4haLhLR12P3dc9hcfAgdkmG2wnylDi+tP4yk8m1Y66fFJQE3yjIG0ps3b94s+Td/+OGHrDfLYPiVCUQYAYouSXfFdHf85z//2b3RJSzBD0+XIu2DXKjjSBdOwfZfTUfuqZMoVA1XEZuYCW3RAPKTHsSDq/8VvdZJmLmqBG1H03FNm4I48i+evAbvzngOnfWbkBLvgckjr42DDTia/mdo1fchJiYOk1/4A9KPtuH0tjT45zoZ8Cgg0TAK378jvbm8vJz1Zt+j5RqZQNAI0F3w3r17kZOTg3Xr1nFcdjdmImSMMvWVflHJS0OexPz8fEnucGMcXIQJMIEQIkBeVvJD/WeffZYzGHkwNyFllOV+k+5UX18vBdanrCd028MbE2ACoU+AdOP9+/dLoRYomiQ93OfNMwIhaZTlIVAMjbfffluaYPrVpQSvvDEBJhB6BOgut7q6euhCauXKlXyX6+U0eaB6e9nCBE4j/2YKpk+/uGSUKX4z/RLzxgTCjgAF1zliD2yjzsU+2TNgvIFQQJzGelTkZkLb6mqJ8Gdo1aYqFkuoPXD9Gq8D4x8n3Zi8qGgjryq6syUvK968IxDSRlkeEvs3yyT4NTwJ3EJX5YvYpnsM9RYBS9d6XNe+iMouaZ2a6yFR9LL/sQNHGvagoPaGy3LWq7/Cz+u6FMeXIGvJbDddvxSnefiWdGOKCkneU0ePHpW8qTjBsocQnRV3O3RRiBSkyHMHDhyQItE1NDSIzz//PER6xt1gAs4JWHTVQqOMPiZHNxuKiOb8PHmvdD5SRGHLdXmX4pWiqeW4OKYo5sO3n3zyiRQF8sknnxQUFZI33xIIiytl5Y+Jo3/zM888A3Kn440JhCaBO+htP4vm5ETMGvKRtS+O6DmL9t4JpjGSoqnVouy1ctQ0trmOGewDOEp/Y1qVS6tz+UGeD8A6VBF2Rlnuv1JvJv9m0ps5uL5Mh19DhoC1D+3H26FaOBsPjfpva8fx9j43l/06G9Ed6N95E2W0xK2tDPmrlyLpiR1olILAOyvv3T4yxpGlG9vzAaqL0WryR0gh7zjLZ436msgHwuVVqTdTMldaOeTeUs5wGSH3M6wJmA3Q9QDJSWo/rAC7H3PzTkCIuzB0nkZ1oQZo24PVz1Wjy1WWDQ9h0l0o3Y2ybuwhuAkUD3ujTGOX42mcO3dOQrFixQrpl51+4XljApFPYBJUKf+IvNLTMLTsQkbbz3GiY2JZ5umuk+4+6S6UvJ/IC4ruTnnzP4GIMMoyJjLOFE+DbrXol531ZpkMvwaNgBRcHejRGYbzuvmtM5OgWrYJOwvhQTD3kZ2hu0y626S7zsDpxs7kBArTWQx1TOpIV0ApJ55in1c59N63xWdWDt18CTW5yVDnHrQHH1IeDOz7iDLKMrpZs2ZJv+zk28x6s0yFX4NCIHY2lmQtGdW09Vofuo3+cF2Lx6ykJI/lElk3prtM2uiuM3D+xvcjcckKaIzNaOqUr/DtmT+gDCZvzywCDTJTpwJkSDetxvpzX0Wp4a5Nxin9Ks6tz8ATFR2KH0Ej2uo+wtSi8xCWT9H2gzRMUc6IVM8z2IFtaD34wnD6KWWZAL6PSKMs86MVgKdOnZJ+8Vlvlqnwa2AJ2AxOct376Bx6qGSPyatZgSWJ9/u4O2b09yZD+7S7ISoheS/JujHdZdLdZqAXf8QmPoosza3hbB5S5g9gXc630XP8N+iVnsfZDDWyH0NqAnyTQ2+wBzWbZIOcjXlDHjI+nhYPqotooyxzoF981ptlGvwaaAKxc1ehZOtlvLa3RYoNbDW2YO9rl7G1ZBXm2v8DrVcbka/+R1SMt6BE2XlaJfjuL9AlB2G3GtGxrxJtj2UjI2H8f22lbkx3laQb011mUDbpjuIRNNsNsLX3Nzjeo8GGTf8NyT296KcHl6bfo6kOyM78JhLgixx6f0JTZSHya+dj94+yQsIgE/vxZy4oM+T7Rllv9j1TrtFdAlOQsvUnKJ1xFClxMYhb9z6SKn6CrSkjbqKdVGZbPh0nJQu1553LrIF+yIvLioELbyBVivWbjNzKX8H8+Hb8eNnMMf+xHXVjupsMflwZu4TRTL7bn0uZR/6Y/Ri+nfr3yEo+J8kakuQjSxe+yKFnrEfZxa+jMOcydpT+AleHuDqZikDu8u1alPCp7Xe/+52gFUkFBQVCp9OFT8e5p0zASwK0+pVWwS5atEhaFRtyq2Etl0W15lFR2PL/ipbCR4Wm+rKwiOv29xfF5eo1QlXYIgak8dP+FAEnqyJHrIAcaBGFKijOo5NvC131GgH7Kktb+QUir6FPWLxk68vTouZK2fGHjvVmRyL8OZIJKP2Ng6Ubj8tXSlZ6F3XVpaium2mP30G58tLRU1eBPXVX7dIF1eS7HHqSvFT+MGo2/wxtQ7r/uL31W4GoNcoyUdabZRL8GokEQko3HhewzdCivhb1SMTshyZJCmv8rEQkt9WjVpdu87qQ6vFlDr0pSHn+VZQnncBrb3UqvDbG7bBfCkS9USaqjnozhSHkeBp++b5xpQEiEJq68XiDlxOmAirJw8JmnmyeGSpgRPwQAL7MoRe/EM+8tAK6gh/jTU8eto43JC+Oh3SQey/G45NT5FQ2M2bMkFYz8Uomn2DlSgJAgPyNOaVaAED7sQk2ymPAJe2N8gVSzNjnn3+ekz6OwYoPBZ8A3d1x8uHgz8NEe8BGeRyCdOVx8uRJ5ObmoqGhAZzmZhxgfDjgBEg3JmN8/fp1KUNP8N3bAo4gohpkTXmc6SS9mdKj37hxQ4qnwXrzOMD4cMAIkG5cUlIixamgi4XQ8DcO2PAjtiG+UvZwauWn2aw3ewiOi/uMgKwbr169GgcOHEB+fn7Al0X7bDBc0SgCIXilfA/Grjpol6oRE5OM3H3npaWpo3o+Yodj4siY4SSSI1ZAAZCiTCmOx6xFjd797A/00I+uSNasWSNdodCVCl2x8MYEAkGAdGO6W6MoiHT3Fow4FYEYZzS3EWJG2Qpz10Gs2/YxMuv7ICxnkXt9D9ZVKiM+OZkuaU28MnGkXEYFTdajSBwa5T1cfb8RdZSpQd68DAqj0WikeBoUK2DatGkcv1nmya9+IUB3aBs3bpS0Y0pSSnEqOEmpX1AHvdIhcxX0nlAHrHqcKH4HaTs3YZlqEhA7E8u2b0VaZQVOuLyapXB+l3Df0X5YhIAY+ruOlsJ/GpnV19yNYz+biqMDluFyTXlDQWE8ZcB6s6fEuLynBJS6Md2d0V0au2h6SjG8yoeUUZYiQzXPRNKs+GGKCd9EZvbVMXKZfYH/nPUkCh2CsFj1/zdKu9MUoRGtMHWcQmXz23jt9Wo0tup9tnKHrljoyoWuYOgpOF3R0JUNb0zAWwJyfGO6C6O7MYpySHdnvEU+gRAyyvasvyp5eaUS/t2hkH7Kvbb3k6Ca+7BD/jOq6zxmPbd8WLqw6vFO6WEYYURb2Q+wenkGntA2+jT7L+vNo2eH93hOwFE3Ju8fuivjLToIhJBRNqNf9/HopZTezANlEG6cie899pXhEIax85DXZICwGNB56i0UZlAC4M147k3fr3VnvdmbSeNzWDfm7wARCCGj7LsJIRmk8e8ykOos0HesCilPbkRpy2/RUpSMtspT6PBDZCjWm303n5FeE+vGkT7Dno0vhIwy5RabA8hZBjwbh6I0SRcd+DspO4Fit+Nb6SGiFoVQ5gVzLDTxz456My3ZZr154lwjoQbWjSNhFn0/hhAyyvbMA45jlDIM3HJwbXMspPgsSRd/qwjxpzjm+FbKNJw08sGiYxkffZb15hdffFHyb6b07ezf7CO4YVgN68ZhOGkB6nIIGWVACtFnT/0yNH6zAbqeR0a6tg0dHP1mTOnCsbjZgN6UfDw919fJKx0bGv4s680LFiyQ/Jtra2tBV0y8RQcBukuiuyXy0mF/4+iYc09HGVJGGbFzsbbkaXS8dhCtlAzSehWteyvRsXUb1g4Zznu42rgZ6qX70EXJFEdsrqULq7EL777bNbQ60Go8j32vX8RjLy1Bwog6/P9BqTf39/dLK7Sam5v93zC3EDQCdFdEd0eUVZ3ultjfOGhTEfINh5ZRRiziUzahvnQ6jqTch5i4PDQlvYr6rWkOLm8uuJJ0cf4bWJs21UmBm7jwP5+AOi4GMepcVJ7/Lzy+c6ttkYqT0oHYRXpzcXGxdMVEkeh8qzdbYWothjpmLQ61tuGINtO+9DwZuRVNDq6AJuhba+xL22kJeia0Na0OZQJBJPLaoLsguhsif2O6O2J/48ibY5+PyJcJ/7iuiRFob2+XklpSMtcbN25MrDJhEQMtRUIFCGQUiQadLd2kxdAsijK+JjLKL4hBqYUBcbk6T6hUOaLygkFKHGkxtIvKnAUCGZWiczAUUklOEEWQTm9qapLm8/XXX/fBfAZpENxswAnQcmPeQoiAnHEYgDhy5IjwPuOwbJRTRGHLdcUIHbIAS9l+nWTylfar7BmFFafz23EJUHZ0ypT+7LPPcqb0cWlxAUcCISZf+PxGIOwqJL2ZkrlSBDD/6M1K18MvYOp8H3XG+Vi84MsjndYlzxSgR2fw2XL0sJsMDzus1I0LCgpw6NAhjlPhIUMuHqGLRyJhYh31Zv/4Nt/Dtb5eKIPmObIzdvfhmuPzVMdCUf5ZqRt/5zvfkXTjxYsXRzkVHr63BPhK2VtyATqP/Jv9d8U1CQ/NToRqjLGoFs7GQ/wtcUmIvGYovjHd1dDdDd3lcJwKl7j4gBsEvuRGGS4SsQTklO6ncf7Sp9gw9+FhCUPyDweSs9Tueb5ELCPnA6M7F3Jxoww05G/M4TSdc+K9nhNgo+w5s8g6IyEV39+dhmWbX8Ubs/ZiS5oKseZLqHlpC8qSCtC5du6woY6skXs1GtKNKcN5W1sb9u3bB5YpvMLIJ41BgG9Mx4ATHYcSMC9vH9qOpuOaNgVxMTGImfzP0KW/Ad3pLUiJ568IfQ9YN46O/4ZQGCUnTg2FWeA+hDQB0o137NghLe55/vnnOQ1TSM9W+HeO5Yvwn0MegZ8IdHd3Y9euXawb+4kvV+ucABtl51x4bxQTIE+K/fv3s24cxd+BYA6dBcNg0ue2Q4oA6cZVVVX4yle+AvY3DqmpiarOsFGOqunmwboi0NjYKPkb03H2N3ZFifcHggDLF4GgzG2ELAFZNyY/Y/Y3DtlpiqqOsVGOqunmwcoEZN2YFoFQnAr2N5bJ8GuwCbB8EewZ4PYDSkDWjWk5NOnGx44dY4Mc0BngxsYjwEZ5PEJhfdwE/Xv7UXzkCnwTU8gEfWMxltICkxg1Mmv+AJO+cTg4fuZ+NL61FjHqYrT6IUP4RKdCqRufPXuW41RMFCif7xcCLF/4BWuIVGrqRHXuXnTv1vikQ1b9O3hp9WnMaehDy6qHEWu9gpqVm1E3pwr9LaswU/qJfxniBz5pzmeVsG7sM5RcUQAIsFEOAOTIauI+TJ/y4Mh4GNOnYHII3nOxbhxZ37yoGY1j1Hv+HCEEpMwhEJTBRPpTFYmWgU9FS2GKQEaheKs8x5YqStpvEcJiEJ0N5SJHJZ+jEhmF1aJFSiN1W+iq1wzXJdc54pUynPzZVk6uU0J5Vxg6a0VhhsrejxxR3qyzp6LyD2vK1nLgwAEpFVNDQ8MEsrf4p39cKxMYi0AIXt9Eze+hfweasAylV1pQqFJBU30ZFkMJliXYp7vtF2ifWgC9uAtD23NISzChq3Ijnnj3AWzqukspwiAsv8XOuONY/lw1usyTMDfvBCy6amiQgsKW6/Yyl1GtUUFV2IIB0YnSZTMcxkSZx7ciJfUo8FIrBoUFg63L0JO7Glsa/+QjnXtkk6wbj+TBn8KPABvl8JuzifdY9QRyn/4G4jEJqrkPI950EScqryE7Nwtpqkm2+mNnImNDFjRtH+Ajwz3v2rR+jKafNQKFWvxo1TzEU7byeY8jN/s+1PysBb2+efo41DfyrPjwww+lz9/61rc4cNAQGX4TTgRYUw6n2fJXX+mq2tAJmPVobfwVblE7ty7gQH4Z2rAGWV62a+39DY43OwbKn45lpZ2SRuJltS5Po4wfZWVlkAPQHz58WPJB5gD0LpHxgRAkwFfKITgpge+SCVdq8qGenITlBy7YjPKUlfhp51vQ4GPo+s2B79IEWiQjfOrUKaxZswbr169HSUkJKDg9b0wgHAiwUQ6HWfJzH8nVbUt+B1Y29MHyy1LkrVqFVav+AeqB/0CPn9v2Z/UajUZKYjpr1ixMmzYNpDeTxMEbEwhlAmyUQ3l2AtI3K8z9vejBfCxe8GWFq9sXGLxlmlAPYhMfRZYG6NEZMHytfQf6mrWIiVmLGv2dCdXvzskkaeTk5EhBhkhvpiSn58+fd+dULsMEgkKAjXJQsAeo0Xg1kpL/ytbY52aYnT5Yk5OntqPu8K9hlMrcg7HjEIo3H4RxIl2NnYOV2ueQVFaKva1XJW8Lq/HXOFx3ERnl27B27v0Tqd2jc6dOnSrpzRR0qLy8HBs3bpS0Z48q4cJMIAAE2CgHAHLQmpCMYjbu5c9H3IN5ONHr4tY9YQl+eLoUaR/kQh1HtvhjOAAADoFJREFUS6hTsP1X05F76iQKVRPp/SSolhWhvnM9LK8tkvL/xakrYNlQj/qtaUHJks1680Tmk88NBAHO0RcIytxGSBIgffnkyZPIzc3FkSNHpAeDJHfwxgSCSYCvlINJn9sOKgGl3nzp0iVJb6YkqbwxgWAS4CvlYNLntkOKgOzfTJ0if2f2bw6p6YmazrBRjpqp5oG6S4C8M1555RVkZGRg+/btvDLQXXBczicEWL7wCUauJJIIUBaSc+fOSUHwyb+5traW/ZsjaYJDfCxslEN8grh7wSFAejNlJ6EkqhQClPybWW8OzlxEW6ssX0TbjPN4vSJAejP5N1+/fp31Zq8I8knuEmCj7C4pLscEAGk1IOvN/FXwJwGWL/xJl+uOOAKsN0fclIbcgNgoh9yUcIdCnQDrzaE+Q+HdP5Yvwnv+uPchQID15hCYhAjqAhvlCJpMHkpwCbB/c3D5R0rrLF9EykzyOIJOwFFvrqqqYv/moM9K+HWAjXL4zRn3OIQJKPVmk8kk+TdTcH3emIC7BFi+cJcUl2MCXhBQ6s27du3CwoULvaiFT4kmAmyUo2m2eaxBI0B6My0+oSBHL7/8MihFFW9MwBkBli+cUeF9TMDHBEhvPnbsmBRPg5Zvs97sY8ARVB0b5QiaTB5KaBOQ9eazZ89KHaV4Gqw3h/acBaN3LF8Egzq3yQQAKUfg22+/Lb2y3sxfCZkAG2WZBL8ygSARYL05SOBDtFmWL0J0Yrhb0UOA9ebomWt3RspG2R1KXIYJ+JkA681+BhxG1bN8EUaTxV2NHgLk38x6c/TMt3KkbJSVNPg9EwgxAqw3h9iEBKA7LF8EADI3wQS8JcB6s7fkwvc8NsrhO3fc8ygh4Epvvn37dpQQiK5hsnwRXfPNo40AAkq9uaCgAHQ1zVvkEGCjHDlzySOJMgJKvfnZZ5+V4mpEGYKIHC4b5YicVh5UtBAgCePMmTPYu3cvcnJysG7dOkydOjVahh+R42RNOSKnlQcVLQRkvfncuXPSkFesWCHF02C9OXy/AWyUw3fuuOcRSeALGBufR0xMjO0vtxFGN8ZJxnnz5s2SQf7www/xzDPPgOQN3sKPAMsX4Tdn3ONoIGBqhXbeenTvbsWZvHnw9Oqpu7sbFOSI4jez3hxeXxhP5zq8Rse9ZQJhScAKU+f7qDMuQdaS2R4bZBoyZTg5deqUFL95/fr1UvzmmzdvhiWNaOs0G+Vom3EebxgQuInOpmYYv5aG/2PO/RPqLwXUZ715QggDfjIb5YAj5waZwDgEvvgTLjZ0QbX6EXz9S+OUdeMw681uQAqhImyUQ2gyuCtMgAhYP/4I7/0xBc8kDeJ/azPtD/0yoW28AvMEEFFewLKyMklrpnyBhYWFUoD9CVQZoqdaYdY3oaK4Hnqrqy7egb5mLWIya8Yo4+Rcsx7vVbyOI/o7Tg76ZhcbZd9w5FqYgI8IfIFPL3WgGV04dq4f8394GmKwB9U5BpStfhUnfGAMIl9vvomO6h+hoMvXhtMKU8dh5BZ8BIuPZttZNWyUnVHhfUwgaARu4fKFTiCjEqcPvoA01SQgfh5WPklLqa/j5uAXPusZ680+Q+nTitgo+xQnV8YEJkjA9Hs01RmgyV6Jb8XL/55fYPAWeU4kYY56Yg/+HHvnqDdTMtfg+Dd/hlZtKmIyD6K1ow7apWqbbKPORcV7+pGyjVmP1hotlsq+3Eu1qGmVy1A9K7C8rAtozkdSXCq0rZ85Dtv5Z6sRXY0VyFXbfcRj1FiqrUGr3kSiEkytOzBv+R4YcRL5SQ9ArW0FHQHuwdil6HNMJrQ1rdCbXWonztuX9wremAATCBkCFl210CBFFLZcH+6T5bKo1qiEKq9B9FuGd/vj3e9+9zvx5JNPimeffVbodDp/NOGizuuipTBFACqRUdggdIM00LvC0LJLZOBxUd75F9t5gz2iOmeBUOVUiQuGu7YyF6pEjkolMsoviEGplL0uTbXQueR1W+iq1wgMlfmL6Cx/XFGvEMLSL1qKNAIZlaJT6o9FDLQUCRXWiGrdbfs47or+hk1CpcoRlRcMQmpO7qOX8yX/FMs2ml+ZABMIGoE76G0/i2aVBpmpcvyKe7h6qgo7elZid8FjmOnn/1hZb165ciXIv7mkpAQB9W9WbcDOHz2FudJdwiSoUv8eaaqLeO+ja7DS1WpHPXa8l46qko02aQeToEp7AQeOboCuoMJ7zd10EScqryE7N8teL4DYmcjYkAVN2wf4yHDP+bfC1I79mxuRvLsIW9JUNp/y+AXIO/AGss+UYH+bm1fpitr9PMWKlvgtE2AC4xC4jkvnLkKV/RhSE2IBup0+shPrV/87Nhz9MTbMSxjnfN8dlvVm8tiYNm1a8OJpxKuRlAz06Awww+6/nfwIFpDWPrTFIn5WIpLxMXT9XvqnJCxDqaETpWk30drYKI23sUaL5Un5aB5qx/GNvMhHjYWzp49c5CP124C6pt/bJQ7Hc11/ZqPsmg0fYQIBJvBl/J8vl2HrtS34a9JL41Kw7Q9J2Kk7iZJlM0f+0wegZ6Q3U+S5GzdugOJpBE9vtg/W+hn6ug1jjNyA7r7P4J2Sa8KVmnyoJydh+YELuEWtTFmJn3a+Bc24xr4LZctnDMcrkeZuPvKb3YlaMno4PnBNH10p72ECTMAbApOgSlmFbUfoz5vz/XMOhQIl/2YKrk++zYcPHwYF16e4GgHdYqdj9kI10O2qVSdXrK6KOuy36t/BlvwOrGzow6FVD9t/AOnhXjN6aNm6Q/mRH9egWleLvLm+eQjLV8oj6fInJsAEXBAgI0zxNNasWRMcvRlTkZqpgarnIi4ZlRqvFeb+XvRgDpJmxbvo/Vi75fPnY/GCLyvuSMjrxeZf4fzsWCSkPoZs1WWcv/TpyCt0cwcqliYis+bKyP3OKxqxl43yCBz8gQkwgfEIaDQaKZ5G4PXmWCSkrcPu757D5uJD6JAMsxXmK3V4af1hJJVvw1rpajUes5Lm2IdxB2bzeL7dsnFtR93hX8Mo6R/3YOw4hOLNBxWhU2Xtmqq24nPz57AmLMHLVek4s/lVvNFhtBlg8xU0vrYTBdiEkrVzFUZ+PLK242yU3ePEpZgAE1AQCJreTJ4NBxtwNP3P0KrvQ0xMHCa/8AekH23D6W1psF0n34/ElRtRdG8HkuLmYPWJ3vGvVhOW4IenS5H2QS7UceSnnILtv5qO3FMnUagaHnhsYia0RQPIT3oQD67+V/RaJ2HmqhK0HU3HNW0K4khPnrwG7854Dp31m5Ay5Gs+XMd47zie8niE+DgTYALjEpD15hkzZgRHbx63h+FTgI1y+MwV95QJhDyB5uZm7NixA0899RSef/55zhfoxYyxfOEFND6FCTAB5wSCpzc770847mWjHI6zxn1mAiFMwJneTFfQvLlHgOUL9zhxKSbABLwkIOvNdHpVVRXIa4M31wTYKLtmw0eYABPwIQG6Wp49e3bgF534cAyBqIqNciAocxtMgAkwATcJsKbsJiguxgSYABMIBAE2yoGgzG0wASbgBgET9I3F9uD1aq+WKLvRSECKWPU1yIzxIMC+olcckEgBg98yASYQPAIUFOil1acxp6EPLUNBgYLXn2C1zFfKwSLP7TIBJuCEwH2YPuVBj+NFOKkobHexUQ7bqeOOM4FIIXAH+pq1iJMCyttjE6uL0WqiyEAm6FtrhnP2jcp/Z8/tt1SLQxW5UFPsiaFzh/k4lRNMrdCqYxS59qi8rb6h/Htj5gOk7lEdlMtvPypyk6WYynTuwHDT9nf2eM3qXOyTAxeNKmPbwUbZBRjezQSYQKAI3I+5eSdg0VVDgxQUtlyHMJRgWYIZV2peQcb6c3iotAsWIWAxvIqHzm1B0hNvoEuZmLTtF2ifWgC9uAtD23NIo8wtii028VFkaZSZQOSsIYCxuw/X5Mj4UuJaIDvzm0gwX0LNptVYf+6rKDXchaC6S7+Kc+sz8ERFhyKZqxFtdR9hatF5CMunaPtBKv5a0Tb9sNA4lu0AdrcewCty2qgRZYY/jOz58H5+xwSYABMILgFTJ/7Xjg6srPrxUP67WNVivHLgDRTqylF8Qj8c/U31BHKf/gbiKWff3Ift0eIU3Y+djSVZSxQG+B6u9fUC63Kwrucs2nvv2DJWd76POlCOxCke5QNUZX8PT1O6rti/xdyvKdN2DSgM8j7kuZHSi42yYt74LRNgAqFCQL6SdQw8D2BE3j53+3s/EpesgKbZboCtfWg/fhXZG76P5clX7bn9bDkAIeVIvIXOpmYYJ5QP8C6uNe3DC/lnkLy7wO0ci2yU3Z1TLscEmEAACdiuZMfKcjdCdnCjZzYJ4yKOt/fBajZA98d0ZH47DUuyZtoSnEo5AO+zSRc+yQd4CbVl/45HCpeiZ0cVTl1VZktx3WE2yq7Z8BEmwASCRmASHpqdCEV8+VE9US2cjYc8sWCShPEIenSf4CrJFF9LxKz4+6V20N0Hg/43ON6TjszUqYCcD3BUq/IOd/IBkj7+c/zLnp3YndyIza/+P7gqa9dyNU5ePRmSk9N5FxNgAkzAHwTkFE3O8t8ZoOsBkpPUo7XjMbtiM/So+wl2VDcjOetRJMba2+mpw549deiRpAsyiz7MBxg7F2tLCpBUU4L9bZ+N2UM6yEZ5XERcgAkwgaAQSEjF93enOeS/u4Sal7agLKnAi/x3dgOMU6itBxbOnm4zgJJGrUNt7aBNupAG624+QHfIxCI+5fuoKH8IZa/VjfQacXI6G2UnUHgXE2ACoUAgAfPy9jnkv/tn6NLfgO70Fq/y3yHhm8jMTgFU5GEx1TZIu2cGHLNhu5UP0F1OU/CtZ/KQpyvHtjc7Fe50o8/nKHGjmfAeJsAEmEDQCPCVctDQc8NMgAkwgdEE2CiPZsJ7mAATYAJBI8BGOWjouWEmwASYwGgCbJRHM+E9TIAJMIGgEfj/AaCFLkGKIoPAAAAAAElFTkSuQmCC"></p>
</div>

<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>There are 54 employees in the company.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee&nbsp;encountered traffic and was late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee&nbsp;was late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee&nbsp;encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {\left( {C \cup B} \right) \cap P'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>∩</mo> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{27}}{{{x^2}}} - 16x,\,\,\,x \ne 0">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>27</mn>
    </mrow>
    <mrow>
      <mrow>
        <msup>
          <mi>x</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
  <mo>−<!-- − --></mo>
  <mn>16</mn>
  <mi>x</mi>
  <mo>,</mo>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mi>x</mi>
  <mo>≠<!-- ≠ --></mo>
  <mn>0</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <em>y</em> = <em>f </em>(<em>x</em>), for −4 ≤ <em>x</em> ≤ 3 and −50 ≤ <em>y</em> ≤ 100.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the tangent to the graph of <em>y</em> = <em>f </em>(<em>x</em>) at the point (–2, 38.75).</p>
<p>Give your answer in the form <em>y</em> = <em>mx</em> + <em>c</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of the function <em>g </em>(<em>x</em>) = 10<em>x</em> + 40 on the same axes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the curve <em>y</em> = 2<em>x</em><sup>3</sup>&nbsp;− 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2, for&nbsp;−1 &lt; <em>x</em> &lt; 3</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the curve for −1 &lt; <em>x</em> &lt; 3 and −2 &lt; <em>y</em> &lt; 12.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A teacher asks her students to make some observations about the curve.</p>
<p>Three students responded.<br><strong>Nadia</strong> said <em>“The x-intercept of the curve is between −1 and zero”.</em><br><strong>Rick</strong> said <em>“The curve is decreasing when x &lt; 1 ”.</em><br><strong>Paula</strong> said <em>“The gradient of the curve is less than zero between x = 1 and x = 2 ”.</em></p>
<p>State the name of the student who made an <strong>incorrect</strong> observation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{dy}}}}{{{\text{dx}}}}"> <mfrac> <mrow> <mrow> <mtext>dy</mtext> </mrow> </mrow> <mrow> <mrow> <mtext>dx</mtext> </mrow> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the stationary points of the curve are at <em>x</em> = 1 and <em>x</em> = 2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em>y</em> = 2<em>x</em><sup>3</sup> − 9<em>x</em><sup>2</sup> + 12<em>x</em> + 2 = <em>k</em> has <strong>three</strong> solutions, find the possible values of <em>k</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 12\,\,{\text{cos}}\,x - 5\,\,{\text{sin}}\,x,\,\, - \pi&nbsp; \leqslant x \leqslant 2\pi ">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>12</mn>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>cos</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>5</mn>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>sin</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mi>x</mi>
  <mo>,</mo>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mo>−<!-- − --></mo>
  <mi>π<!-- π --></mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>x</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>2</mn>
  <mi>π<!-- π --></mi>
</math></span>,&nbsp;be a periodic function with&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = f\left( {x + 2\pi } \right)">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>x</mi>
      <mo>+</mo>
      <mn>2</mn>
      <mi>π<!-- π --></mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span></p>
<p>The following diagram shows the graph of&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">There is a maximum point at A. The minimum value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> is −13 .</p>
</div>

<div class="specification">
<p>A ball on a spring is attached to a fixed point O. The ball is then pulled down and released, so that it moves back and forth vertically.</p>
<p style="text-align: center;"><img 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"></p>
<p>The distance, <em>d</em> centimetres, of the centre of the ball from O at time <em>t</em> seconds, is given by</p>
<p style="padding-left: 90px;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d\left( t \right) = f\left( t \right) + 17,\,\,0 \leqslant t \leqslant 5.">
  <mi>d</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>+</mo>
  <mn>17</mn>
  <mo>,</mo>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>5.</mn>
</math></span></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>, write down the amplitude.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>, write down the period.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span> in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p\,\,{\text{cos}}\,\left( {x + r} \right)">
  <mi>p</mi>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>cos</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>x</mi>
      <mo>+</mo>
      <mi>r</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum speed of the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the first time when the ball’s speed is changing at a rate of 2 cm s<sup>−2</sup>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{1}{3}{x^3} + \frac{3}{4}{x^2} - x - 1">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mn>1</mn>
    <mn>3</mn>
  </mfrac>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mfrac>
    <mn>3</mn>
    <mn>4</mn>
  </mfrac>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>1</mn>
</math></span>.</p>
</div>

<div class="specification">
<p>The function has one local maximum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
  <mi>x</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span> and one local minimum at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = q">
  <mi>x</mi>
  <mo>=</mo>
  <mi>q</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = f\left( x \right)">
  <mi>y</mi>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span> for −3 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> ≤ 3 and −4 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span> ≤ 12.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the range of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right)">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket is travelling in a straight line, with an initial velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="140">
  <mn>140</mn>
</math></span> m s<sup>−1</sup>. It accelerates to a new velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500">
  <mn>500</mn>
</math></span> m s<sup>−1</sup> in two stages.</p>
<p>During the first stage its acceleration, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> m s<sup>−2</sup>, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds is given by&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a\left( t \right) = 240\,{\text{sin}}\left( {2t} \right)">
  <mi>a</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>240</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>sin</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mn>2</mn>
      <mi>t</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>, where&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant k">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>k</mi>
</math></span>.</p>
</div>

<div class="specification">
<p>The first stage continues for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span> seconds until the velocity of the rocket reaches <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="375">
  <mn>375</mn>
</math></span> m s<sup>−1</sup>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v"> <mi>v</mi> </math></span> m s<sup>−1</sup>, of the rocket during the first stage.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the distance that the rocket travels during the first stage.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During the second stage, the rocket accelerates at a constant rate. The distance which the rocket travels during the second stage is the same as the distance it travels during the first stage.</p>
<p>Find the total time taken for the two stages.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>

<div class="specification">
<p>A second person is chosen from the group.</p>
</div>

<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>

<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>

<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that both people chosen are <strong>not </strong>allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy </strong>and complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this adult is allergic to nuts and the liquid turns blue.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the liquid turns blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = x - 8">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>8</mn>
</math></span>,&nbsp;&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( x \right) = {x^4} - 3">
  <mi>g</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>4</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>3</mn>
</math></span>&nbsp; and&nbsp; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right) = f\left( {g\left( x \right)} \right)">
  <mi>h</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>g</mi>
      <mrow>
        <mo>(</mo>
        <mi>x</mi>
        <mo>)</mo>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h\left( x \right)"> <mi>h</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span> be a point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>. The tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span> is parallel to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>.</p>
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-coordinate of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{C}}"> <mrow> <mtext>C</mtext> </mrow> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {{\text{e}}^{2\,{\text{sin}}\left( {\frac{{\pi x}}{2}} \right)}}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mn>2</mn>
        <mspace width="thinmathspace"></mspace>
        <mrow>
          <mtext>sin</mtext>
        </mrow>
        <mrow>
          <mo>(</mo>
          <mrow>
            <mfrac>
              <mrow>
                <mi>π<!-- π --></mi>
                <mi>x</mi>
              </mrow>
              <mn>2</mn>
            </mfrac>
          </mrow>
          <mo>)</mo>
        </mrow>
      </mrow>
    </msup>
  </mrow>
</math></span>, for <em>x</em>&nbsp;&gt; 0.</p>
<p>The <em>k </em>th&nbsp;maximum point on the graph of <em>f</em> has <em>x</em>-coordinate <em>x<sub>k</sub></em> where&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k \in {\mathbb{Z}^ + }">
  <mi>k</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <msup>
      <mrow>
        <mi mathvariant="double-struck">Z</mi>
      </mrow>
      <mo>+</mo>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <em>x<sub>k</sub></em><sub> + 1</sub> = <em>x<sub>k</sub></em> + <em>a</em>, find <em>a</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the value of <em>n</em> such that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sum\limits_{k = 1}^n {{x_k} = 861} "> <munderover> <mo movablelimits="false">∑</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mrow> <msub> <mi>x</mi> <mi>k</mi> </msub> </mrow> <mo>=</mo> <mn>861</mn> </mrow> </math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The population of fish in a lake is modelled by the function</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( t \right) = \frac{{1000}}{{1 + 24{{\text{e}}^{ - 0.2t}}}}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>1000</mn>
    </mrow>
    <mrow>
      <mn>1</mn>
      <mo>+</mo>
      <mn>24</mn>
      <mrow>
        <msup>
          <mrow>
            <mtext>e</mtext>
          </mrow>
          <mrow>
            <mo>−<!-- − --></mo>
            <mn>0.2</mn>
            <mi>t</mi>
          </mrow>
        </msup>
      </mrow>
    </mrow>
  </mfrac>
</math></span>, 0&nbsp;≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>&nbsp;≤ 30 , where&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is measured in months.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the population of fish at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> = 10.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the rate at which the population of fish is increasing at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> = 10.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> for which the population of fish is increasing most rapidly.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^4} - 54{x^2} + 60x">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>4</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>54</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>60</mn>
  <mi>x</mi>
</math></span>, for&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 1 \leqslant x \leqslant 6">
  <mo>−<!-- − --></mo>
  <mn>1</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>x</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>6</mn>
</math></span>.&nbsp;The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
  <mi>x</mi>
  <mo>=</mo>
  <mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
  <mi>x</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span>. There is a maximum at point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
  <mrow>
    <mtext>A</mtext>
  </mrow>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
  <mi>x</mi>
  <mo>=</mo>
  <mi>a</mi>
</math></span>, and a point of inflexion at point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
  <mrow>
    <mtext>B</mtext>
  </mrow>
</math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
  <mi>x</mi>
  <mo>=</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the tangent to the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}"> <mrow> <mtext>B</mtext> </mrow> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}"> <mrow> <mtext>B</mtext> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis and the lines <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p"> <mi>x</mi> <mo>=</mo> <mi>p</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b"> <mi>x</mi> <mo>=</mo> <mi>b</mi> </math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> is rotated 360º about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = \ln x">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>ln</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = 3 + \ln \left( {\frac{x}{2}} \right)">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>3</mn>
  <mo>+</mo>
  <mi>ln</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mfrac>
        <mi>x</mi>
        <mn>2</mn>
      </mfrac>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x > 0">
  <mi>x</mi>
  <mo>&gt;</mo>
  <mn>0</mn>
</math></span>.</p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span> can be obtained from the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> by two transformations:</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{a horizontal stretch of scale factor }}q{\text{ followed by}}} \\ {{\text{a translation of }}\left( {\begin{array}{*{20}{c}} h \\ k \end{array}} \right).} \end{array}">
  <mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
    <mtr>
      <mtd>
        <mrow>
          <mrow>
            <mtext>a horizontal stretch of scale factor&nbsp;</mtext>
          </mrow>
          <mi>q</mi>
          <mrow>
            <mtext>&nbsp;followed by</mtext>
          </mrow>
        </mrow>
      </mtd>
    </mtr>
    <mtr>
      <mtd>
        <mrow>
          <mrow>
            <mtext>a translation of&nbsp;</mtext>
          </mrow>
          <mrow>
            <mo>(</mo>
            <mrow>
              <mtable rowspacing="4pt" columnspacing="1em">
                <mtr>
                  <mtd>
                    <mi>h</mi>
                  </mtd>
                </mtr>
                <mtr>
                  <mtd>
                    <mi>k</mi>
                  </mtd>
                </mtr>
              </mtable>
            </mrow>
            <mo>)</mo>
          </mrow>
          <mo>.</mo>
        </mrow>
      </mtd>
    </mtr>
  </mtable>
</math></span></p>
</div>

<div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h(x) = g(x) \times \cos (0.1x)">
  <mi>h</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>×<!-- × --></mo>
  <mi>cos</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mo stretchy="false">(</mo>
  <mn>0.1</mn>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 < x < 4">
  <mn>0</mn>
  <mo>&lt;</mo>
  <mi>x</mi>
  <mo>&lt;</mo>
  <mn>4</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
  <mi>h</mi>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
  <mi>y</mi>
  <mo>=</mo>
  <mi>x</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.34.27.png" alt="M17/5/MATME/SP2/ENG/TZ1/10.b.c"></p>
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
  <mi>h</mi>
</math></span> intersects the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}">
  <mrow>
    <msup>
      <mi>h</mi>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>1</mn>
      </mrow>
    </msup>
  </mrow>
</math></span> at two points. These points have <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> coordinates 0.111 and 3.31 correct to three significant figures.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>;</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>;</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x} "> <msubsup> <mo>∫</mo> <mrow> <mn>0.111</mn> </mrow> <mrow> <mn>3.31</mn> </mrow> </msubsup> <mrow> <mrow> <mo>(</mo> <mrow> <mi>h</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area of the region enclosed by the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{h^{ - 1}}"> <mrow> <msup> <mi>h</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> be the vertical distance from a point on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> to the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span>. There is a point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(a,{\text{ }}b)"> <mrow> <mtext>P</mtext> </mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mrow> <mtext>&nbsp;</mtext> </mrow> <mi>b</mi> <mo stretchy="false">)</mo> </math></span> on the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span> where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="d"> <mi>d</mi> </math></span> is a maximum.</p>
<p>Find the coordinates of P, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.111 < a < 3.31"> <mn>0.111</mn> <mo>&lt;</mo> <mi>a</mi> <mo>&lt;</mo> <mn>3.31</mn> </math></span>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves in a straight line such that its velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>&#8202;</mo><mtext>m&#8202;s</mtext><msup><mrow></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is given by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfenced><mi>cos</mi><mo>&#8202;</mo><mi>t</mi></mrow><mn>4</mn></mfrac><mo>,</mo><mo>&#160;</mo><mn>0</mn><mo>&#8804;</mo><mi>t</mi><mo>&#8804;</mo><mn>3</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine when the particle changes its direction of motion.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the times when the particle’s acceleration is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the particle’s acceleration when its speed is at its greatest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A scientist conducted a nine-week experiment on two plants, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>, of the same species.&nbsp;He wanted to determine the effect of using a new plant fertilizer. Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> was given fertilizer&nbsp;regularly, while Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> was not.</p>
<p>The scientist found that the height of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mo>&#160;</mo><msub><mi>h</mi><mi>A</mi></msub><mo>&#160;</mo><mtext>cm</mtext></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> weeks can be modelled by the&nbsp;function <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>sin</mi><mo>(</mo><mn>2</mn><mi>t</mi><mo>+</mo><mn>6</mn><mo>)</mo><mo>+</mo><mn>9</mn><mi>t</mi><mo>+</mo><mn>27</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>&#8804;</mo><mi>t</mi><mo>&#8804;</mo><mn>9</mn></math>.</p>
<p>The scientist found that the height of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>,</mo><mo>&#160;</mo><msub><mi>h</mi><mi>B</mi></msub><mo>&#160;</mo><mtext>cm</mtext></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> weeks can be modelled by the function <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>B</mi></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mn>8</mn><mi>t</mi><mo>+</mo><mn>32</mn></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>&#8804;</mo><mi>t</mi><mo>&#8804;</mo><mn>9</mn></math>.</p>
</div>

<div class="specification">
<p>Use the scientist&rsquo;s models to find the initial height of</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> correct to three significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the values of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>h</mi><mi>A</mi></msub><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>h</mi><mi>B</mi></msub><mfenced><mi>t</mi></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>9</mn></math>, find the total amount of time when the rate of growth of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> was greater than the rate of growth of Plant <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A manufacturer makes trash cans in the form of a cylinder with a hemispherical top. The trash can has a height of 70 cm. The base radius of both the cylinder and the hemispherical top is 20 cm.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>A designer is asked to produce a new trash can.</p>
<p>The new trash can will also be in the form of a cylinder with a hemispherical top.</p>
<p>This trash can will have a height of <em>H</em> cm and a base radius of <em>r</em> cm.</p>
<p style="text-align: center;"><img 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ccf746K9xBAAIFOArFuWVq324033ujv1BNPPOGPDu20h7zQScC6Yq1gWpflqlWr/AscxP3HhV28wS4lmDzZ6OBg0FP4PfvxwIQAAgikKxDLYmmtyYqKCv+CAnYxARu4Efcv+3QTlsn57MT9u+66y78O7d///d8PyGvQ5uXlyfO8TLKxLgQQyEGB2HXDWgvilltuSQzgufPOOymUR/nBtdHBdik4m+x6t7l2mslRsrEYAgjkoECsiqV1uwYXxbZjVLk4yjXTn1Eb6GIXZ7DuWDvNxC7ewIQAAggg0FEgNsXSiuPZZ58tu6DAI488MiC7DDumJtpn5mqn2tilAO28TM5HjNafrSGAgNsCsThmaa0du+C5jeQMWpZus8Y3OuvmNuOCggK/lRn3m1FzzDK+n0UiR8AlAadblta6sXMnrVBaq4dCmf2PjhVHu9bsiBEjfG8rnkwIIIBArgs427K0QmkDed555x3/qjzJLRxrMTBlViA8ajTs/8wzz8T2jh20LDP7GWFtCOSqgJPFMvxFbccqkwulJYsvwcx+ZLvyDLrArWUfxwFVXe1XZvVYGwIIDHSBY1zbwXQKpWsxD+R4gpsm20jZt956iws/DORks28IINClgFMty94USloMXeb0qN7oydNamDZStquW/lFtNIKFetqvCEJgEwggMAAEnBrgY1eR6eoY5QCwjvUuWAuzqKiIQT+xziLBI4DA0Qo407IMjo3t2rUr5THK5B2kxZAs0rfn6XiGW/525Z843Lkjnf3qmxxLI4BALgg4USztGqUzZ870Tw9JdxAJX4KZ/Xim62kF0+5YYqeW2MUhXL8mb7r7lVlN1oYAAgNNoN+7Ye0SdlYo7YID6RbKgZaEOO2PFUfrBbDu8ocffjhOoRMrAgggcNQC/dqyDK4WYzfttQui92aixdAbrZ7n7a2n/cixyw+6flWl3u5Xz1LMgQACuSjQb8UyOP5l6EfTnceXYGY/rkfjaSNj58yZ498v0tX7Qx7NfmVWlrUhgMBAEOi3bti1a9f6XXk2Ajay414HN2pJQZ5/QQP7Eu3qX8GSjTqoz7RxybQu58krmKcVLzeoOeWn4Es1rPyev2zrulLOJDU3aOPzKzQvHNPFS7SyqlYNzS3tC7XF3eW6/PcLNHPlNoWWal8+S4/s8oOLFy/WNddcw4XXs2TMahFAwA2BfimW1oU3b9483XvvvWmNfM0Y1QmX6MFGz78ZsF3azTtQo7J8Kb+sRgfsedu/xgcv0QnBRvOXqubAkcR7rfMcUP1jp+pXxXO0qOrjzgWqZac2Pfdb3Vb+Q5255hXVHUxRwlo+VtWiObrmxeN109bft63/iA797BLte+FmFd20RtvCBTOIx7G/d999tx8Rxy8dSwzhIIBARgUiL5bW/XrjjTfqvvvuk918OJ7TCZpQcpt+WPaftPJnNfqoQy1s0cHa1brrvYv0F9f/ta488xd68PmGpIJq8/xMC1eernuXLdD0/GPbGAZpyISZum3ZrTpz9aP6+ZZ9zvNYr8ATTzyhZcuWyX4EMSGAAAIDUSDyYllRUeE73nrrrQPD872PtLtDC3Cf6jZUS9d+W9OGjtWMK89R9XP/llRQ/6BPd36kpi4EBk2Yrw1enR68ZHgXc7j18tSpU/0fP/YjyH4MMSGAAAIDTSDSYtnQ0ODfbsu67CI7TpmtjLV8pp1vN0pnjteoISHGg+9qwxrp2pln6QQdp/EzLldx9Uva9NGXoUiO0/iZf635+Wu1oOj7WvH8C9rYcDD0fvweBj9+6I6NX+6IGAEEehYIfcv3PHNf57B7U9qAkNifT9nSpC0//gfdVX2y5n//Uo1PKH6phucf13IVa+a0YT7XoPHn68riTbqr4t8ULoeDTp2tH9e+pPLL3tTiubN16cQTlZdXoIuXPKmqjakHDjUtv1QnphqYdOKlWt5VM7WvSUtz+XB3rP0oYkIAAQQGkkDiaz7bO2WnGbzwwgu64447sr2pzK6/6R906Ylf6zgq9msFmv32mXqsrlpPlpymBKI/sGeT8q0L9oS2VweN0YwrZ6ip00Cf1uOTt696T0ca67SuslJryy9T/fIbNefSiZowb1WnAT7JA5GCAUnBQKXM7njv12bdsfZjyH4UMSGAAAIDSSDxPZ/NnbLjWA888IB/AnscrifawaLDaNgDqq9cqiIV69pL/ov+/Oz89kIpqeWjf9Nz1U3q2AI8XhMXrJWaqrWhLvWAnUH5hZpVUqK/un2VGr3WbUxcvVSLfpE8MKhDZE4+sR9D9qPILmHIhAACCAwUgUiKZTCo54orroi5m42C/ZGeqfwzrbluge54+v3QeZafqbbip6ourlD9kfbTUFpbf3tVUyYtf/B/q8FGzrZs08qZBUp93uQJmjC7VNcWK8XAIPf57MfQo48+qrvuuovBPu6niwgRQCBNgawXy3379vmDeuycytgP6vFRj9Wps5fqmaUFWr3gDj2+dX8rtT+w5/dJxzCDLAzTtJnFyg8G+nTZNRvMb38Hq/jK80PHQ8Pvuf14wYIFfoDr1693O1CiQwABBNIUyHqxfPbZZzVr1qwYn1OZQnLQqbrkzntUXvSmFt/+c21t/koH617RGn1Xf/Pt0R26ZluXHqQTps/WbUVv6rlNO9Wi4zThe3+niste1DU3P6SqrU2J8zBbmrZo1dJFWvCHm3T/9yakWFeKeBx7yX4UWXesdb1zKoljySEcBBA4KoGsFsugVWmDPgbcNGSafrBisYpqy3X7/3hQ997zC028bbamBwN7knd4yFn6y2vPUfVdq1VrV/QZMlnzf16tF0tO1K9vL9TX2ka5fq3wJ9p77lLVv7hIheFTUpLX5/jzoMud1qXjiSI8BBBISyCrF1JfvXq1fzunLVu2pBVMb2biAtm90ep53mx42ghoa12++uqr/dYFn4396lmTORBAYKAJZK1lad1vdt/D2J0qMtAy3I/7U1RUpDfeeENvvvlmP0bBphFAAIG+C2StWL722mt+dEF3XN9DZQ1xEwhGxpaXl8ctdOJFAAEEOghkrVj+9Kc/VWlpab91v3XYS570m4BdLN/Ou+SqPv2WAjaMAAIZEMjKMUv7Ypw4caJ27dqVtVtwcSwqA9kPrSKbnjfccIOmTJmihQsXhrYYzcNs7lc0e8BWEEDABYGstCzt6i3XX3991gqlC3DEkL7A3LlzZYO9OI0kfTPmRAABtwSyUizti9G+IJkQMIELL7yQgT58FBBAINYCGS+WdgNgGwE5bdq0WMMQfOYE7CIFdrNvO4WECQEEEIijQMaL5aZNm/wu2NhdMD2O2YtRzBdddJGWLVtGV2yMckaoCCDQLpDxYkkXbDsuj9oFzjnnHP8J51y2m/AIAQTiI5DRYmmjYOmCjU/yo4zUumLtsodvvfVWlJtlWwgggEBGBDJaLDdv3uxfND2qLlg7LYB/mTHIyKeph5V8+9vf9kfF9jAbbyOAAALOCRyTyYjsqj0lJSWZXGWX67L7RDLFS+CMM87wex52797NaUXxSh3RIpDzAhltWT711FM666yzch4VgNQCo0aN0rnnnqsPPvgg9Qy8igACCDgqkLFiGVzOzK7cw4RAVwKzZ89WXV1dV2/zOgIIIOCkQMaK5fvvv+8fr7SBHEwIdCUwadIkZeOWbV1tj9cRQACBTAhkrFhu27ZN06dPz0RMrGMAC0yePNm/sDqXvhvASWbXEBiAAhkb4GOtBbvLSK5PQXd0Vw6DBw/O6cEto0eP9mnsIvsTJkzoionXEUAAAacEMlYs7TZMy5cvd2rn0g3m9ddf1549e2St4/3793dazO7HWFlZ2eNI36qqKs2ZM6fT8skv9DSSN7hry6xZs1IWFGudDRkyRHZz5ahO00neh6N9bt30Nshn586dKfftaNfLcggggEA2BTJSLIPW1PDhw7MZa8p122kIhw8f9v/t2LHDnydc9K6++mpNnTo15bLBi9u3b5cdc/3mN78pO6aWPNmJ9PZeT5MVr3QKYU/rsdZXfX29X1Cam5s7zW7ns9pk3d49FUsbUBO04IIia4V2zJgx/jqC9zptJIsvmNOnn36axS2wagQQQCCzAhm5n6VdPP3ss8/usVBkNnT5FyQIr9OuEGOTFbaCggL/sRUUO2UhVydr7QZTUGTtx431BATThg0bZDdpjmqySyLaj5MoeiK4n2VUWWU7CAxsgYy0LK1FZ/ev7MtkAz7sOJZ9iTY2NspaRD0VOWt95foxwJ7MwxeJCD+25QLz4Dhid+uyAmct0rFjx8p6EHrKTXfrsvV8/vnn3c3CewgggIBTAhkplrZHJ510Uq92zFo3Vhity9QGBwUtHTtOZ61BK4I9Tf3RhdhTTHF6344fpmt48OBBP1/hY7LWkreuXbsQhbXme+oSDmys4NoFLJ588sngJf4igAACTgtkpBu2rKzM/7JcuHBhWjtrXWM2WWG064XaF7YdQ0v3izutjTBT1gTsOPHHH3+s4FivDYCyKZ1BUDZfMICpp+O7mdgBumEzocg6EEAgYy3L4BhhOqTWfWpdf1zAIB0t9+axLlj7d8EFF/jB2bFHK4DpdOfaAkGvAdeIdS+3RIQAAqkFMlYsU68+9au0IFO7xPnV3uQ0ON5po5iZEEAAgTgIZOQKPtaqsEEbNio2PPoyDgDEGJ2AtSRtoBBX74nOnC0hgEBmBDJSLG1wzqZNm/zTR2wkKxMCqQSsJfnYY4/plltuSfU2ryGAAALOCmSkWNre3XPPPX7BTHeQj7MiBJY1AeuqffXVV7O2flaMAAIIZEsgY8Xy0UcfTQz4yFawrDf+Ajao68EHH/R3xC55x4QAAgjEQSBjxbKwsDAO+0uMDggE52P29txcB0InBAQQyFGBjBXLRYsWyQZwMCHQk4Adt7TJLmjAhAACCMRBIGPFcsqUKf5dOewOHkwIpBLYt2+f7AIWNiLWJs6zTaXEawgg4KJAxorlI488IhvcM2PGDP+6rhRNF9PdPzFZj4O1Jk8++WT/mrCcXtQ/eWCrCCBw9AIZK5bWSrCbP9vVeezarlY07a99SdI9e/QJiuuS1oqsrq7WDTfc4F/Z55VXXvFHS9v1YIOLEsR134gbAQRyTyAj14ZNdf1N+7Ksra31u9zsPEy74a8VUyuiEydOpAtuAH7Wgovjr1+/3r9QepBzu/1X8hV+Un1mskES1XayETvrRAABdwSyVizDu2gtyw8++EDWugguum239Lrwwgs1btw4nXbaabQ2wmAxeBzc3svuHGP3yUzOq92JpLubbkdVxKLaTgxSRogIINAHgUiKZXJ8QQvEbs+1bt06vfHGG/4swS2fTjnlFP8uJFxsPVmuf55bvvbu3as9e/b4hdGeB7dUC3LW29t0RVXEotpO/2SGrSKAQFQC/VIsk3fOumw/+eQT2U2kk+9vafPaF/LQoUM1adIkjRw5UiNGjPBvQBycr5e8Pp73XsAKoF2OznLQ3Nzs37syXBStS7WoqMg/3SMTvQFRFbGottN7cZZAAIE4CThRLLsCC3+BWxHdv3+/fxw0aInacsGXuD0+77zz/FUFBdWe5Hrr1LrAg7t7WJepTXb9Xvtx8vnnn/vHFv0X2/5j3eN2sQCztIvj231Ghw8fnvaNncPr6u5xVEUsqu10t6+8hwAC8Rdwulh2xxsUAbtkmrWEggJgy9jAonBBDdZjN5sODzQJimvw/tixYxP3Wgxes7/hZcKvZ/txsI/J2wmKXvB68EMieB4cPwyeB3+DQhi00u314MIAUf+oiKqIRbWdwJi/CCAwMAViWyzTTYe1ToMpXGSCrsbgPfvbVZEJz9PTY+sy7m4Kd212N1937wVFL5gnXPzstXDRz0arMNhuX/5GVcSi2k5fLFgWAQTcFxjwxbKvKQhGfaaznuCYX3fzhruIu5vP3nO10PUUdzrvR1XEotpOOvvMPAggEF8BimV8cxfryKMqYlFtJ9bJIHgEEOhRIGNX8OlxS8yAAAIIIIBATAUoljFNHGEjgAACCEQnQAJdLUEAABQISURBVLGMzpotIYAAAgjEVIBiGdPEETYCCCCAQHQCFMvorNkSAggggEBMBSiWMU0cYSOAAAIIRCdAsYzOmi0hgAACCMRUgGIZ08QRNgIIIIBAdAIUy+is2RICCCCAQEwFKJYxTRxhI4AAAghEJ0CxjM6aLSGAAAIIxFSAYhnTxBE2AggggEB0AhTL6KzZEgIIIIBATAUoljFNHGEjgAACCEQnQLGMzpotIYAAAgjEVIBiGdPEETYCCCCAQHQCFMvorNkSAggggEBMBSiWMU0cYSOAAAIIRCdAsYzOmi0hgAACCMRUgGIZ08QRNgIIIIBAdAIUy+is2RICCCCAQEwFKJYxTRxhI4AAAghEJ0CxjM6aLSGAAAIIxFSAYhnTxBE2AggggEB0AhTL6KzZEgIIIIBATAUoljFNHGEjgAACCEQnQLGMzpotIYAAAgjEVIBiGdPEETYCCCCAQHQCFMvorNkSAggggEBMBSiWMU0cYSOAAAIIRCdAsYzOmi0hgAACCMRUgGIZ08QRNgIIIIBAdAIUy+is2RICCCCAQEwFKJYxTRxhI4AAAghEJ0CxjM6aLSGAAAIIxFSAYhnTxBE2AggggEB0AhTL6KzZEgIIIIBATAUoljFNHGEjgAACCEQnQLGMzpotIYAAAgjEVIBiGdPEETYCCCCAQHQCFMvorNkSAggggEBMBSiWMU0cYSOAAAIIRCdAsYzOmi0hgAACCMRUgGIZ08QRNgIIIIBAdAIUy+is2RICCCCAQEwFKJYxTRxhI4AAAghEJ0CxjM6aLSGAAAIIxFSAYhnTxBE2AggggEB0AhTL6KzZEgIIIIBATAUoljFNHGEjgAACCEQnQLGMzpotIYAAAgjEVIBiGdPEETYCCCCAQHQCFMvorNkSAggggEBMBSiWMU0cYSOAAAIIRCdAsYzOmi0hgAACCMRUgGIZ08QRNgIIIIBAdAIUy+is2RICCCCAQEwFKJYxTRxhI4AAAghEJ0CxjM6aLSGAAAIIxFSAYhnTxBE2AggggEB0AhTL6KzZEgIIIIBATAUoljFNHGEjgAACCEQnQLGMzpotuSbw1VatGJ+nvLzwvx+oqukrSbtUNW980nsXa8XWZtf2gngQQCACAYplBMhswlGBYwp1+0d7VVNWKGmySive0yHvcZXkHyNptEpWva/6irmS8lW0tFqNR/5VtxcOcXRnCAsBBLIpQLHMpi7rjoHAF9r/6X6p+FYtu26yOpbCZu2u3yHlX6cf3nGp8vm/JQb5JEQEsiPA//7ZcWWtcRE4+Bv9+uXtyp86Rqck/9/w1cd6s3KrdNk0nX5C8ptx2UHiRACBTAjwDZAJRdYRU4EWHax7RWuaCnXtzLN0QtJetOx4Ry9vz1fxRWdoZNJ7PEUAgdwSsIMzTAjkqMAf9OnOj9SkrVp+6QgtT6lQpPIpo8SvypQ4vIhAzgjwHZAzqWZHOwm07NSm5zZJxRWqP+LJ88L/PlFl6Tgp/891zp8N7rQoLyCAQG4JUCxzK9/sbVhgzwd6tbpJ4y6borHJ/ye0HcvkeGUYjMcI5K5A8ldE7kqw5zkm0KKDH9bpZRVqzjmnKfl4xFe/eVOVTRyvzLEPBbuLQJcCFMsuaXhjYAvsU92GajVpmr51+tCkXf1SO97Zou2aoStnjOF4ZZIOTxHIRQGKZS5mPef3uUXN236lVWu2SsXTNXlkx3ZlS9NrenrNJmncdE0Ze1zOawGAAAJSnmejGvo42eXCMrCaPkbB4nESiOoz03k7dhm7izVn9fYQ1/dV2fiYSvK/1NYV39W0xbWh94pUXvciV+4JifAQgVwUoFjmYtYd2OfORSw7QUW1nexEz1oRQMAVAbphXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCFEtnU0NgCCCAAAKuCFAsXckEcSCAAAIIOCtAsXQ2NQSGAAIIIOCKAMXSlUwQBwIIIICAswIUS2dTQ2AIIIAAAq4IUCxdyQRxIIAAAgg4K0CxdDY1BIYAAggg4IoAxdKVTBAHAggggICzAhRLZ1NDYAgggAACrghQLF3JBHEggAACCDgrQLF0NjUEhgACCCDgigDF0pVMEAcCCCCAgLMCxzgbWQwDa2ho0Pvvv99j5CUlJd3O88UXX2jXrl2JeYYPH65hw4YlnvMAAQQQQCBagQFcLHepat7FmrN6u5S/VDXb/k6n/2at/uftS7Rm+jPa9uAlOiHD1nv37tXmzZt7XGtPxdIK5cSJE7tdz7nnnquqqiqNGjWq2/msgI8ePVrHH398t/PxJgIIIIBA1wIDuFiOVsmqzao55XJdo4s18Tdr9c/7/rPGH1ugK741TkO6Njnqdy644ALZv75OEyZMkOd5idXs3r1bhw8fTjy3B1aYBw8e3OG1VE+Si+7ixYv92b75zW+qoKBAQ4YM0bRp02Lfck1lFHjYD4bkyYyZEEAAgXQF8rzwt3K6SyXNl5eX1+HLPent/nt6cKOWTLpGW666VtNHzdEPb52elSLZfzuY3paDYmEFd8eOHf5C27Zt0/79+2XvWQHNRJFPL5rWuTL9mbFW9pw5c9IK4b777tOdd96Z1rzMhAACCJiAE8XSvrB37typTz/91D/mV15ervr6evX1139Lw0pdMXGBqoseUt2Li1Q4hPFMR/uxv+GGG/xF//RP/1STJk3S5MmT+9S9m+liacHNnj1bL7zwQo+7+Lvf/S72Leked5IZEEAgowL9Uizffvttvfvuu3rttdf01FNP+Ttkx+CKiop03nnnaeTIkTrnnHP6eJztSzWsLNXEBTtUVvOSHrxkeEbhcm1l9oPGBi81NjbqnXfeSeRt1qxZmj59ut+V25vu3GwUS4sxuds5OU+VlZXq6Zhx8jI8RwABBPqlWNoXpXX9WWEcO3as7PhZ5kd7fqaNSy7XpW//N9Wvn68JNCoz/mkPegTq6uq0bt06Pfzww2l352ajWNoOlpWVyXomUk1W2P/pn/6pjz/CUq2Z1xBAYKALRFIs7VSI9evXy46TRXasqO145dv3btT6+ZMURa204mEt5VtuuaXHUaoD/YPV0/5lq1ju27dPJ598csrNb9q0Ke1innIFvIgAAjkrkPUa8vrrr+uqq67yB1/YgJKoppZPd+rtpgJNHTM8kkIZ7Je1auxUjdWrV8t+JDBFK2A9FKtWreq00f4YxNQpCF5AAIHYCmSsWFphuP/++/1uMNOwofzWJTZjxoy0Bl1kWnDQhPna4NX127HKefPm6aKLLlJ1dXWmdy2267MfTjYIx1rg2Zzmzp0rOwYenq6//vrwUx4jgAACvRLIWLG0rkc7bnXNNdfoscce81tXXR076lWEMZ75jTfe0MyZMyMpEHFgOv300/3BQD0NwunrvtgFGO69997Eah599NE+j6xOrIwHCCCQkwIZK5Z2kvxtt90m+wV/88035yRmVzttpzNYgbCWth1Ty9XJukjtmLUVL5uyaVFcXOx/Fq2FefXVV+cqOfuNAAIZEsjYAB87qd262Zh6FuD0BckG+NjpQ2eeeWbPYEc5h3X32ukunCpylIAshgACCYGMtCxtSP7555/f6ThRYittD2yQhV0waKD+swsp9DSZgZ1PmstT0KI86aSTsspgF7WgUGaVmJUjkDMCGbk27I9+9COdffbZ+pd/+Rdt376dbtgUHx/7QbF8+fKcP3ZmhXLJkiX+ebY9XQQ+BSMvIYAAAv0ikJGW5dSpU2Vdi9/5znf0ySefaMuWLf6XYb/skWMbtWNmZmODn/p6+T7Hdq1X4dhoabt+6+WXX+4vd/fdd/dqeWZGAAEE+lMgI8XSdsC6u6wb0o4T2eXPhg4dqp///OeyFlWuTjaQ5dVXX83prkBrSdo5p3YazQMPPKA77rhDTz75JFfRydX/KdhvBGIqkLFiaftvLSdrQdmVUv793/9df/u3f6sjR47kXLesHZe0e1IuXLgwJ4uCFUg7v9Quvm5X07FTiaxIvvTSSzn9wyGm3xGEjQACmbrrSFeS9qX5y1/+0u9+s9MnrJgGJ+vbOXeZvx5sV5FE87pdiOGzzz6TdUvn0mRdrNarEL44vnU/l5aW+helyDWPXMo9+4pArghk5NSRdLCscH744Yd+t6S1Pu2EfftCtSu6ZOKWT+nEwDyZEbCudrulmv0N34HEWtR2cXy7fVcuH5/NjDJrQQABlwQiK5bJOx0UTxs9a+fCBVf7sQJqp1bYF+4pp5yiMWPGaPjw4QOuFZrs4eJzK4Z2sYk9e/Zo8+bN+vzzz1PemstyRHF0MYPEhAACmRLot2KZagesG/Pjjz9OfDnbl3X4Zr52dSA7N89aLzbZ7b0GDx7cp5sQp4ojV14zX5usldjc3OzfFcYudl9bW+u3/AMHazHabdSsIFphtAvF2yXlmBBAAIFcEXCqWHaFbkX08OHDfgvUvtStJRpu5QTLBa1Se24t0yFDhvhvBUXVngz0VmpQAG1fgyJoj61laFMqNxuxbIXQCmJBQYF/8+0RI0ZQFH0x/oMAAghIsSiWPSUqKBBBl6HNHxQHexx08aZaT9BaDb8XtFzDr9njkSNHyopItif7MZBqamxs9M9jDb/X3b4FRdDmDwqhPbYfEjYN9B8O/k7yHwQQQCADAgOiWPbGIWilBsskF6ag5Rq8H/6b3D0Zfi+Tj1MVcFu/nbtqg6HCU7jVbK/TRRrW4TECCCCQGYGcK5aZYWMtCCCAAAK5JJDRixLkEhz7igACCCCQOwIUy9zJNXuKAAIIIHCUAhTLo4RjMQQQQACB3BH4/xg02SjPlYhNAAAAAElFTkSuQmCC"></p>
<p>There is a design constraint such that <em>H</em> + 2<em>r</em> = 110 cm.</p>
<p>The designer has to maximize the volume of the trash can.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the height of the cylinder.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total volume of the trash can.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the height of the <strong>cylinder</strong>, <em>h</em> , of the new trash can, in terms of <em>r</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume, <em>V</em> cm<sup>3</sup> , of the new trash can is given by</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = 110\pi {r^3}"> <mi>V</mi> <mo>=</mo> <mn>110</mn> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>3</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your graphic display calculator, find the value of <em>r</em> which maximizes the value of <em>V</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The designer claims that the new trash can has a capacity that is at least 40% greater than the capacity of the original trash can.</p>
<p>State whether the designer’s claim is correct. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P moves along a straight line. The velocity <em>v</em> m s<sup>−1</sup> of P after <em>t</em> seconds is given by <em>v</em> (<em>t</em>) = 7 cos <em>t</em> − 5<em>t </em><sup>cos <em>t</em></sup>, for 0 ≤ <em>t</em> ≤ 7.</p>
<p>The following diagram shows the graph of <em>v</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial velocity of P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum speed of P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of times that the acceleration of P is 0 m s<sup>−2</sup> .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of P when it changes direction.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P moves along a straight line. Its velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}}{\text{ m}}\,{{\text{s}}^{ - 1}}">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>P</mtext>
      </mrow>
    </msub>
  </mrow>
  <mrow>
    <mtext>&nbsp;m</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>1</mn>
      </mrow>
    </msup>
  </mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}} = \sqrt t \sin \left( {\frac{\pi }{2}t} \right)">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>P</mtext>
      </mrow>
    </msub>
  </mrow>
  <mo>=</mo>
  <msqrt>
    <mi>t</mi>
  </msqrt>
  <mi>sin</mi>
  <mo>⁡<!-- ⁡ --></mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mfrac>
        <mi>π<!-- π --></mi>
        <mn>2</mn>
      </mfrac>
      <mi>t</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>8</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{P}}}">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>P</mtext>
      </mrow>
    </msub>
  </mrow>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.04.21.png" alt="M17/5/MATME/SP2/ENG/TZ1/07"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the first value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> at which P changes direction.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <strong>total </strong>distance travelled by P, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8">
  <mn>0</mn>
  <mo>⩽</mo>
  <mi>t</mi>
  <mo>⩽</mo>
  <mn>8</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second particle Q also moves along a straight line. Its velocity, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{Q}}}{\text{ m}}\,{{\text{s}}^{ - 1}}">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>Q</mtext>
      </mrow>
    </msub>
  </mrow>
  <mrow>
    <mtext>&nbsp;m</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mrow>
        <mo>−</mo>
        <mn>1</mn>
      </mrow>
    </msup>
  </mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{Q}}} = \sqrt t ">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>Q</mtext>
      </mrow>
    </msub>
  </mrow>
  <mo>=</mo>
  <msqrt>
    <mi>t</mi>
  </msqrt>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 8">
  <mn>0</mn>
  <mo>⩽</mo>
  <mi>t</mi>
  <mo>⩽</mo>
  <mn>8</mn>
</math></span>. After <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span> seconds Q has travelled the same total distance as P.</p>
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{16}}{x}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>16</mn>
    </mrow>
    <mi>x</mi>
  </mfrac>
</math></span>. The line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</mi>
</math></span>&nbsp;is tangent to the graph of&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> at&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8">
  <mi>x</mi>
  <mo>=</mo>
  <mn>8</mn>
</math></span>.</p>
</div>

<div class="specification">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L">
  <mi>L</mi>
</math></span> can be expressed in the form <em><strong>r</strong></em>&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \left( {\begin{array}{*{20}{c}}  8 \\   2  \end{array}} \right) + t">
  <mo>=</mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mtable rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mn>8</mn>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mn>2</mn>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo>)</mo>
  </mrow>
  <mo>+</mo>
  <mi>t</mi>
</math></span><em><strong>u</strong></em>.</p>
</div>

<div class="specification">
<p>The direction vector of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x">
  <mi>y</mi>
  <mo>=</mo>
  <mi>x</mi>
</math></span> is&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\begin{array}{*{20}{c}}  1 \\   1  \end{array}} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <mtable rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mn>1</mn>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mn>1</mn>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em><strong>u</strong></em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acute angle between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = x"> <mi>y</mi> <mo>=</mo> <mi>x</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L"> <mi>L</mi> </math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {f \circ f} \right)\left( x \right)"> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo>∘</mo> <mi>f</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f^{ - 1}}\left( x \right)"> <mrow> <msup> <mi>f</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the obtuse angle formed by the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 8"> <mi>x</mi> <mo>=</mo> <mn>8</mn> </math></span> and the tangent line to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 2"> <mi>x</mi> <mo>=</mo> <mn>2</mn> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f''\left( x \right) = \left( {{\text{cos}}\,2x} \right)\left( {{\text{sin}}\,6x} \right)">
  <msup>
    <mi>f</mi>
    <mo>″</mo>
  </msup>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mrow>
        <mtext>cos</mtext>
      </mrow>
      <mspace width="thinmathspace"></mspace>
      <mn>2</mn>
      <mi>x</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mrow>
        <mtext>sin</mtext>
      </mrow>
      <mspace width="thinmathspace"></mspace>
      <mn>6</mn>
      <mi>x</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>, for 0&nbsp;≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>&nbsp;≤ 1.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{f''}">
  <mrow>
    <msup>
      <mi>f</mi>
      <mo>″</mo>
    </msup>
  </mrow>
</math></span> on the grid below:</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxAAAAG0CAYAAACi68EsAAAgAElEQVR4Ae3dD5Qd5Xnn+ecKQkyswTZmZmmBNz5BRyKTYextNayG5UzUwhH2RF77tIyZ4EEywhnPxoZpCLQQgbETsEGCSLLHztheI8zFMOFP90L8J0iLhDwHPI5CN856MkF9tD5kAbXPIcFI0RrMWl173tv9NtW3q6rr3qrnVj1V33sO6ttVb73v7/28L9393n5vdSMIgkB4IIAAAggggAACCCCAAAIpBE72ZRqNhn/KRwQQQAABBBBAAAEEEEBggYD73cPcAsKd5ZcRC4w4gAACCCCAAAIIIIAAAiLif+GwBA0EEEAAAQQQQAABBBBAIK0AC4i0UpRDAAEEEEAAAQQQQAABYQHBJEAAAQQQQAABBBBAAIHUAiwgUlNREAEEEEAAAQQQQAABBFhAMAcQQAABBBBAAAEEEEAgtQALiNRUFEQAAQQQQAABBBBAAAEWEMwBBBBAAAEEEEAAAQQQSC3AAiI1FQURQAABBBBAAAEEEECABQRzAAEEEEAAAQQQQAABBFILsIBITUVBBBBAAAEEEEAAAQQQYAHBHEAAAQQQQAABBBBAAIHUAiwgUlNREAEEEEAAAQQQQAABBFhAMAcQQAABBBBAAAEEEEAgtQALiNRUFEQAAQQQQAABBBBAAAEWEMwBBBAoh8DUmGxqNKTh/hvcKePHp2dyHdsvW5adJ1eN/a3MHilHXlIggAACCCBQUwEWEDUdeLqNQOkE+obk3uA1OXT3pSIH/qv81ZE3ZiIuXSmXfPxX5cVXXytdZAIhgAACCCBQRwEWEHUcdfqMQGkF3iK/9p4L5Bx5WV75h1/MpFzyTjl7+W/Ib73nTOELVmkHjmAIIIAAAjUS4PtxjQabriJgQWDJPzpdzpEX5Ed/+9NW3OmXvis7Dv7P8jv/09stxCcjAggggAAClRdgAVH5IaaDCNgSWPKP3i5nzkV+VZ59aFLW3bJezuKr1ZwKTxBAAAEEEChSgG/JRerTNgIILBR469vlzL7/W57+8f8jL+z/uoz+6u/Ih886ZWE5jiCAAAIIIIBAIQIsIAphp1EEEIgV+JW3yT/+FZGfPbtbdh14j1z94V/lvQ+xWJxAAAEEEECg9wIn975JWkSgHgLXXnttq6M7d+5sffSfu0+ijsUdTyobrrOb69014TqytuUzhOv0x1K39ceflNPP6ZNjz74of/+O78j23//uPK+DBw/K2WefLcuWLWsdz9RWh2OTpi3f37iy7Q6+vPvoHu3XuWPt49Lf3y8TExOt8v5c1LVJ56LqbVUY0V74eHs+30b4eNSxuPaSyobrjLveH09TtixtuczhvGXJFc7kXduz+uNpyib1q73epLJFteUzuaw8EECgTSCYfYiIf8pHBBDIQWB4eDiHWuZX0Ww25x/I6TONrC5aV3lP/E1w9+bbgn1Hfr6gd6Ojo4H7WnXeeecFP/vZzxacz3Kgq6wpGtSwtZTVEWnk1XAl68yE1rDVmAMurUZWrXkwo8u/CNgW8OsFtjC1Laj4FIG8BHj1qhvJV2X8Cw+K3HC1rO2b/76HV155RTZs2CBnnnmmvPbaa3OvynfTSi+v0ZgHV1xxhUoXNLKqBDVWKa7GBoy4CCCwqEDDrYNcKffXX2efLnoRBRBAAIH8BF6V8bv+jXxwakjuOft5+e//8jq5dtXCW7aOjIzIgQMH5KKLLpKTTz5Z7rzzTnn22Wflve99b35RqAkBBBBAAAEEYgX8eoHfQMQScQKBbALt+3az1Vblq38hR1/+iUxNHJKf/Mv/Tf59xOJh7969rQXD1772tdbiYfXq1fKJT3xCPvvZz7Z+G1FmHY15cN9996l0WSOrSlBjleJqbMCIiwACiwqwgFiUiAIIVF+g2B9wzpC1256R4MltsmlV34I7LrntSjfffLPccMMNrd82PPnkk60B+cxnPiOPPfaYPPzww9UfIHq4QKDYObsgTqUOWLK1lLVSk4TO1F6ABUTtpwAAlgS0XnnWMsgjr98/fuONN86L6e7ENDo6Kps2bZLJycl557r5JI+s3bRbh2ss2ZJVZ0ZacnUC1vLqjBq1IhAvwAIi3oYzCCBQsMAPf/hD+YM/+AO57bbb5PTTT1+Q5gMf+IB86EMfam1vWnCSAwgggAACCCCgIsACQoWVShF48979WHQv4N7j4N7rsG7dushKTj31VNm+fbt8/etfl7GxscgyRR/0v0HJMwd3YcpTU78ujTmgn5oWEEAAgXgBFhDxNpxBIJMAe3Mz8bUuHhoaEvdeh6THihUr5KmnnpKlS5cmFSvsnMY80NpeoZG1MPgSNYxriQaDKAggkIsAt3HNhZFKEFgo4H5o4JXHhS5Zj7jbubq7MLnFhYWHxjxwCwiN30JoZLUwRtoZcdUWpn4EEOiVALdx7ZU07SCAAAIIIIAAAgggUCEBtjBVaDDpCgLdCrhXSK08/G1creQlp46ApTmrI6BXqyVbS1n1RoyaEei9AAuI3pvTYk0ENLYvae191xoSS3m1smrMA43tS24OaGR19WrZasxbjay42poD1uasxv8H1InAYgIsIBYT4jwCCCCAAAIIIIAAAgjMCbCAmKPgCQL5CvCr9Xw9rdamMQ80XiV3vhpZrY5bnrlxzVOTuhBAoAwCLCDKMApkQAABBBBAAAEEEEDAiAALCCMDRUwEnIC1ve8aeQcHB1Umg0ZWlaAGK9Ww1XpfgUZWrSHTyqphaymrGy+tvFpzgXoR6LUAfwei1+K0hwACmQSs/R2ITJ3lYgQQQAABBEokwN+BKNFgEAWBogUs7dHmNq5Fz5ZytG9pzpZDLH0KS7aWsqYfAUoiUH4BtjCVf4xIaFRA4xub1ptntYgt5dXKamkeaGR1c0vLVmPeamTF1dYcsDZnNf4/oE4EFhNgC9NiQpxHoEsB90NDf39/62q/nzbqh5Ms59rri6or6pgLFXU86pgvm6atTsp229aDDz4o55xzjgwMDLT6kCZXUlsuc5o6XDn3iKsr7tzExIT6PJhJFt8Pdz6uj+FzUVnD53073qDbc+Esvq7wMVevOx51zLfZnjWpbHvuqLLtx3wG356vw3+Myx11XThr1HlfZ9Zz7X2Iyhh1zLeb5vpOypalLZc53Le0uXw5dz0PBBCYEfBbmCSYfYjMPfWH+IgAAhkEhoeHM1wdfWmz2Yw+kfGoRlYXSSPvwMBAMDo6mrHHCy/XyOpa0bC1llUjr4ar1py1lJU5O/O1QWPOztTMvwjYFvDrBbYwsaREAAEEEEAAAQQQQACB1AJsYUpNRUEEqivgtltp3LpRQ+z888+XrVu3ytDQkEb11GlEwNKcNUI6F9OSraWsc8A8QcCwgN/CxALC8CASHYE6CnAb1zqOOn1GAAEEECiDgF9AsIWpDKNBhkoKuFfGeCCgMQ/CbwjNU1gja575rNaFq9WRIzcCCMQJsICIk+E4AiUUsPaDo0Zerb8DoZG1hFOo55Gcq4at1g/lGlm10LWyathayurGSyuv1lygXgR6LcACotfitIcAAggggAACCCCAgGEBFhCGB4/o5Raw8qbkcivaT6cxD7TuT6+R1f4IZu8BrtkNqQEBBMolwAKiXONBGgQQQAABBBBAAAEESi3AAqLUw0M4ywIa+4i1XnnWcraUVyurxjzQ2p+tkdW5atlqzFuNrBquru8aWTVMrWW1mFdr3KgXgTgBFhBxMhxHoEYClrZYDA4O1mhk6GqcgKU5G9eHsh63ZGspa1nHm1wIdCPAAqIbNa5BAAEEEEAAAQQQQKCmAiwgajrwdNumgKWtK05YIy+3cbU1d90c0JgHWtuCNLJqjZhWVg1bS1m1vnZpzQPqRaAIARYQRajTZi0E+NV6LYZ50U5qzAOtve8aWRcFqkEBXGswyHQRgZoJsICo2YDT3d4JaLyK17v0tJSXgMY8sPZqbl6WVuvRmANWLciNAALVEGABUY1xpBcI9FhgWo5PHpCxR+6STctvkv3HplO2Py3H9t8kyxoNafj/Ltktk2kvT9kKxRBAAAEEEEBAT+BkvaqpGQEE8hbQ2rrSac7pyW/Iv/7D78nbnmzKA7JVNsVUsCDv9AvyxP3fkqm58n2y7rILZXkJXspYkHUuI0+yCFhztZSXrFlmZvK1lmyTe8JZBHQEWEDouFIrAqYEOt2jvWTFZvn2/ZfL5O7X5IGb03Z1Wo4/OyZfPeMLcjRYK6elvaytHLdxbQOp6aedztmaMnXVbUu2lrJ2NRhchEBJBUrwul9JZYiFQEYBvrG1A74iBx+6X/Zu3yaf2z0m+yePtReo5Oca80Dr1VGNrJUc1A47hWuHYBRHAIHSC7CAKP0QERCBNwWsvXk2nHd68s9k2/ZxEdkr26/aIBevvFS2jD0nx9/sXqpn3MY1FVNpCrk5EJ4HeQXTemOyRta8+txej1ZWDVtLWZ2zVt72MeRzBKwKsICwOnLkLr2Axjfh0nc6IaDb9rQnCOTEkWfk0btHZI1bSGy4Xr4y/mrCVfZPacwDrR9uNLLaH8HsPcA1uyE1IIBAuQQaQRAELpK7I8rs03IlJA0CRgX8Dw1++4L/3HUn6pg/Hi7nj7mP7nh/f79MTEy4T1t1JJVtFVqkLV9vmrIL27pdJndvlJXXPC8bNl0o7zql0arG9c2X9Xmj+vvHI/9Kbr58k3zx+IWy6aJ3ySmzIXbt2uXjJH4cHh7O1SApqwsS7pcPFtWvqGP+en+d9/Gf+2vc52nO+axZ6g1fG9dm1PGoY+25fX98WZ+3/fhiGfz1rpx7dHq9uyZcR9T1vl5fLilre1n3uXtE1Rt1rJuyPtdMS/PbSpPVXReuIylXuFxcVn88TdlwWz5rJ9d3UjbclrvOP6KORx1z5d1x3y+XV2uroM/GRwQsCsytF9wCwj1E3PqBBwII5CUwPDycV1Vz9TSbzbnneT7pLutrwaG7Lw2kb2uw7+iJyDjJeU8ER/dtDfoSro+qdGBgIBgdHY06lelYctbuq+7ONrk9sgaBhqtT17C1lNUZaOTVcNXKqjUPXL08ELAu4NcL3IXJ4vKPzCYE/KtcJsIWEnKJLD17uZx3nsjZS6u7m1JjHmi9MqqRtZCpVbJGcS3ZgBAHAQQyC7CFKTMhFSBQV4HXZ7Yw3bxc9j13m6w9rdNFgPujctvlDvmEfH7tGakRR0ZGZPXq1TI0NJT6GgoigAACCCCAQHYBv4Wp0+/42VumBgRqIuD30taku23dfENeGvu0LBvcKePH3Z+ZfkOmxr8rj41PycwfnX5Dpg5+TT53YJVcvSb94qGtEROfaswD3kRtYujnQmrMgbnKeYIAAggUIMACogB0mkSgbAId/4BzbL9sWXaqrLzqYZGp2+Xit50tl+x+bnZxENO7o38puwaWyUmNhizb9EV5+vhaueWPfkv6OvwqpHUb15jUHC6pQMdztqT9KGMsS7aWspZxrMmEQLcCHX7r7rYZrkMAgTwEtF557jjbaWtl25Ggdec2dw+GIDgiezafK29+QTlFzhr6kmzbfIasar2/4RTpW/sZebJVNpAj914vH1m7QpZ23LDeBaWx1etiITVbc7WUl6x6U9qSrZ4CNSMQL/Dm9/v4MpxBAAEEEEAAAQQQQAABBFoCLCCYCAgoCXDnFSVYY9VqzAPuwmRrEmjMAVsCpEUAgaoJsICo2ojSHwQQQAABBBBAAAEEFAW4jasiLlXXW8C9uY9XHvOfA9Zu46oxD9z+bI3fQmhkzX8G2KsRV3tjRmIEEIgW4Dau0S4cRQABBBBAAAEEEEAAgQQBtjAl4HAKgboIuFdIrTy4jauVkdLNaWnO6krkX7slW0tZ8x8pakSgOAEWEMXZ03LFBTS2L1m7taClvFpZNeaBxvYl97+jRlYtV60vHxp5NVxd/zWyWnLVymrNVtOBuhGIE2ABESfDcQQQQAABBBBAAAEEEFggwAJiAQkHEMhHgF+t5+NovRaNeaD1yrNGVuvjl0d+XPNQpA4EECiTAAuIMo0GWRBAAAEEEEAAAQQQKLkAC4iSDxDxEAgLWNr77nJr5B0cHAyT5PZcI2tu4QxXpOWq9b4CrbwaQ6iVVcPWUlY3Vlp5NeYBdSJQhAALiCLUaRMBBBBAAAEEEEAAAaMC/CE5owNHbATqKmDtD8nVdZzoNwIIIIBA9QT4Q3LVG1N6VDIBjTdOWnvzrEZerb8DoZHVTcm6zwNLrm68NPJqzAGtrMxZJ6AzD2Zq5l8EqiHAFqZqjCO9QAABBBBAAAEEEECgJwJsYeoJM43UUcC96tjf39/qun9DXtSrm1nOtdcXVVfUMRcq6njUMV82TVudlE3b1saNG1uG4X+uueYaGRgYaPUhTa6ktly9aerw7cfV5c5HnZuYmFCfBz5bXD+S+hg+F5U1fN634/vZ7blwTl9X+Jir1x2POubb9FmTrvdl3Uf3SCrb3lZS+U7P+aytEAk5Oq13sfqi+ht1zLfbbpC1bNbrO8mV1JarJ9y3pLJR5bwzHxFAQMRvYZJg9iEy99Qf4iMCCGQQGB4eznB19KXNZjP6RMajGlldJI28AwMDwejoaMYeL7xcI6trRcOWrDquWnNWYw5oZWXOOgGdr10zNfMvArYF/HqBLUwsJxFQEtC4FaJSVKpVFNCYB/4V1Lxja2TNO6PF+nC1OGpkRgCBJAG2MCXpcA4BBEonwF2YSjckBEIAAQQQqImA38LEbyBqMuB0s/cCWnde6X1PaDGLgMY8CO/TzpKt/VqNrO1t1PFzXOs46vQZgWoLsICo9vjSu4oJWPvBUSOvtdu4VmwKdtwdjTngQmj9UK6Vt2O4FBdoZdWwtZTV0WvlTTGsFEHAhAALCBPDREgEEEAAAQQQQAABBMohwAKiHONACgQQQAABBBBAAAEETAiwgDAxTIS0KMCdVyyOWv6ZNeYBd2HKf5w0a9SYA5p5qRsBBBBYTIAFxGJCnEegSwGNfcRdRuGyAgU05oHW/myNrAXSl6ZpXEszFARBAIGcBFhA5ARJNQj0QsDaK88aeQcHB1WoNbKqBDVWqZar1qv6Wnk1hk0rq4atpaxurLTyaswD6kSgCAEWEEWo0yYCCCCAAAIIIIAAAkYFWEAYHThi11NAa+uKlqalvJayao2XRr3WXC3lJavGjJ2p05KtngI1IxAvwAIi3oYzCGQS0NgGkClQwsWW9mhr/R2IBJ5MpzTmgdb2Co2smfASLrY0Zy25OnJLtpayJkxnTiFgToAFhLkhIzACCCCAAAIIIIAAAsUJsIAozp6WKy7AK2MVH+CU3dOYB1rbKzSypmSqdDFcKz28dA6BWgqwgKjlsNNpBBBAAAEEEEAAAQS6E2AB0Z0bVyFQiIC1ve8aebmNayFTr+tGNeaAC6P1vgKtvF0DJlyolVXD1lJWR66VN2E4OYWAKYFGEASBS9xoNGT2qakOEBYBBOolMDIyIqtXr5ahoaF6dZzeIoAAAgggULCAXy/wG4iCB4LmEehEQGvveycZOilrKa+lrJ2MQdFlrblayktWvdltyVZPgZoRiBdgARFvwxkEMglYeuOkpazWbuOqYav1w41G1kz/EyVcTNYEnIynsM0IyOUI1ECALUw1GGS6WIyA/ybs9xP7z12aqGP+eLicP+Y+Rh2POtZeNqmtTsqmacvnTVM2KVf4+l27drlq5z3Wr18vy5cvbzmGy7pCUfVGHeumbB5tuXbj6kl7rr+/XyYmJlzxuf6mvbZ10ew/nbj4tuKyh493Um9S2XCdvn33MXw86fpOyobrjGvLH09Ttpe5etlWXgZpDPNqy9UTbi/JK6qcu54HAgjMCPgtTO59D62HyNxTf4iPCCCQQWB4eDjD1dGXNpvN6BMZj2pkdZE08g4MDASjo6MZe7zwco2srhUNW7LquGrNWY05oJWVOesEdL52zdTMvwjYFvDrBbYwsaREAAEEEEAAAQQQQACB1AIsIFJTURCBzgT8r8k7u6qY0payat3GVUtew1brFpMaWS25knVGgHmgNROoF4HqCLCAqM5Y0pOSCYT30uYVTesHx7zytddjKa9WVo15YOlN1Fqu7XMtr8818mrMAddfjax5ObbXYymrNdt2az5HoBcCLCB6oUwbCCCAAAIIIIAAAghURIAFREUGkm7UQ8DSK89uRDTyat3GVSNrPWZlci+1XLVe1dfKm6zU3VmtrBq2lrK60dDK291IcxUC5RNgAVG+MSERAggggAACCCCAAAKlFWABUdqhIZh1AUtvRLRuXeb8GvNAaz+5RtYyj02vsuHaK2naQQCBXgmwgOiVNO0ggAACCCCAAAIIIFABARYQFRhEulBOAY19xFo9tfQKqbXbuGrMA6392RpZmbPz/wqylkee9Vr6emApa55jRF0IFC3AAqLoEaB9BDoQ0Nq60kGEjopaymspa0eDUHBha66W8pJVb3JbstVToGYE4gVYQMTbcAYBBBBAAAEEEEAAAQTaBFhAtIHwKQJlFrC2dUUjL7dxLfMMXZhNYw64VrS2W2nlXSiT/YhWVg1bS1ndyGjlzT7q1IBAOQRYQJRjHEhRQQH25lZwULvoksY80NpeoZG1C7LKXYJr5YaUDiFQewEWELWfAgBoCWi8iqeVlXr1BDTmgdaroxpZ9WTt1IyrnbEiKQIIpBNgAZHOiVIIIIAAAggggAACCCAgIiwgmAYIICCWtlhYu40r00tHwNKc1RHQq9WSraWseiNGzQj0XoAFRO/NaRGBrgW09r53HWiRCy3ltZR1EfZSnbbmaikvWfWmuiVbPQVqRiBeoBEEQeBONxoNmX0aX5ozCCCAQMECIyMjsnr1ahkaGio4Cc0jgAACCCBQLwG/XuA3EPUad3prXMDam2c18nIbV1uTWGMOOAGtNyZr5dUYNa2sGraWsrqx0sqrMQ+oE4EiBFhAFKFOm7UQ0PgmXAu4inVSYx5o/XCjkbViw9lVd3Dtio2LEECgxAJsYSrx4BDNtoD7oaG/v7/VCb+fNuoHvyzn2uuLqivqmAsVdTzqmC+bpq1OyqZta+PGjS3D9n+azWarD2lyJbXl6k1Th28/ri53PurcxMSE+jzw2eL6kdTH8LmorOHzvh3fz27PhXP6usLHXL3ueNQx36bPmnS9L+s+ukdS2fa2ksp3es5nbYVIyNFpvYvVF9XfqGO+3XaDrGWzXt9JrqS2XD3hviWVjSrnnfmIAAKhtzy490C4h4h7CwQPBBDIS2B4eDivqubqaTabc8/zfKKR1eXTyDswMBCMjo7m2f1WXRpZXcUatmTVcdWasxpzQCsrc9YJ6HztmqmZfxGwLeDXC2xhYjmJgJIAtxdUgjVWrcY88K+g5k2hkTXvjBbrw9XiqJEZAQSSBNjClKTDOQQQKJ0Ad2Eq3ZAQCAEEEECgJgLchakmA003ixPgjZPF2ZepZY15EN6nnWdfNbLmmc9qXbhaHTlyI4BAnABbmOJkOI5ACQW0fnDU6qqlvJayao2XRr3WXC3lJavGjJ2p05KtngI1IxAvwAIi3oYzCNRGwNIrpFp/B6I2g12Rjlqas9bILdlaymptHpAXgSQBFhBJOpxDAAEEEEAAAQQQQACBeQIsIOZx8AkC+Qlw55X8LC3XpDEPuAuTrRmhMQdsCZAWAQSqJsAComojSn8QQAABBBBAAAEEEFAU4DauirhUXW8BtzeXVx7znwPWbuOqMQ/cGzw1fguhkTX/GWCvRlztjRmJEUAgWoDbuEa7cBQBBBBAAAEEEEAAAQQSBNjClIDDKQTKJmDt1oKW8lrKWrZ5mZTHmqulvGRNmnnZzlmyzdZTrkagOwEWEN25cRUCiwpY2r7ktlhYeVi7javGPNDYvuTGXyOr1ryyNGctubrxsmRrKavW/wvUi0ARAiwgilCnTQQQQAABBBBAAAEEjAqwgDA6cMQuvwCvjJV/jHqRUGMeaG2v0MjaC+Oyt4Fr2UeIfAgg0KkAC4hOxSiPAAKLCEzL8ckDMvbIXfLV6x+W/cemFynPaQQQQAABBBCwJHCypbBkRaDuAhb2vk9PfkP+9R9+T972ZFOePmlr7kM2ODiYe52uQi1blbCGKtVy1XpfgVZejSHTyqphaykrXw80Zit1Vk2A30BUbUTpDwIFCyxZsVm+ff9X5TO3XVpwEppHAAEEEEAAAQ0B/pCchip1IlB7gddlcvdGWXnzctn33G2y9rT8Xquw9ofkaj8VAEAAAQQQqIwAf0iuMkNJR8oqoPHGSXNvnn3tv+U+PFq3cbVkS1a9W41q2Gp8LXD/Y2lkdfVq5LWUVdM29y+IVIhAQQL5vSxYUAdoFgEEEEAAAQQQQAABBHonwBam3lnTUs0E/Kt4/g2J/nPHEHXMHw+X88fcx6jjUcfayya11UnZNG35vNdee4389K8fl3u//3bZsOlCeeTLu9ypeX2Iy7Vr10zZ1gUJ/wwPD7cc0+SKayvqeNQxF8Mdz6Otdgdft+9qXBvh6/r7+2ViYqJ1ic8bPu/rSjrnyvjzcW1GHY861t52J/UmlS1bW96sbLmSDDsZmzT9ysugl211a+Bd3fU8EEBgRsBvYZJg9iEy99Qf4iMCCGQQGB4eznB19KXNZjP6RMaj+Wd9LTh096WBvP2Dwb6jJzKmm3/5wMBAMDo6Ov9gDp/ZsQ0CsgZB/nN2ZhJp2FrK6hQ08mq4amV19WrlnZll/IuAXQG/XmALE0tKBJQELL16ZSmr1m1clabB3Kv8edZv7ZaYefbd12VpzlrK6nwt5bWU1c9dPiJQBQG2MFVhFOkDAqUT4C5MpRsSAiGAAAIIIJBRwG9h4jcQGSG5HIE4gfY9vnHlOF5tAY15YO2ONtUe4cV7pzEHFm+VEggggICeAAsIPVtqRiB3ARM/OB7bL1uWnSorr3pYZOp2ufhtZ8slu5+T6Zw0rN3GNadum63GxJwN6WrlDTWR21OtrBoLHktZ3QBp5c1t8KkIgYIFWEAUPAA0j0DlBE5bK9uOBO6uDNJsNmpa6S8AACAASURBVCUIjsiezecKX2wqN9J0CAEEEECgpgJ8T6/pwNNtfQHe3KdvbKEFjXnAm6gtjPybGTXmwJu18wwBBBDovQALiN6b0yICCCCAAAIIIIAAAmYFWECYHTqCl11AYx9x2ftMvoUCGvNAa3+2RtaFIvU7gmv9xpweI1B1ARYQVR9h+lcpAWtbVzTyav0dCI2slZp8XXZGy1VrW5BW3i75Ei/TyqphaymrQ9fKmzignETAkAALCEODRVQEEEAAAQQQQAABBIoWYAFR9AjQPgIdCFjbuqKRl9u4djBhSlBUYw64bmltC9LKqzEUWlk1bC1ldWOllVdjHlAnAkUIsIAoQp02ayGgsQ2gFnAV66TGPNDaXqGRtWLD2VV3cO2KjYsQQKDEAiwgSjw4REMAAQQQQAABBBBAoGwCLCDKNiLkqYyAxjaAyuDUqCMa80Bre4VG1hoNdWxXcY2l4QQCCBgVYAFhdOCIjQACCCCAAAIIIIBAEQIsIIpQp00EuhSwtvddIy+3ce1y8hR0mcYccF3Rel+BVl4Nfq2sGraWsrqx0sqrMQ+oE4EiBBpBEASu4UajIbNPi8hBmwgggEAqgZGREVm9erUMDQ2lKk8hBBBAAAEEEMhHwK8X+A1EPp7UgoBpAUt7tLVu42p6AGsY3tKctTY8lmwtZbU2D8iLQJIAC4gkHc4hkEFA4xub1ptnM3Qz8VJLebWyWpoHlrImTrwMJzXmgYar66JG1gx0iZdaymrNNhGekwgoCbCFSQmWahFwPzT09/e3IPx+2qhvolnOtdcXVVfUMRcq6njUMV82TVudlE3b1saNG1uG4X+uueYaGRgYaPUhTa6ktly9aerw7cfV5c5HnZuYmFCfBz5bXD+S+hg+F5U1fN634/vZ7blwTl9X+Jir1x2POubb9FmTrvdl3Uf3SCrb3lZS+U7P+aytEAk5Oq13sfqi+ht1zLfbbpC1bNbrO8mV1JarJ9y3pLJR5bwzHxFAIPSWB/ceCPcQcW+B4IEAAnkJDA8P51XVXD3NZnPueZ5PNLK6fBp5BwYGgtHR0Ty736pLI6urWMOWrDquWnNWYw5oZWXOOgGdr10zNfMvArYF/HqBLUwsJxFAAAEEEEAAAQQQQCC1AFuYUlNREIHqCrjtVhq3btQQO//882Xr1q3chUkD11CdluasIdZWVEu2lrJamwfkRSBKgLswRalwDIEcBdw3NisPK4sH56n1dyC0xkpjHoT3aeeZWyNrnvnCdVmas5ZcnbElW0tZw/OX5whYF2ALk/URJD8CCCCAAAIIIIAAAj0UYAHRQ2yaQiCrgLVXnjXyav0dCI2sWce7CtdruWq9qq+VV2MstbJq2FrK6sZKK6/GPKBOBIoQYAFRhDptIoAAAggggAACCCBgVIAFhNGBI3b5BdibW/4x6kVCjXng72Ofd36NrHlntFgfrhZHjcwIIJAkwAIiSYdzCCCAAAIIIIAAAgggME+ABcQ8Dj5BID8BjX3EWq8859fr+TVZyquVVWMeaO3P1siq5Tp/puX3mUZeDVfXY42s+UnOr8lSVmu286X5DIHeCLCA6I0zrSBQagFLWyys3ca11ANvOJylOWuN2ZKtpazW5gF5EUgSYAGRpMM5BBBAAAEEEEAAAQQQmCfAAmIeB58gUG4BS1tXnKRGXm7jWu452p5OYw64NrS2BWnlbXfJ43OtrBq2lrK6sdHKm8e4UwcCZRBgAVGGUSBDJQX41Xolh7XjTmnMA6395BpZOwar4AW4VnBQ6RICNRdgAVHzCUD39QQ0XsXTS0vNWgIa80Dr1VGNrFqulurF1dJokRUBBNIIsIBIo0QZBBBAAAEEEEAAAQQQaAmwgGAiIGBIQGvrihaBpbyWsmqNl0a91lwt5SWrxoydqdOSrZ4CNSMQL8ACIt6GMwjURsDSHm1u41qbaZnYUUtzNrEjJTxpydZS1hIONZEQ6FqgEQRB4K5uNBoy+7TryrgQAQQQ0BYYGRmR1atXy9DQkHZT1I8AAggggAACIQG/XuA3ECEUniJQdgFrb57VyMttXMs+S+fn05gDrgWtNyZr5Z2vks9nWlk1bC1ldaOjlTefkacWBIoXYAFR/BiQoKICGt+EK0pV6W5pzAOtH240slZ6cFN2DteUUBRDAAEzAmxhMjNUBLUm4H9o8Ht0/eeuH1HH/PFwOX/MfYw6HnWsvWxSW52UTdOWz5umbFKu8PW7du1y1c57rF+/XpYvX95yDJd1haLqjTrWTdk82nLtxtWT9lx/f79MTEy44nP9TXtt66LZfzpx8W3FZQ8f76TepLLhOn377mP4eNL1nZQN1xnXlj+epmwvc/WyrbwM0hjm1ZarJ9xekldUOXc9DwQQmBHwW5jc+x5aD5G5p/4QHxFAIIPA8PBwhqujL202m9EnMh7VyOoiaeQdGBgIRkdHM/Z44eUaWV0rGrZk1XHVmrMac0ArK3PWCeh87ZqpmX8RsC3g1wtsYWJJiYCSgH+VS6l6qjUioDEPtG4xqZHVyDCpxsRVlZfKEUCgAAG2MBWATpMIINC9AHdh6t6OKxFAAAEEEMgi4Lcw8RuILIpci0CCQHgvbUIxTlVcQGMe8CZqW5NGYw7YEiAtAghUTYAFRNVGlP4g0IWApR9wtG7j2gUblxQoYGnOFsjUVdOWbC1l7WowuAiBkgqwgCjpwBALgSgBrVeeo9rK45ilvJay5jE2varDmqulvGTVm8WWbPUUqBmBeAEWEPE2nEEAAQQQQAABBBBAAIE2ARYQbSB8ikBeAtx5JS9J2/VozAPuwmRrTmjMAVsCpEUAgaoJsICo2ojSn9IIsDe3NENRaBCNeaC1vUIja6H4JWkc15IMBDEQQCA3ARYQuVFSEQL6AtZeedbIOzg4qAKtkVUlqLFKtVy1XtXXyqsxbFpZNWwtZXVjpZVXYx5QJwJFCLCAKEKdNhFAAAEEEEAAAQQQMCrAAsLowBEbgTwFLG2x4DaueY683boszVlrypZsLWW1Ng/Ii0CSAAuIJB3OIZBBQGMbgNbe9wzdTLzUUl6trBrzQGt7hUZWLdfEiZfhpEZeDVfXRY2sGegSL7WU1ZptIjwnEVASYAGhBEu1CCCAAAIIIIAAAghUUYAFRBVHlT6VQoBfrZdiGAoPoTEPtF7N1cha+ACUIACuJRgEIiCAQK4CLCBy5aQyBBBAAAEEEEAAAQSqLcACotrjS+8qJmBp77uj18jLbVxtTWqNOeAEtN5XoJVXY9S0smrYWsqq9bVLYw5QJwJFCbCAKEqedhFAAAEEEEAAAQQQMCjQCIIgcLkbjYbMPjXYDSIjgEBdBEZGRmT16tUyNDRUly7TTwQQQAABBEoh4NcL/AaiFMNBiCoKaLxx0tqbZzXyav0dCI2sbl7XfR5YcnXjpZFXYw5oZWXOOgGdeTBTM/8iUA0BFhDVGEd6gQACCNRKQGOfvgPU2quvMThaWbVsNQyoEwEEihFgC1Mx7rRaAwH3qmN/f3+rp/4bfdSrm1nOtdcXVVfUMRcqfHxiYqKVNXwsPETueJq2fL1pyqZta+PGjeEoc8+bzWarD1nbchWmqcM3HJfbnY86523jzndbb/t17vO4fqQ9F5U17bWd5AnnjDJzdbnj4XL+mM/jsyZd78u6j+6RVLa9raTynZ5zWd1D6+tBUr9cu+G+JZX15dLY+rKtjsXYpmkr6Xp3ztWR1FaarN0Y+LZ9Pj4igMCMgN/C5N730HqIzD31h/iIAAIZBIaHhzNcHX1ps9mMPpHxqEZWF0kj78DAQDA6Opqxxwsv18jqWtGwtZRVax5ouGplZR7ofC3QctWcB65uHghYFvDrBX4DwZISAQRa+/StbFs4//zzZevWrbyJuubz1v2Gz8qctTZUlmwtZbU2D8iLQJSA/w0EC4goHY4hgEBpBbgLU2mHhmAIIIAAAhUX8AsI3kRd8YGme8UJuFfGeCCgMQ/a94TnpayRNa9s1uvB1voIkh8BBMICLCDCGjxHoOQC1n5w1Mhr7TauJZ9SPYmnMQ+0fiDXyKqFrJVVw9ZSVjdeWnm15gL1ItBrARYQvRanPQQQQAABBBBAAAEEDAuwgDA8eEQvtwBv8Cz3+PQqncY88LfHzLsPGlnzzmi1Pmytjhy5EUAgSoAFRJQKxxBAAAEEEEAAAQQQQCBSgAVEJAsHEcguoLGPWOuV5+y9ja7BUl6trBrzQGt/tkZWNzO0bKNnXbajWlk1bLWyZhOMvtpSVtcDa3mj1TmKgJ4ACwg9W2pGwIyApe0Vg4ODZlwJqidgac7qKejUbMnWUlad0aJWBIoRYAFRjDutIoAAAggggAACCCBgUoAFhMlhI3RdBaxtXdHIy21c7c1+jXmgsSXIyWpk1RoxrawatpayWpsHWvOLehFIEmABkaTDOQQyCPCr9Qx4FbpUYx5o7c/WyFqhoczUFWwz8XExAgiUTIAFRMkGhDjVEdB4Fa86OvXpicY8sPZqbn1GO76nGvMgvjXOIIAAAroCLCB0fakdgYoKvCFT4/fJlsFl0micJ5t2Pi1T02m6Oi3H9t8kyxoNafj/Ltktk6muTVM/ZRBAAAEEEEBAW4AFhLYw9SNQOYFpOT7+Zbn8+h/LJQ88L8GJx2XTy7fL5TsOyvHF+jr9gjxx/7dkaq5cn6y77EJZzleiORGeIIAAAgggUHYBvm2XfYTIh0BIoBR736cn5aGbHpELbvmUrO07RWTJWbL2xuvkgh13yUOTr4fStt9LfVqOPzsmXz3jC3I0CCRo/XdE9mw+Vzr5QqR1G1ct23kgNf1Ew1brPQUaWbWGXSurhq2lrG68tPJqzQXqRaDXAo3AfRcXaW0nmH3a6wy0hwAChgSmJ3fLB1Y+LpcdasrmFW+ZTf53sn/Lh2Tbyrvlz2MXBK7M++Xi7e+Ukbs/KZdc9D5Zu+K0jns+MjIiq1evlqGhoY6v5QIEEEAAAQQQ6F7AbT9264VOXvjrvjWuRACBXASKf/Ps63L4qcdlb99yefeZp7T16eey98Hvy+HQ+xnCeacn/0y2bR8Xkb2y/aoNcvHKS2XL2HOLb3tqa4XbuLaBGPg0PA/yiqv1pmSNrHn1ub0erawatpayOmetvO1jyOcIWBVgAWF15MhdegGNb8LFd/q4vHjoxyLnLZezl3b25WPJis2yJwjkxJFn5NG7R2SNW0hsuF6+Mv5q8d1STKAxD7R+uNHIqkhrqmpsTQ0XYRFAYBEBtjAtAsRpBLoV8D8w+P3E/nNXX9SxuONJZcN1xl3vj6cpu3hbr8kLT/0fMvrye+TQj/fKiiUiM/XOP/6ffv9a1+zcI6rePx75V3Lz5Zvki8cvlE0XvUv87zN27do1d13Sk+Hh4ZZj1n65NsJ1RGV1ZdzxcDl/rP16fzyubFx5d9w92q9zx9oz9ff3y8TERKu8Pxd1bdK5qHpbFUa0Fz7ens+3ET4edSyuvaSy4TrjrvfH05RNasvVE64jqWy4nG+/k+s7KZumLZ8hTdms/cqrrbwNkvrVbVu+Tnc9DwQQmBHwW5jcPqbWQ2TuqT/ERwQQyCAwPDyc4eroS5vNZvSJjEfTZ30tOHT3pYH0bQ32HT0RavXlYN/IqkDW3R0cCh1OznsiOLpva9C3oK5QtRFPBwYGgtHR0Ygz2Q4lZ+2+7vS26duwlNX1SiOvhqtWVlevRl4NV7I6AZ05O1Mz/yJgW8CvFzrbg8DyCwEEai7wFll+0ftlXbvC9N/J8z98tcNbsi6RpWcvl/O62A7V3jyfI4AAAggggEDvBNjC1DtrWkKgGgLTz8nuD1wlh7Y8JtvWnjHTp2P7Zcu5X5GVB8J3Zlqsu+6Pym2XO+QT8nlfz2KXiAh3YUqBRBEEEEAAAQQUBPwWJn4DoYBLlQg4gfb9yJVRWbJCPvr5j8jBW78s+6feEJl+SfbfsUMOXne9fHTutq5vyEtjn5Zlgztl/Li7LZP7y9XflcfGp2TmJk1vyNTBr8nnDqySq9fMLkIqAzS/IxrzgDdRzze28JnGPLDQbzIigEA1BVhAVHNc6RUCigJLZOmqT8kD286Qe1f9sjRO2ix7Vv4HeeC6C2RpUqtH/1J2DSyTkxoNWbbpi/L08bVyyx/9lvTxVShJjXMIIIAAAgiUToBv3aUbEgIhEC9QnleeT5G+Cz4l9x5xf1F6j2zbdEHbQuAUOWvoS7Jt8xmyqnW711Okb+1n5MnZv0B95N7r5SNrVyQvOGIY+DsQMTAlPqwxb7Ve0dfIqjU0Wlk1bC1ldeOllVdrLlAvAr0WYAHRa3HaQwABBBBAAAEEEEDAsAALCMODR/RyC3AP8XKPT6/SacyDK664QiW+RlaVoAYrxdbgoBEZAQRiBVhAxNJwAgEEEEAAAQQQQAABBNoFuI1ruwifI5CTgNtHzKuOOWGGqrF2G1eNeeD2Z2v8FkIja2joav0U21oPP51HoDIC3Ma1MkNJRxBAAAEEEEAAAQQQ6J0AW5h6Z01LCCCAAAIIIIAAAgiYF2ABYX4I6UBZBTS2L2ndWtBtr9B4aOS1dhtXjXmgsX3Jjb9GVlevxjywNGe1bDVcXVYNW0tZteasq5cHAlURYAFRlZGkHwgggAACCCCAAAII9ECABUQPkGmingIar+LVU9J2rzXmgbVXc22PYD7pNeZBPsmoBQEEEOhcgAVE52ZcgQACCCCAAAIIIIBAbQVYQNR26Ok4Am8KaO19f7OF/J4NDg7mVxk1mRWwNGetIVuytZTV2jwgLwJJAiwgknQ4h0DJBLTePKvVTUt5LWXVGi+tei3ZklVnFlhydQLW8uqMGrUiEC/AH5KLt+EMAgiUUMDaH5IrISGREEAAAQQQ6EqAPyTXFRsXIVCsgLU3z2rktXYb12JnTDla15gHWm9K1siqNQpaWTVsLWV146WVV2suUC8CvRZgC1OvxWmvNgIa34Rrg1ehjmrMA60fbjSyVmgoM3UF20x8XIwAAiUTYAtTyQaEONURcD8w9Pf3tzrk99NG/eCX5pyrpP1ad13UsSxl47L0uq1wHzZu3NgybP+n2Wy29imnMUjqV7gt30ZceXe+03MTExO5zYP2vobzJPUj7bmorGmvdeXcw/u45+15/bnw8ahjvp5wOX/M19ueNamsu8Y9ktpy59PUMVNTfF1x7bTnjWov7tq0babJn2SQ5nqfMU3ZpLba+59Utqi2fCbvz0cEEBDxW5gkmH2IzD31h/iIAAIZBIaHhzNcHX1ps9mMPpHxqEZWF0kj78DAQDA6Opqxxwsv18jqWtGwtZRVax5ouGplZR7ofC3QctWcB65uHghYFvDrBbYwsZxEQEmA2wsqwRqrVmMeaL0yqpHV2HCpxcVWjZaKEUCgAAG2MBWATpMIINC9AHdh6t6OKxFAAAEEEMgi4Lcw8RuILIpci0CCAG+aTMCp0SmNedC+JzwvTo2seWWzXg+21keQ/AggEBZgARHW4DkCJRfQ+sFRq9uW8lrKqjVeWvVasiWrziyw5OoErOXVGTVqRSBegAVEvA1nEKiNgKVXR7X+DkRtBrsiHbU0Z62RW7K1lNXaPCAvAkkCLCCSdDiHAAIIIIAAAggggAAC8wRYQMzj4BME8hPgriv5WVquSWMecBcmezNCYx7YUyAxAghURYAFRFVGkn6UToBfrZduSAoJpDEPtPZna2QtBL2EjWJbwkEhEgIIdC3AAqJrOi5EoPcC1l551sg7ODioAq+RVSWowUo1bLVe0dfIqjVkWlk1bC1ldeOllVdrLlAvAr0WYAHRa3HaQwABBBBAAAEEEEDAsAALCMODR/T6CWhtXdGStJTXUlat8dKq15ItWXVmgSVXJ2Atr86oUSsC8QIsIOJtOINAJgGNbQCZAiVcbGl/trXbuGrMA63tFRpZE6ZdplOW5qzrKLaZhjv2YmvzILYjnEDAmAALCGMDRlwEEEAAAQQQQAABBIoUYAFRpD5tV1qAV8YqPbypO6cxD7S2V2hkTQ1V8YLYVnyA6R4CNRNgAVGzAae7CCCAAAIIIIAAAghkEWABkUWPaxHosYC1ve8aebmNa48nXQ7NacwDrfcUaGTNgTCyCq2sGraWsjpsrbyRA8lBBAwKNIIgCFzuRqMhs08NdoPICCBQF4GRkRFZvXq1DA0N1aXL9BMBBBBAAIFSCPj1Ar+BKMVwEAKBdAJae9/Ttd55KUt5LWXtfCSKvcKSLVl15oolVydgLa/OqFErAvECLCDibTiDQCYBS2+atJTV2m1cNWy1frjRyJrpf6KEiy1ldd2wlJesCROPUwgg0BJgAcFEQAABBBBAAAEEEEAAgdQCvAciNRUFEehMwL+K59+Q6D93tUQdizueVDZcZ9z1/niasmVpy2X2eXft2uU+XfAYHh5uOfpyvkBUH6KOufJRx6OO+bJp2lqsrDsfV0/UOV9f+Fx/f79MTEy4Q3N9CJ9vnVjkXPjauDxRx6OOtbedZNhJ2TRt+X6kKdvLXL1sKy+DNIZ5tZX3PNDw9nW6rDwQQGBGwL8Hwr1xuvUQmXvqD/ERAQQyCAwPD2e4OvrSZrMZfSLjUY2sLpJG3oGBgWB0dDRjjxderpHVtaJhaymr1jzQcNXKyjzQ+Vqg5ao5D1zdPBCwLODXC2xhYkmJgJKApVevLGXVuo2r0jSY9xuCvNrQusWkpXlgKasbd0t5yZrX/6nUg0B1BdjCVN2xpWcIVFKA27hWcljpFAIIIICAAQG/hYnfQBgYLCLaFGjfT2yzF6TOKqAxD7gLU9ZR6f31GvOg972gRQQQQGBGgAUEMwEBQwLWfnDUyKt1G1eNrIamlmpUDVutH8g1smrhamXVsLWU1Y2XVl6tuUC9CPRagAVEr8VpDwEEEEAAAQQQQAABwwIsIAwPHtHLLWDpjYjllrSdTmMe8CZqe3NCYx7YUyAxAghURYAFRFVGkn4ggAACCCCAAAIIINADARYQPUCmiXoKaOwj1pK09Oqotdu4aswDrf3ZGlmZszMC2OrMBEtfu3QEqBWBYgRYQBTjTqsIdCWgtXWlqzApLrKU11LWFPSlKmLJlqw6U8eSqxOwlldn1KgVgXgBFhDxNpxBAAEEEEAAAQQQQACBNgEWEG0gfIpAmQWsbV3RyMttXMs8Q6OzacwDrS1BGlmjVbIf1cqqYWspqxsZrbzZR50aECiHAAuIcowDKSoowN7cCg5qF13SmAda2ys0snZBVslLsK3ksNIpBGorwAKitkNPx7UFNF7F085M/fkLaMwDrVdHNbLmL2qzRmxtjhupEUAgWoAFRLQLRxFAAAEEEEAAAQQQQCBCgAVEBAqHEKibgKXtFdZu41q3udSr/lqas70yyasdS7aWsuY1PtSDQBkEWECUYRTIgEBKAa297ymb77iYpbyWsnY8EAVfYMmWrDqTxZKrE7CWV2fUqBWBeIFGEASBO91oNGT2aXxpziCAAAIFC4yMjMjq1atlaGio4CQ0jwACCCCAQL0E/HqB30DUa9zprXEBa2+e1cjLbVztTWKNeaD1pmSNrFojppVVw9ZSVjdeWnm15gL1ItBrARYQvRanvdoIaHwTrg1ehTqqMQ+0frjRyFqhoczUFWwz8XExAgiUTIAtTCUbEOJUR8D9wNDf39/qkN9PG/WDX5pzrpL2a911UceylI3L0uu2wn3YuHFjy7D9n2az2dqnnMYgqV/htnwbceXd+U7PTUxM5DYP2vsazpPUj7TnorKmvdaVcw/v45635/Xnwsejjvl6wuX8MV9ve9aksu4a90hqy51PU8dMTfF1xbXTnjeqvbhr07aZJn+SQZrrfcY0ZZPaau9/Utmi2vKZvD8fEUAg9JYH9x4I9xBxb4HggQACeQkMDw/nVdVcPc1mc+55nk80srp8GnkHBgaC0dHRPLvfqksjq6tYw9ZSVq15oOGqlZV5oPO1QMtVcx64unkgYFnArxfYwsRyEgEEEEAAAQQQQAABBFILsIUpNRUFEUCgDALchakMo0AGBBBAAIE6CnAXpjqOOn3uqQBvmuwpd2kb05gH7XvC8+q8Rta8slmvB1vrI0h+BBAIC7CFKazBcwRKLqD1g6NWty3ltZRVa7y06rVkS1adWWDJ1QlYy6szatSKQLwAC4h4G84gUBsBS6+Oav0diNoMdkU6amnOWiO3ZGspq7V5QF4EkgRYQCTpcA4BBBBAAAEEEEAAAQTmCbCAmMfBJwjkJ7Bz5878KqMmswIa80Dr/vQaWc0OXM7Bsc0ZlOoQQKBQARYQhfLTOAIIIIAAAggggAACtgS4jaut8SKtIQG3N5dXHfMfMGu3cdWYB+4Nnhq/hdDImv8MsFkjtjbHjdQIIDBfgNu4zvfgMwQQQAABBBBAAAEEEEghwBamFEgUQQABBBBAAAEEEEAAgRkBFhDMBASUBDS2L2ndm9xtr9B4aOTVuo2rRlZnqjEPNLYvaWV19WrYWpqzWrYari6rhq2lrFpz1tXLA4GqCLCAqMpI0g8EEEAAAQQQQAABBHogwAKiB8g0UU8BjVfx6ilpu9ca88Daq7m2RzCf9BrzIJ9k1IIAAgh0LsAConMzrkAAAQQQQAABowLNZlO+9KUvyWuvvWa0B8RGoHgBFhDFjwEJEEgtoLX3PXWADgtaymspa4fDUHhxS7Zk1ZkuZXI988wz5eqrr5bf/M3flKeffjqyw2XKGxmQgwgULMACouABoHkEyiCg8UZfrX4NDg5qVU29hgQszVlDrK2olmy7ybpu3Tr5+7//e1mzZo1cdNFF4v62zCuvvGJtmMiLQKEC/CG5QvlpHAEEOhWw9ofkOu0f5RFAoHcCe/fulZtvvrnV4I033ihDQ0O9a5yWEDAowB+SMzhoRLYloPGmSWtvntXIa+02rswDbuPqvnLVfR5ofC3Iw9X9NuJ73/uefPjDH5YNGzbI7/7u78qLL76ocuthW9/BSItAssDJyac5iwAC3QocP35cJicnu7088rqfSU/+XAAAHNpJREFU/OQnudfpGvrpT3+qUq9G3tdff12OHDmyaN7nn39e3BikfTzzzDPy1re+NW3x1OUOHz4sY2NjqcunKWgpq+uPRl4NV62srl6NvBquZcv6gx/8wEWKfTz11FOtLUixBTo4sWnTJjlw4IB8/etfl1tuuaWDKymKQP0E2MJUvzGnxz0ScL/m41GcwDnnnCPveMc7WgH8+ybaf3sRPu5+GBsYGJDwsXB6dzzp+riy7fW6cnH1RJ1zx9oz+TrD56Ku9ddFnQtf6/P4ev11/rgr6x5pDdqvT6q3vexsU4u25evMkivclnvu+uvr7TZXVJ3uWFK93bbl63T1uzqixsv3Ky5X+Li/3tfbba5wneH2k+qNa8u92fnhhx/2VbY+Xnnlla2P99xzj3z729+W9evXS/hYuHDU8ahj7hr3nojbbrtNXn31VfnYxz4m3/zmN8NV8RwBBETEb2FiAcF0QEBJwP9Plmf1bhvAxo0bJQiCPKud+4KQa6WhLzR51nv++efL1q1bc9+rrDFert8a9WrUqZVVq14MdOaW1niV+WuXewP1HXfcIXfeeafccMMN4t4L8Z3vfEe4E5ObDTwQmC/gv/ayhWm+C58hgAACCCCAQE0Ewm+i3rNnj7j3RPBAAIHFBbiN6+JGlECgNAKVfkVsekrG790ig42GNJZtkp0Hp2Q6Qt5vdYg4xSEEECipQNm+drk3Srs3TF9yySWtN1A//vjj8xYPZctb0mElVo0FWEDUePDpOgLlEXhVxnf8nlx/6H3ywIlAToz/G3l5y+/JjvFXyxORJAggUAkB91uHd73rXfJXf/VX8uyzz8pNN90kp59+eiX6RicQ6JUAC4heSdMOAjkJ5P3+BxdreHg4p3Tzq0mbdXpyTG7a8etyy40XS98SkSV9F8uNt/y67LhpTCbbfg3h3+g5v6Xsn6XN2mlLGrbNZrPTGIWW17DVcHVIGlm18LWyVt3W3R3u3nvvbd2+9b3vfa/W8FAvApUWYAFR6eGlc1UT0LqXupZTuryvy+GnHpe95y2Xs5f6L0lL5LSB98kVP3pcnjr8ula8efWmyzrvEj5JKWDJlqwpB7XDYmVydTeicP+deuqpsb0oU97YkJxAoEAB/926wAg0jQACtRaYfl6eevAp6Xvvu+XMBV+RnpIHn3o+8r0QtTaj8wggoCTwgoxtWt5aYDQa6+Uut41yekoO7twkyxoNWX7XuPxCqWWqRcCSAHdhsjRaZEWgigLHj8ihH4mcd9kyWVrB/u3cuTP3XvEGz9xJqRCBWYF3ydC9h+XeVf9evnfHF2XHQ3vkPf/lOXnhA/9Rjlx7L0oIIDArsOD1PmQQQAABBPITuPbaa/OrbLYmtlfkTkqFRgW03q/ReMdK+dgVq2Rq+23yp7/6cfn4uacZFSI2AjoCLCB0XKkVAZU3Jmu98qzxKrmbAqnyLl0mK88T+dGhI3I8xbzRuo1rqqwp8lkuovXDmIZtoXO2i0HWsNVwdV3TsLWU1RlcccW/k4FL1kmf/Lr8L//sfxB+WOpi0nNJpQX4f6LSw0vnEDAgsOTdctFlFy0IOv2T5+WHUxfJZRe9m2/eC3Q4gAACugK/kH949ZiI8D4sXWdqtyrAAsLqyJEbgRwFNLbZpI/3Fll+0fvlvPuekGeO+Xu2TsvxFw/Lj9a9Xy5a/pZ5VWndxnVeI3xSeoFi52xanmMyuf8xeeSuTXLPUy+I+3HUwsOG7YykVtbpl74tt37nl+V31qT/7aiFsSUjAnkJsIDIS5J6aibwhkyN3ydbBpdJo3GebNr5tEz5n31nJaK3AUzLsf03te7m0XB/cdn9d8nuBX/rIA7T2t73tHmXrBiSz1/3N3LrHftajtNT++SOW/9Grvv8kKzo0VeptFnjxibuePQ8iCud7njn20EWn6+u5cisx/bLlmWzc7U1Zz8quyc7u7Wulm06rc5K5Zf1dZncfa384b3fkGtuaMqvrP29zoKkKJ1f1hSNZSzSXdY3F2DLt+zvYAH2d7J/y8DM19fWnF0ml+x+Lv3d3Kb/Vq7duFvW/dFn5JNXXCRT7sWNl34gO296TF5q+zqfkYXLETAr0KNvzWZ9CI5AhMC0HB//slx+/Y/lkgeel+DE47Lp5dvl8h0HF9/DP/2CPHH/t2RqrtY+WXfZhbK89v8nvl1WXfcnsu0ff1NWndSQky5/Qlbe9Sdy3aq3z0nxpFuBDPNV3pCXnhiT+96csCIRvxXqNlm1r3uLrNh8t9x/z+1y27q+andVpXfzF2A/66CN6Zf+i9x/33joipRbIX8xLnctb0jj4q+KvP9/laGzlsqy9/wLWTP1Dbn1i0fkt2/6oJxV+6/VIVae1lqA/xVqPfx0viuB6Ul56KZH5IJbPiVr+04RWXKWrL3xOrlgx13yUOiV2YW/Wp+W48+OyVfP+IIcDYLWX7wNgiOyZ/O57PF3A7GkTy649l454mye3CabVvVVwmXhPOhq1s27qKNXc1POV9fAgqzHfyj/+aunyzePnpidr4EEezb37LdC8zpt/JNj+//EeA96Hb/bBdir8ux/fkzO+ObLb87Z4CHZvGL+VsjI3py8Sq4/7L7+fF4GznR/ZG6JLF11rTwZHJEntw3Jirk/dBl5NQcRqJUAC4haDTedzUNg+vD35cG9Z8nKs0N/teC0fy6XXPHSIn/07BU5+ND9snf7Nvnc7jHZP2llR3QeatRRlED383Vajh18VHbs/brc+rm7ZWz/5OK/YSuqk7SLgBc4NiEP7WjK9lvvlN1jB2TyOHuOPA0fEchTgAVEnprUVQOB1+XwU4/L3r7l8u4zT2nr789l74Pfl8Mx36+mJ/9Mtm13v1bfK9uv2iAXr7xUtow919EPZZ3vfW+LGPNp5N73mLKdHNbIy21cOxmB7uerTE/KI9u+IVMyJQe2/1vZcPEa+eCWsa5+INOYB5bmbCcj1klZDVfXvoZtb7K+LpOPfEW2uy13B7bLVRsGZeUHb5axLl6s0crbyfhSFoEyC7CAKPPokK2EAsflxUM/FjlvuZy9yK+z278JL1mxWfYEgZw48ow8eveIrHELiQ3Xy1fGXy1hP4mUl0D7PMij3vQ/3KSfry7XvKxLzpXNe45IcOKIPPPo12RkjfuZ7NPyya8809GiN4/+VqGO0xTeRF0Fl3z74LY9PSRB8HM58sy35O6RdSIHbpcNn7xbxvlNRL7U1FZ7ARYQtZ8CAPRaYEnfKvnQ5m2y78he2bpmQnY8NNHB3UV00i7Y+67TTC61chvXXBjTV7KkT1Z96Hdl276/lH1bz5MDOx6Vg3O3201fTd4lLc3ZvPuuXZ8l2+isp0jfqvWyedu35Mi+z8qaA/fLQwdf0WajfgRqJcAColbDTWdjBabGZJO/rWrsx0G5a1zk7JW/JvKjw/LiIq9oRX9jezPBkr6L5cZbPi4y7+8fvHk+6llHb56NqqDHxyzl1cq62DzoZkjSZ12aer66HIlZWzcL2CIjslf2PNPZD2Pp83ajke81Wlk13kStlTVf0Znaisl6ivSt/ZTcMiJy357/q6MXaorJqyFPnQjoCDSCIAhc1e5+9LNPdVqiVgQqIjA9uVs+sOawbHnuNll72uwafPo52f2B9fLgZd+WP5+9q5L7Yay/v7/Va7/lpP2bUvCT78n9T1wo//HPN8tf3H/fAiF/nTvRfq07F3UsS1nfXlS9Uce02mqvN5zrwQcflHPOOUcGBgYkrUH4ele3f3R63F0Xd03cuYmJiUXnQdy1i+UMX+eeR42Rn6/9nz1X/umpjZkqgyn5/+7/2tx8vf++mbkXlXVevcGUfO+uR+XCR/bP3dUmqs2ZRqLzzKsvwXOxsW3PGpcjfDxu7Do97voQd82Ccy2z2+VPf/li2XHNh8Td2yf1tR5y9uNi14X7uiDHInW4utNc7+tNUzYub9TxqGOttj52vnzivf9CRv/HfyfbLvunsX6x119xqUzuvko+8v33yPW/2Sfu/4D4svMNfLlZOj4ggEB4veAWEO4h4tYPPBBAYFGBE38T3L3uwmBk38tvFj26LxjpuzS4+9Brc8eGh4fnnkc/OREc3Xd7sDVcT3TBuaPNZnPueZ5PFs/aXWt55HVfm6L+6y5R/FV5ZI2qXcO2o6wp56vLvmjWo/uCrVv3BUejOppwrKO8CfWETy2aNVy4g+e5Z2359wVvHdjQsdtisXPPOtughm3XWWf9+kai593iWV8O9m29Pdh39MRinPPOd513Xi18gkD1BPx6gS1MrCcR6FRgyQr56Oc/Igdv/bLsn3pDZPol2X/HDjl43fXy0bl7jb8hxw8/KcsGd86+ec/9JeDvymPjU7N/DfUNmTr4NfncgVVy9ZozOk1Qq/Lu9Y3wf+43D6Ojo7UyyNTZlPP1pbFPy//+yMTcm02np8blscfG5/7C+vTU07LzcxPyvqsvktMyBarLxbN/df6kX5er9k7J//vMqLyt0flf8a6LVlf9nP5bOfx/PiCDd83+Ec/pKRl/7Lsy7r4uu8f0lBzcuUMOvO8KWeN/W9xVQ1yEAAILBPzayK8o/Od8RACBJIGfB0f+4kvBxj736vi6YOQbfxEcmfcC18+DF0c/FfSt2RE88w/uxM+DI/s+G6yZfTW9b+OdwcP7DgX/kNRED88t/ipeD8Ms0tTAwEAwOjq6SClOzxfodL4GwYkje4Ota/pmfvvTtzG48+Eng0OtuTy/5qI+szRnizLqtt1y2Lrf0G4N+ub9BnL+b3mDE88H63/jnwRr7vyLma+lJ14M9m1dN/sby38WbLzzT4N9hzr9fVm3alyHQD0E/HqB90AsWFJxAAEEyiwwMjIiq1evlqGhoTLHJBsCCCCAAAKVE/DvmWYLU+WGlg6VRSDxjjZlCUkOdQGNedD+Bta8OqGRNa9s1uvB1voIkh8BBMICLCDCGjxHoOQC1n5w1Mir9XcgNLKWfDr1LJ6GrdYP5BpZtaC1smrYWsrqxksrr9ZcoF4Eei3AAqLX4rSHAAIIIIAAAggggIBhARYQhgeP6OUW2LlzZ7kDkq4nAhrzQOv+9BpZe4JsoBFsDQwSERFAILUAC4jUVBREAAEEEEAAAQQQQAABFhDMAQSUBDT2EWu98qxEMPcXX7Xqz7NeLVuNeaC1P1sjqxsjLds8x9/XpZVVw1Yrq7fI86OlrK7f1vLmOVbUhUAaARYQaZQog0DFBSxtrxgcHKz4aNC9NAKW5mya/pSpjCVbS1nLNMZkQSCrAAuIrIJcjwACCCCAAAIIIIBAjQRYQNRosOmqfQFrW1c08nIbV3vzWGMeaGwJcrIaWbVGTCurhq2lrNbmgdb8ol4EkgRYQCTpcA6BDAL8aj0DXoUu1ZgHWvuzNbJWaCgzdQXbTHxcjAACJRNgAVGyASFOdQQ0XsWrjk59eqIxD6y9mluf0Y7vqcY8iG+NMwgggICuAAsIXV9qRwABBBBAAAEEEECgUgIsICo1nHSm6gJaW1e03CzltZRVa7y06rVkS1adWWDJ1QlYy6szatSKQLwAC4h4G84gUBsBS/uzuY1rbaZlYkctzdnEjpTwpCVbS1lLONREQqBrgUYQBIG7utFoyOzTrivjQgQQQEBbYGRkRFavXi1DQ0PaTVE/AggggAACCIQE/HqB30CEUHiKQNkFrL15ViMvt3Et+yxdmE9jHmi9KVkj60KRfI5oZdWwtZTVjY5W3nxGnloQKF6ABUTxY0CCigpofBOuKFWlu6UxD7R+uNHIWunB7aBz2HaARVEEECi9AFuYSj9EBLQq4H9g8Ht0/eeuP1HH4o4nlQ3XGXe9P56mbFnacpl93l27drlP5z3Wr18vy5cvbzn6cr5AVB+ijrnyUcejjvmyadparKw7H1dP1DlfX/hcf3+/TExMuENzfQifb51Y5Fz42rg8UcejjrW3nWTYSdk0bfl+pCnby1y9bCsvgzSGebWV9zzQ8PZ1uqw8EEBgRsBvYXLve2g9ROae+kN8RACBDALDw8MZro6+tNlsRp/IeFQjq4ukkXdgYCAYHR3N2OOFl2tkda1o2FrKqjUPNFy1sjIPdL4WaLlqzgNXNw8ELAv49QJbmFhSIqAkwKtXSrDGqtWYB1q3mNTIamy41OJiq0ZLxQggUIAAW5gKQKdJBBDoXoC7MHVvx5UIIIAAAghkEfBbmPgNRBZFrkUgQaB9P3FCUU5VWEBjHvAmansTRmMe2FMgMQIIVEWABURVRpJ+IJBBwNIPN1q3cc3Ax6UFCFiaswXwZGrSkq2lrJkGhYsRKJkAC4iSDQhxEEgS0HrlOanNLOcs5bWUNcuYFHGtJVuy6swQS65OwFpenVGjVgTiBVhAxNtwBgEEEEAAAQQQQAABBNoEWEC0gfApAnkJcNeVvCRt16MxD7gLk705oTEP7CmQGAEEqiLAAqIqI0k/EEAAAQQQQAABBBDogQC3ce0BMk3UU8C9uY9XHfMfe2u3cdWYB25/tsZvITSy5j8DbNaIrc1xIzUCCMwX4Dau8z34DAEEEEAAAQQQQAABBFIIsIUpBRJFEEAAAQQQQAABBBBAYEaABQQzAQElAY3tS1q3FnTbKzQeGnm1/g6ERlZnqjEPNLYvaWV19WrYWpqzWrYari6rhq2lrFpz1tXLA4GqCLCAqMpI0g8EEEAAAQQQQAABBHogwAKiB8g0UU8BjVfx6ik5v9fvfOc75Qc/+MH8gyX+TGMeWHs1t8TD07NoGvOgZ+FpCAEEEGgTYAHRBsKnCCBQboFf+qVfKndA0iGAAAIIIFBxARYQFR9gulctAWt73zXyXnnllSqDqpFVJajBSjVsNd5b4mg1smoNmVZWDVtLWa3NA635Rb0IJAmwgEjS4RwCCCCAAAIIIIAAAgjME+APyc3j4BMEECi7wNjYWOs9ENu3by97VPIhgAACCCBQKQH+kFylhpPOlFFA402T1t48q5H3nnvuURlujawuKPOA27gyD3TmgJarq1fr64GrmwcCVRBgC1MVRpE+IIAAAggggAACCCDQIwG2MPUImmbqJ+Beee7v72913L+BMOpVrTTnXCXt17rroo5lKRuXpddthfuwcePGlmH4n9/+7d+Wyy67rPWG1zQGSf0Kt+XbiCvvznd6bmJiIrd50N7XcJ6kfqQ9F5U17bWunHt4H/e8Pa8/Fz4edczXEy7nj/l627MmlXXXuEdSW+58mjpmaoqvK66d9rxR7cVdm7bNNPmTDNJc7zOmKZvUVnv/k8oW1ZbP5P35iAACIn4LkwSzD5G5p/4QHxFAIIPA8PBwhqujL202m9EnMh7VyOoiaeRdv359cMMNN2Ts8cLLNbK6VjRsLWXVmgcarlpZmQc6Xwu0XDXngaubBwKWBfx6gS1MLCcRUBLQuBWiUlSqVRSwNA8sZVUcMpWqsVVhpVIEEChIgC1MBcHTLAIIdCfAXZi6c+MqBBBAAAEEsgr4LUz8BiKrJNcjECOgcfedmKY4XGIBS/PAUtYSD3lkNGwjWTiIAAJGBVhAGB04YtdToP3NhHkpaP1wo5HX2m1c8xqjcD0aruH6836ukdfSnM3b09en4erq1rC1lNUZaOX1Y8dHBKwLsICwPoLkRwABBBBAAAEEEECghwIsIHqITVMIIIAAAggggAACCFgXYAFhfQTJX1oB7rpS2qHpaTBL88BS1p4OYg6NYZsDIlUggEBpBFhAlGYoCFI1AY19xFUzqkN/LM0DS1mtzR1srY0YeRFAIEmA27gm6XAOgQwC7gcGXnXMABhzqbXbuFqaB5ayxkyP0h7GtrRDQzAEEOhAgNu4doBFUQQQQAABBBBAAAEEEJgRYAsTMwEBQwLWbi1oKS9Z9f5HwFbHFlcdV1erJVs9BWpGIF6ABUS8DWcQyCRgafuS217R2eMNmRq/T7YMLpNG4zzZtPNpmZpOU8O0HNt/kyxrNMT9GrT13yW7ZTLVtTP1a/0diDTpuyljaR5Yytr5nO1m9PK7Btv8LMM1WZsH4ew8R8CyAAsIy6NHdgQKEZiW4+Nflsuv/7Fc8sDzEpx4XDa9fLtcvuOgHF8sz/QL8sT935KpuXJ9su6yC2U5X4nmRHiCAAIIIIBA2QX4tl32ESKfWYHKvjI2PSkP3fSIXHDLp2Rt3ykiS86StTdeJxfsuEsemnw9Ybym5fizY/LVM74gR4NAgtZ/R2TP5nOlyl+ILM0DS1kTJlopT2FbymEhFAIIdClQ5e/bXZJwGQIIJAlMH/6+PLj3LFl59tI3i532z+WSK16SB596XuJ3I70iBx+6X/Zu3yaf2z0m+yePvXk9zxBAAAEEEEDAjAALCDNDRVAERK644goVhvT7s1+Xw089Lnv7lsu7zzylLcvPZe+D35fDoRVEOO/05J/Jtu3jIrJXtl+1QS5eealsGXtu8W1Pba1ceeWVbUfy+TScNZ8a9WqxlNUpaORNP2c7GweNrJ0lSF9aK6uGraWsWnM2/chSEoHyC7CAKP8YkdCogMY34eIpjsuLh34sct5yOXtpZ18+lqzYLHuCQE4ceUYevXtE1riFxIbr5SvjrxbfLcUEluaBpayKQ6ZSNbYqrFSKAAIFCXT2E0BBIWkWAQRmBKzdWjAq75K+VfKhzdtk35G9snXNhOx4aELKsJkpKmtZ552lrM7QUl6y6sx6S67W5qzOiFErAskCLCCSfTiLQNcClt40ee2//aBs8rdVjf04KHeNi5y98tdEfnRYXjwe2qvUhdKSvovlxls+LnLfE/LMsfR1WbuNq6l50PHtfLsY+JwuseTqumwpL1lzmqRUg0CFBRqBuxWKSOt+7LNPK9xduoZA7wT8N2G/dcF/7hJEHYs7nlQ2XGfc9f54mrJp2gp++tfy6COvyu4jP5C1py2Z+cEo+Kn89aOPyuSKD8uP935Dfr/tB9Goet2x6cnd8mvr/lTWfPg35B0Nl1Rk165dM08W+Xd4eLjlmLVfrplwHVFZXRl3PFzOH2u/3h9PU7YsbbX3IWuupOvzbisv77xzWTRIM2fr5O3H0PWZBwIIzAi4v9/k1gssIJgRCCDQmcD0c7L7A1fJoS2Pyba1Z8xce2y/bDn3K7LyQFM2r3hLyvrcH5XbLnfIJ+Tzvp6UV1IMAQQQQAABBHov4BcQbGHqvT0tImBbYMkK+ejnPyIHb/2y7J96Q2T6Jdl/xw45eN318tG5xcMb8tLYp2XZ4E4Zb211cn+5+rvy2PjU7G1e35Cpg1+Tzx1YJVevmV2E2FYhPQIIIIAAArURYAFRm6GmowjkJbBElq76lDyw7Qy5d9UvS+OkzbJn5X+QB667QEJ/GWJhY0f/UnYNLJOTGg1ZtumL8vTxtXLLH/2W9PFVaKEVRxBAAAEEECixAFuYSjw4REMAAQQQQAABBBBAoCwCbGEqy0iQAwEEEEAAAQQQQAABQwJsHjA0WERFAAEEEEAAAQQQQKBoARYQRY8A7SOAAAIIIIAAAgggYEiABYShwSIqAggggAACCCCAAAJFC7CAKHoEaB8BBBBAAAEEEEAAAUMCLCAMDRZREUAAAQQQQAABBBAoWoAFRNEjQPsIIIAAAggggAACCBgSYAFhaLCIigACCCCAAAIIIIBA0QIsIIoeAdpHAAEEEEAAAQQQQMCQAAsIQ4NFVAQQQAABBBBAAAEEihZgAVH0CNA+AggggAACCCCAAAKGBFhAGBosoiKAAAIIIIAAAgggULQAC4iiR4D2EUAAAQQQQAABBBAwJMACwtBgERUBBBBAAAEEEEAAgaIFWEAUPQK0jwACCCCAAAIIIICAIYGTw1kbjUb4U54jgAACCCCAAAIIIIAAAvME5hYQQRDMO8EnCCCAAAIIIIAAAggggEC7AFuY2kX4HAEEEEAAAQQQQAABBGIF/n9K5lyCIkNv9QAAAABJRU5ErkJggg=="></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-coordinates of the points of inflexion of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> for which the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> is concave-down.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in metres.</strong></p>
<p>&nbsp;</p>
<p>Consider the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \sqrt {\frac{{4 - {x^2}}}{8}} ">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <msqrt>
    <mfrac>
      <mrow>
        <mn>4</mn>
        <mo>−<!-- − --></mo>
        <mrow>
          <msup>
            <mi>x</mi>
            <mn>2</mn>
          </msup>
        </mrow>
      </mrow>
      <mn>8</mn>
    </mfrac>
  </msqrt>
</math></span>, for −2 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>&nbsp;≤ 2.&nbsp;In the following diagram, the shaded&nbsp;region is enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">A container can be modelled by rotating this region by 360˚ about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis.</p>
</div>

<div class="specification">
<p>Water can flow in and out of the container.</p>
<p>The volume of water in the container is given by the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
  <mi>g</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> ≤ 4 , where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is measured in hours and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g\left( t \right)">
  <mi>g</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
</math></span> is measured in m<sup>3</sup>. The rate of change of the volume of water in the container is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g'\left( t \right) = 0.9 - 2.5\,{\text{cos}}\left( {0.4{t^2}} \right)">
  <msup>
    <mi>g</mi>
    <mo>′</mo>
  </msup>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>0.9</mn>
  <mo>−<!-- − --></mo>
  <mn>2.5</mn>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>cos</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mn>0.4</mn>
      <mrow>
        <msup>
          <mi>t</mi>
          <mn>2</mn>
        </msup>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>The volume of water in the container is increasing only when&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>&nbsp;&lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>&nbsp;&lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the volume of the container.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the&nbsp;value of&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span> and of&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During the interval&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>&nbsp;&lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span>&nbsp;&lt; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>,&nbsp;he volume of water in the container increases by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> m<sup>3</sup>. Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> = 0, the volume of water in the container is 2.3 m<sup>3</sup>. It is known that the container is never completely full of water during the 4 hour period.</p>
<p>&nbsp;</p>
<p>Find the minimum volume of empty space in the container during the 4 hour period.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves along a straight line so that its velocity,&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
  <mi>v</mi>
</math></span> m s<sup>−1</sup>, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v\left( t \right) = {1.4^t} - 2.7">
  <mi>v</mi>
  <mrow>
    <mo>(</mo>
    <mi>t</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mn>1.4</mn>
      <mi>t</mi>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>2.7</mn>
</math></span>, for 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> ≤ 5.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find when the particle is at rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of the particle when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 2">
  <mi>t</mi>
  <mo>=</mo>
  <mn>2</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by the particle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = x{{\text{e}}^{ - x}}">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mi>x</mi>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mi>x</mi>
      </mrow>
    </msup>
  </mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = &nbsp;- 3f(x) + 1">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>3</mn>
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>+</mo>
  <mn>1</mn>
</math></span>.</p>
<p>The graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span> intersect at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
  <mi>x</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = q">
  <mi>x</mi>
  <mo>=</mo>
  <mi>q</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p < q">
  <mi>p</mi>
  <mo>&lt;</mo>
  <mi>q</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area of the region enclosed by the graphs of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g">
  <mi>g</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The displacement, in centimetres, of a particle from an origin, O, at time <em>t</em> seconds, is given&nbsp;by <em>s</em>(<em>t</em>) = <em>t </em><sup>2</sup> cos <em>t</em> + 2<em>t</em> sin <em>t</em>, 0 ≤ <em>t</em> ≤ 5.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum distance of the particle from O.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of the particle at the instant it first changes direction.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = (2x + 2)(5 - {x^2})">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo stretchy="false">(</mo>
  <mn>2</mn>
  <mi>x</mi>
  <mo>+</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
  <mo stretchy="false">(</mo>
  <mn>5</mn>
  <mo>−<!-- − --></mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span>.</p>
</div>

<div class="specification">
<p>The graph of the function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g(x) = {5^x} + 6x - 6">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <msup>
      <mn>5</mn>
      <mi>x</mi>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>6</mn>
  <mi>x</mi>
  <mo>−<!-- − --></mo>
  <mn>6</mn>
</math></span> intersects the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Expand the expression for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Draw </strong>the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 3 \leqslant x \leqslant 3">
  <mo>−</mo>
  <mn>3</mn>
  <mo>⩽</mo>
  <mi>x</mi>
  <mo>⩽</mo>
  <mn>3</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 40 \leqslant y \leqslant 20">
  <mo>−</mo>
  <mn>40</mn>
  <mo>⩽</mo>
  <mi>y</mi>
  <mo>⩽</mo>
  <mn>20</mn>
</math></span>. Use a scale of 2 cm to represent 1 unit on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis and 1 cm to represent 5 units on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the point of intersection.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>In this question distance is in centimetres and time is in seconds.</strong></p>
<p>Particle A is moving along a straight line such that its displacement from a point P, after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{A}}} = 15 - t - 6{t^3}{{\text{e}}^{ - 0.8t}}">
  <mrow>
    <msub>
      <mi>s</mi>
      <mrow>
        <mtext>A</mtext>
      </mrow>
    </msub>
  </mrow>
  <mo>=</mo>
  <mn>15</mn>
  <mo>−<!-- − --></mo>
  <mi>t</mi>
  <mo>−<!-- − --></mo>
  <mn>6</mn>
  <mrow>
    <msup>
      <mi>t</mi>
      <mn>3</mn>
    </msup>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>0.8</mn>
        <mi>t</mi>
      </mrow>
    </msup>
  </mrow>
</math></span>, 0 ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> ≤ 25. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>Another particle, B, moves along the same line, starting at the same time as particle A. The velocity of particle B is given by&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_{\text{B}}} = 8 - 2t">
  <mrow>
    <msub>
      <mi>v</mi>
      <mrow>
        <mtext>B</mtext>
      </mrow>
    </msub>
  </mrow>
  <mo>=</mo>
  <mn>8</mn>
  <mo>−<!-- − --></mo>
  <mn>2</mn>
  <mi>t</mi>
</math></span>, 0&nbsp;≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>&nbsp;≤ 25.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial displacement of particle A from point P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> when particle A first reaches point P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> when particle A first changes direction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by particle A in the first 3 seconds.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that particles A and B start at the same point, find the displacement function <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{s_{\text{B}}}">
  <mrow>
    <msub>
      <mi>s</mi>
      <mrow>
        <mtext>B</mtext>
      </mrow>
    </msub>
  </mrow>
</math></span> for particle B.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the other value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> when particles A and B meet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves along a straight line so that its velocity,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>&#8202;</mo><msup><mtext>m&#8202;s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, after&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>&nbsp;seconds is given&nbsp;by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><msup><mtext>e</mtext><mrow><mi>sin</mi><mo>&#8202;</mo><mi>t</mi></mrow></msup><mo>+</mo><mn>4</mn><mo>&#8202;</mo><mi>sin</mi><mo>&#8202;</mo><mi>t</mi></math>&nbsp;for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>&#8804;</mo><mi>t</mi><mo>&#8804;</mo><mn>6</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> when the particle is at rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of the particle when it changes direction.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by the particle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves in a straight line such that its velocity, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>&nbsp;seconds is given by</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>4</mn><msup><mi>t</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>t</mi><mo>+</mo><mn>9</mn><mo>-</mo><mn>2</mn><mo> </mo><mi>sin</mi><mfenced><mrow><mn>4</mn><mi>t</mi></mrow></mfenced><mo>,</mo><mo>&nbsp;</mo><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>1</mn></math>.</p>
<p style="text-align: left;">The particle’s acceleration is zero at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>T</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>1</mn></msub></math> be the distance travelled by the particle from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>T</mi></math> and let <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub></math> be the distance&nbsp;travelled by the particle from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>T</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn></math>.</p>
<p>Show that&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub><mo>&gt;</mo><msub><mi>s</mi><mn>1</mn></msub></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Note: In this question, distance is in metres and time is in seconds.</strong></p>
<p>A particle P moves in a straight line for five seconds. Its acceleration at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 3{t^2} - 14t + 8">
  <mi>a</mi>
  <mo>=</mo>
  <mn>3</mn>
  <mrow>
    <msup>
      <mi>t</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>14</mn>
  <mi>t</mi>
  <mo>+</mo>
  <mn>8</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5">
  <mn>0</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>t</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>5</mn>
</math></span>.</p>
</div>

<div class="specification">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 0">
  <mi>t</mi>
  <mo>=</mo>
  <mn>0</mn>
</math></span>, the velocity of P is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="3{\text{ m}}\,{{\text{s}}^{ - 1}}">
  <mn>3</mn>
  <mrow>
    <mtext>&nbsp;m</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>1</mn>
      </mrow>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = 0">
  <mi>a</mi>
  <mo>=</mo>
  <mn>0</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find all possible values of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> for which the velocity of P is decreasing.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for the velocity of P at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by P when its velocity is increasing.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider a function&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>, for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≥</mo><mn>0</mn></math>.&nbsp;The derivative of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is given by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac></math>.</p>
</div>

<div class="specification">
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is concave-down when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mi>n</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>''</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup></mfrac></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mfrac><mrow><mn>6</mn><mi>x</mi></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfrac><mtext>d</mtext><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> be the region enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math>, the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis and the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>3</mn></math>. The area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>.</mo><mn>6</mn></math>, correct to three significant figures.</p>
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle P starts from a point A and moves along a horizontal straight line. Its velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v{\text{ cm}}\,{{\text{s}}^{ - 1}}">
  <mi>v</mi>
  <mrow>
    <mtext>&nbsp;cm</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <msup>
      <mrow>
        <mtext>s</mtext>
      </mrow>
      <mrow>
        <mo>−<!-- − --></mo>
        <mn>1</mn>
      </mrow>
    </msup>
  </mrow>
</math></span> after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span> seconds is given by</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="v(t) = \left\{ {\begin{array}{*{20}{l}} { - 2t + 2,}&amp;{{\text{for }}0 \leqslant t \leqslant 1} \\ {3\sqrt t + \frac{4}{{{t^2}}} - 7,}&amp;{{\text{for }}1 \leqslant t \leqslant 12} \end{array}} \right.">
  <mi>v</mi>
  <mo stretchy="false">(</mo>
  <mi>t</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <mo>{</mo>
    <mrow>
      <mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
        <mtr>
          <mtd>
            <mrow>
              <mo>−<!-- − --></mo>
              <mn>2</mn>
              <mi>t</mi>
              <mo>+</mo>
              <mn>2</mn>
              <mo>,</mo>
            </mrow>
          </mtd>
          <mtd>
            <mrow>
              <mrow>
                <mtext>for&nbsp;</mtext>
              </mrow>
              <mn>0</mn>
              <mo>⩽<!-- ⩽ --></mo>
              <mi>t</mi>
              <mo>⩽<!-- ⩽ --></mo>
              <mn>1</mn>
            </mrow>
          </mtd>
        </mtr>
        <mtr>
          <mtd>
            <mrow>
              <mn>3</mn>
              <msqrt>
                <mi>t</mi>
              </msqrt>
              <mo>+</mo>
              <mfrac>
                <mn>4</mn>
                <mrow>
                  <mrow>
                    <msup>
                      <mi>t</mi>
                      <mn>2</mn>
                    </msup>
                  </mrow>
                </mrow>
              </mfrac>
              <mo>−<!-- − --></mo>
              <mn>7</mn>
              <mo>,</mo>
            </mrow>
          </mtd>
          <mtd>
            <mrow>
              <mrow>
                <mtext>for&nbsp;</mtext>
              </mrow>
              <mn>1</mn>
              <mo>⩽<!-- ⩽ --></mo>
              <mi>t</mi>
              <mo>⩽<!-- ⩽ --></mo>
              <mn>12</mn>
            </mrow>
          </mtd>
        </mtr>
      </mtable>
    </mrow>
    <mo fence="true" stretchy="true" symmetric="true"></mo>
  </mrow>
</math></span></p>
<p>The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
  <mi>v</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_16.40.29.png" alt="N16/5/MATME/SP2/ENG/TZ0/09"></p>
</div>

<div class="specification">
<p>P is at rest when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1">
  <mi>t</mi>
  <mo>=</mo>
  <mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
  <mi>t</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span>.</p>
</div>

<div class="specification">
<p>When <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q">
  <mi>t</mi>
  <mo>=</mo>
  <mi>q</mi>
</math></span>, the acceleration of P is zero.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the initial velocity of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P">
  <mi>P</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i)     Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q">
  <mi>q</mi>
</math></span>.</p>
<p>(ii)     Hence, find the <strong>speed </strong>of P when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = q">
  <mi>t</mi>
  <mo>=</mo>
  <mi>q</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i)     Find the total distance travelled by P between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = 1">
  <mi>t</mi>
  <mo>=</mo>
  <mn>1</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
  <mi>t</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span>.</p>
<p>(ii)     Hence or otherwise, find the displacement of P from A when <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = p">
  <mi>t</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span>.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = {({x^2} + 3)^7}">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mrow>
    <mo stretchy="false">(</mo>
    <mrow>
      <msup>
        <mi>x</mi>
        <mn>2</mn>
      </msup>
    </mrow>
    <mo>+</mo>
    <mn>3</mn>
    <msup>
      <mo stretchy="false">)</mo>
      <mn>7</mn>
    </msup>
  </mrow>
</math></span>. Find the term in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{x^5}">
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>5</mn>
    </msup>
  </mrow>
</math></span> in the expansion of the derivative, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f’(x)">
  <msup>
    <mi>f</mi>
    <mo>′</mo>
  </msup>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>Consider the function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> defined by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>90</mn><msup><mtext>e</mtext><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mi>x</mi></mrow></msup></math>&nbsp;for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><msup><mi mathvariant="normal">ℝ</mi><mo>+</mo></msup></math>.</p>
<p>The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math> intersect at point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
</div>

<div class="specification">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> has a gradient of <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math> and is a tangent to the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> at the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>.</p>
</div>

<div class="specification">
<p>The shaded region <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> is enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the lines <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the exact coordinates of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Q</mtext></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equation of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>&nbsp;is&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo> </mo><mi>ln</mi><mo> </mo><mn>45</mn><mo>+</mo><mn>2</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinate of the point where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> intersects the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> is tangent to the graphs of both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the inverse function <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p>Find the shaded area enclosed by the graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> and the line <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A particle moves in a straight line. The velocity,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><msup><mtext>ms</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>,&nbsp;of the particle at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is&nbsp;given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>t</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>t</mi><mo>-</mo><mn>3</mn></math>, for <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mn>10</mn></math>.</p>
<p>The following diagram shows the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the smallest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> for which the particle is at rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the total distance travelled by the particle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the acceleration of the particle when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>7</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Hyungmin designs a concrete bird bath. The bird bath is supported by a pedestal.&nbsp;This is shown in the diagram.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The interior of the bird bath is in the shape of a cone with radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> and a constant&nbsp;slant height of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mtext>cm</mtext></math>.</p>
</div>

<div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of the bird bath.</p>
</div>

<div class="specification">
<p>Hyungmin wants the bird bath to have maximum volume.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an equation in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> that shows this information.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>2500</mn><mtext>π</mtext><mi>h</mi></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mtext>π</mtext><msup><mi>h</mi><mn>3</mn></msup></mrow><mn>3</mn></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><mi>V</mi></mrow><mrow><mtext>d</mtext><mi>h</mi></mrow></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to <strong>part (c)</strong>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> for which <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> is a maximum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the maximum volume of the bird bath.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>To prevent leaks, a sealant is applied to the interior surface of the bird bath.</p>
<p>Find the surface area to be covered by the sealant, given that the bird bath has maximum volume.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All lengths in this question are in metres.</strong></p>
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) = &nbsp;- 0.8{x^2} + 0.5">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>0.8</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>0.5</mn>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - 0.5 \leqslant x \leqslant 0.5">
  <mo>−<!-- − --></mo>
  <mn>0.5</mn>
  <mo>⩽<!-- ⩽ --></mo>
  <mi>x</mi>
  <mo>⩽<!-- ⩽ --></mo>
  <mn>0.5</mn>
</math></span>. Mark uses <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x)">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
</math></span> as a model to create a barrel. The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = &nbsp;- 0.5">
  <mi>x</mi>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>0.5</mn>
</math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0.5">
  <mi>x</mi>
  <mo>=</mo>
  <mn>0.5</mn>
</math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis. This is shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-03_om_15.49.19.png" alt="N16/5/MATME/SP2/ENG/TZ0/06"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the model to find the volume of the barrel.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The empty barrel is being filled with water. The volume <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V{\text{ }}{{\text{m}}^3}"> <mi>V</mi> <mrow> <mtext>&nbsp;</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></span>&nbsp;of water in the barrel after <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t"> <mi>t</mi> </math></span> minutes is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="V = 0.8(1 - {{\text{e}}^{ - 0.1t}})"> <mi>V</mi> <mo>=</mo> <mn>0.8</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mrow> <msup> <mrow> <mtext>e</mtext> </mrow> <mrow> <mo>−</mo> <mn>0.1</mn> <mi>t</mi> </mrow> </msup> </mrow> <mo stretchy="false">)</mo> </math></span>. How long will it take for the barrel to be half-full?</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <em>g</em>(<em>x</em>) = −(<em>x</em> − 1)<sup>2</sup> + 5.</p>
</div>

<div class="specification">
<p>Let <em>f</em>(<em>x</em>) = x<sup>2</sup>. The following diagram shows part of the graph of <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The graph of <em>g</em> intersects the graph of <em>f</em> at <em>x</em> = −1 and <em>x</em> = 2.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of the vertex of the graph of <em>g</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the grid above, sketch the graph of g for −2 ≤ <em>x</em> ≤ 4.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area of the region enclosed by the graphs of <em>f</em> and <em>g</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Let&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \,\,{\text{sin}}\,\left( {{e^x}} \right)">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mspace width="thinmathspace"></mspace>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mtext>sin</mtext>
  </mrow>
  <mspace width="thinmathspace"></mspace>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mrow>
        <msup>
          <mi>e</mi>
          <mi>x</mi>
        </msup>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span> for 0&nbsp;≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>&nbsp;≤ 1.5.&nbsp;The following diagram shows the graph of&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <em>x</em>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>, the<em> y</em>-axis and the <em>x</em>-axis is rotated 360° about the <em>x</em>-axis.</p>
<p>Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
  <mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>

<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
  <mn>0.5</mn>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>m</mtext>
      </mrow>
      <mn>3</mn>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>

<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
  <mn>2000</mn>
  <mrow>
    <mtext>&nbsp;c</mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>m</mtext>
      </mrow>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 66 people went on holiday to Hawaii. During their stay, three trips were arranged: a boat trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
  <mi>B</mi>
</math></span>), a coach trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
  <mi>C</mi>
</math></span>) and a helicopter trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span>).</p>
<p>From this group of people:</p>
<table style="width: 691.333px;">
<tbody>
<tr>
<td style="width: 182px; text-align: right;">3&nbsp;</td>
<td style="width: 526.333px;">went on all three trips;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">16&nbsp;</td>
<td style="width: 526.333px;">went on the coach trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">13&nbsp;</td>
<td style="width: 526.333px;">went on the boat trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">5&nbsp;</td>
<td style="width: 526.333px;">went on the helicopter trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;"><em>x&nbsp;</em></td>
<td style="width: 526.333px;">went on the coach trip and the helicopter trip <strong>but not</strong> the boat trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">2<em>x&nbsp;</em>
</td>
<td style="width: 526.333px;">went on the boat trip and the helicopter trip <strong>but not</strong> the coach trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">4<em>x&nbsp;</em>
</td>
<td style="width: 526.333px;">went on the boat trip and the coach trip <strong>but not</strong> the helicopter trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">8&nbsp;</td>
<td style="width: 526.333px;">did not go on any of the trips.</td>
</tr>
</tbody>
</table>
</div>

<div class="specification">
<p>One person in the group is selected at random.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a Venn diagram to represent the given information, using sets labelled <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
  <mi>B</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
  <mi>C</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
  <mi>x</mi>
  <mo>=</mo>
  <mn>3</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n(B \cap C)">
  <mi>n</mi>
  <mo stretchy="false">(</mo>
  <mi>B</mi>
  <mo>∩</mo>
  <mi>C</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person</p>
<p>(i) &nbsp; &nbsp; went on at most one trip;</p>
<p>(ii) &nbsp; &nbsp; went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the curves&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo> </mo><mi>sin</mi><mo> </mo><mi>x</mi></math>&nbsp;and&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>-</mo><msqrt><mn>1</mn><mo>+</mo><mn>4</mn><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></math>&nbsp;for&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi mathvariant="normal">π</mi><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>0</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-coordinates of the points of intersection of the two curves.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the area, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>, of the region enclosed by the two curves.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = 4 - 2{{\text{e}}^x}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>4</mn>
  <mo>−<!-- − --></mo>
  <mn>2</mn>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mi>x</mi>
    </msup>
  </mrow>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-intercept of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>, the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis and the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-axis is rotated 360º about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mfenced><mrow><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mo>d</mo><mi>x</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn></math>&nbsp;and&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>7</mn><mo>.</mo><mn>32</mn></math>, find&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Violeta plans to grow flowers in a rectangular plot. She places a fence to mark out the perimeter of the plot and uses 200 metres of fence. The length of the plot is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> metres.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.40.47.png" alt="M17/5/MATSD/SP2/ENG/TZ2/05"></p>
</div>

<div class="specification">
<p>Violeta places the fence so that the area of the plot is maximized.</p>
</div>

<div class="specification">
<p>By selling her flowers, Violeta earns 2 Bulgarian Levs (BGN) per square metre of the plot.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the width of the plot, in metres, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="100 - x"> <mn>100</mn> <mo>−</mo> <mi>x</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the area of the plot in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span> that maximizes the area of the plot.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that Violeta earns 5000 BGN from selling the flowers grown on the plot.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = \frac{{48}}{x} + k{x^2} - 58">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>48</mn>
    </mrow>
    <mi>x</mi>
  </mfrac>
  <mo>+</mo>
  <mi>k</mi>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>−<!-- − --></mo>
  <mn>58</mn>
</math></span>, where <em>x</em> &gt; 0 and <em>k</em> is a constant.</p>
<p>The graph of the function passes through the point with coordinates (4 , 2).</p>
</div>

<div class="specification">
<p>P is the minimum point of the graph of <em>f </em>(<em>x</em>).</p>
</div>

<div class="question">
<p>Sketch the graph of <em>y</em> = <em>f</em> (<em>x</em>) for 0 &lt; <em>x</em> ≤ 6 and −30 ≤ <em>y</em> ≤ 60.<br>Clearly indicate the minimum point P and the <em>x</em>-intercepts on your graph.</p>
</div>
<br><hr><br><div class="specification">
<p>The function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is defined by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac></math>, where&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&#8712;</mo><mi mathvariant="normal">&#8477;</mi><mo>,</mo><mo>&#160;</mo><mi>x</mi><mo>&#8800;</mo><mo>-</mo><mn>4</mn></math>.</p>
</div>

<div class="specification">
<p>For the graph of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></p>
</div>

<div class="specification">
<p>The graphs of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> intersect at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>q</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&#60;</mo><mi>q</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>write down the equation of the vertical asymptote.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>find the equation of the horizontal asymptote.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mi>x</mi></mfenced></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using an algebraic approach, show that the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is obtained by a reflection of the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math>-axis followed by a reflection in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the area enclosed by the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> and the graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>f</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Haruka has an eco-friendly bag in the shape of a cuboid with width 12 cm, length 36 cm and height of 9 cm. The bag is made from five rectangular pieces of cloth and is open at the top.</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img 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"></p>
</div>

<div class="specification">
<p>Nanako decides to make her own eco-friendly bag in the shape of a cuboid such that the surface area is minimized.</p>
<p>The width of Nanako’s bag is <em>x </em>cm, its length is three times its width and its height is <em>y </em>cm.</p>
<p>&nbsp;</p>
<p style="text-align: center;"><img 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8JfnRY9f/58mTlzpnziE5/gvjB56Eu9fqelpcUZ2WloaHBOY5kRsxkzZsiUKVPyUCt2iQACCCRLgHBjWX9roNm5c6e4f3Hq6IxeN8OFrtHrTO2vl19+WR5//PF0AF20aJEQdKLXV9QIAQTiI0C4saAv9ZSTXgS8ZcuW9EiABprZs2dzysOC/jNVdJ86vOuuu0RH2jToVFRUEEwNEl8RQAABHwQINz4gBlGEnt54/vnnZdOmTc5f/Ob6GQJNENrhl6lBp7m5OT2io/2rQUfvtswyE+H3B3tEAIF4CRBuItafehpDLwjWURq9u+7atWs5hRGxPvK7Ohp0fvnLX6ZPNeo0cw0711xzjd+7ojwEEEAgEQKEm4h08+7du51TTjptW3+xffvb33amFnP/lIh0UEjV2Ldvn/zbv/2b6GkrM5qjs644DkLqAHaDAAKxECDc5LEb9dSTznQy19LoKA3XX+SxQyK0a3Od1X333Zcewfv617/OKasI9RFVQQCB6AoQbvLQNybU6C8u3ZYtWyZf/OIX+cWVh76I+i7NtVc6oqerqt97773yla98hQuQo95x1A8BBPIqUJjXvSds5/rX+Lp165y1mjTY3HHHHc5N9/RCUi4iTdjBkGNz9XSUXnuj12G98MILzornutxDTU2N6M0D2RBAAAEE+goQbvqa+P6M/vWt96U5//zz5amnnpJdu3Y5N9/T6dxcS+E7d2wL1BsA1tbWOjcJ1EYScmLb1TQMAQRGKEC4GSHgQG83oUbvGKwjNfX19c5f4MyCGUiNnw0moDdrzA45OiKoI4NsCCCAAAIiXHMT0FGgs5/0Oon29nbn9BMzXgKCplgxx5pek6MBmmONgwIBBJIuQLjx+QjQ+9SsWbPGCTY6+2nJkiWcevLZmOK8BRobG+Xuu+92frh69Wruk+PNxLMIIJAAAU5L+dTJegpKp3SPHz/eKfHw4cPOLCiuqfEJmGIGFdDbCOiq8Dr7Tteu0ouOOVU1KBsvQACBGAoQbnzoVJ21snDhQmcm1Pbt253rIcaNG+dDyRSBwNAENEzr7Dtdmfydd95xLmLXi9nZEEAAgSQJEG5G0NtmtEZnrUyfPt35q1n/emZDIN8CetHx+vXrnWtw9GL2pUuXip4yZUMAAQSSIEC4GWYvu0dr9P4jK1as4NqaYVrytuAE9HYD27Ztc3agp0z1uhw2BBBAIO4ChJth9LAO87tHa/T+I2wIRFVAbxBpRnHmzJnjXIujo45sCCCAQFwFCDdD6Fn9haAXaS5YsED02hpGa4aAx0vzLqCjOHqhu4466r2XuMNx3ruECiCAQEAChJscYfV6BfMLQX9BcG1NjnC8LFICeqH7Y489JvPnz3dGHzlNFanuoTIIIOCTAOEmB0i9SZper1BeXu78YmAmVA5ovCSyAjqjSkcd9YZ/eppK727MhgACCMRJgJv4DdKbeu+aqqoq2bx5szPFdpCX82MErBLYt2+f3HTTTTJ58mTn5pPcl8mq7qOyCCDQjwDhph8YfVr/or3llluchS5ZD2oAKH5ktYCectXrcTTg3H///axQb3VvUnkEEFABTkt5HAd64fDKlSudOw7rNG+CjQcST8VGQE+z6p2NdZs7dy73w4lNz9IQBJIrwMhNVt9rsFm+fLm8+OKLolO+ub4mC4hvYyvAsR/brqVhCCROgJEbV5fz4e7C4GHiBPR6G130VU9P6Wkq7micuEOABiMQGwHCjasrv/e97zFi4/LgYfIECDjJ63NajEAcBQg3vb2qFw83NTVxKiqORzltGpJAdsDREU02BBBAwCYBrrlxzYrSlZR1wUE2BBAQMadp1UJPVzFNnKMCAQRsERhRuNGlCOrq6mxpK/VEAIGYCqxdu1aWLVsW09bRLAQQGKoAp6WGKsbrEUAgcgJ6Pyr9Y4tTaJHrGiqEQF4ERhRu3n///bxUmp0igAAC2QI6iqy3cSDgZMvwPQLJExg1kiafeeaZnm/Xhfk+9alPef6MJxFAAAE/BMrKyvoU8/DDDzvPcY1QHxqeQCBRAiMKN/1JLVy4kCUL+sPheQQQCFTABBy9tQM34QyUmsIRiKzAiE5LuVv1t3/7t+5vZcaMGc7yBRlP8g0CCCAQkMCNN96YLlkDDjciTHPwAIHECfgWbvSuprt27coA1NW09f4xbAgggEDQAnoqyh1wnnvuOQJO0OiUj0BEBXwLN9o+XWAyO+DoLAYCTkR7n2ohECMBc/PB6urqdKtMwGltbU0/xwMEEIi/gK/hRrk04OhK2ldddVVaTwOOrrLNLIY0CQ8QQCAAAQ04tbW1ove9MZsGHL34ePfu3eYpviKAQMwFfA836jVlyhRnGQN3wLnrrruYphnzg4nmIRAVAb2hnzvgaL30OkACTlR6iHogEKxAIOFGq6yzFBoaGjJGcPQiP+5DEWyHUjoCCPQIEHA4EhBIrkBg4UZJTcCZN29eWtgEnM7OzvRzPEAAAQSCENCAk30doI7gcB1gENqUiUB0BAINN9pMDTh6Uz/3LAYNOHPnzpW2trboSFATBBCIpQATHWLZrTQKgQEFAg83unczi8EdcMwsBgLOgP3DDxFAwAcBAo4PiBSBgEUCoYQb9Rgo4DBN06IjhqoiYKmABpyWlpaM6wB1JufSpUuZyWlpn1JtBPoTCC3caAU04Kxfvz5jFgPTNPvrGp5HAAG/BSZOnMhEB79RKQ+BCAqEGm5M+5nFYCT4igACYQuYiQ7uW1WYiQ7ciyvs3mB/CAQjkJdwo00h4ATToZSKAAKDC5iA474OUAOOLvrLdYCD+/EKBKIukLdwozAacLZv355hxDTNDA6+QQCBgAQ04GSvR/XEE0+wHlVA3hSLQJgCeQ032tCKioo+96FgPaowDwH2hUByBQaa6MAITnKPC1puv0Dew40SMk3T/gOJFiBgq4AJOF4Lbu7bt8/WZlFvBBItEIlwoz2gAcdrwc2amhqmaSb6EKXxCAQvoAHHa8HNqVOnsh5V8PzsAQHfBSITbrRlXgtu1tXVsR6V791OgQgg4CXARAcvFZ5DwD6BSIUb5TOzGJimad/BRI0RiINAfwGnsbExDs2jDQgkQiBy4UbVTcDxWnCTi/wScVzSSATyKqABJ3vBzTlz5rDgZl57hZ0jkLtAJMONVl8DjteCm5WVldyHIvf+5ZUIIDBMASY6DBOOtyEQAYHIhhu1MbMY3DfaYsHNCBw1VAGBhAgQcBLS0TQzdgKRDjeqbQKO1zRNFtyM3fFIgxCInIAGHBbcjFy3UCEEBhSIfLjR2vc3TbOsrIxpmgN2Lz9EAAE/BFhw0w9FykAgPAErwo3h6G8Ww+7du81L+IoAAggEImAmOjCTMxBeCkXAVwGrwo22nIDja/9TGAIIDEFAA862bdvEfR0gC24OAZCXIhCSgHXhRl28pmmy4GZIRwy7QSDhAsXFxSy4mfBjgOZHX8DKcKOszGKI/sFFDRGIq4CZ6OAewWEmZ1x7m3bZKGBtuFFsAo6Nhxx1RiAeAibg3HvvvekGmYDDgptpEh4gkBcBq8ONivU3TZMFN/NyPLFTBBIloAFnxYoVsnbt2nS7NeCw4GaagwcI5EXA+nCjal7TNFlwMy/HEztFIJECTHRIZLfT6AgLxCLcqC/TNCN8lFE1BBIgoAFn8+bNGS3ViQ4suJlBwjcIhCIQm3CjWibguC/y02may5cvZz2qUA4ndoJAsgUWLVrEgpvJPgRofUQEYhVu1FQDzpo1a/rch4IFNyNyxFENBGIuwESHmHcwzbNCIHbhRtXNLAb3CI6ZxdDW1mZFx1BJBBCwV2CggHPy5El7G0bNEbBEIJbhRu1NwPFacJNpmpYcnVQTAYsFNOAcPnxY3Ms13HLLLc5pcgKOxR1L1a0QiG24UX0NOLW1tUzTtOJQpJIIxE/AXAfoDjjmOkACTvz6mxZFRyDW4cYwM03TSPAVAQTCFiDghC3O/hAQSUS40Y7uL+AwTZN/BgggELSABhyvBTdnzpzJTM6g8Sk/kQKJCTfauxpwdu3aldHRc+bMkXXr1mU8xzcIIICA3wJeC24y0cFvZcpDoEcgUeFGmzzQLAYOCgQQQCBIATPRgZmcQSpTNgIJOi3l7mwCjluDxwggEKaACTheC27u3r07zKqwLwRiK5C4kRvTkxpwWlpa+kzTXLp0qTCLwSjxFQEEghDQgOO14KYu10DACUKcMpMmkNhwox3tteAm0zST9k+A9iKQP4H+JjoQcPLXJ+w5HgKJDjfahUzTjMeBTCsQsFVAA47XgpsNDQ22Nol6I5B3gcSHG+0BE3DcF/npCM7ChQuZppn3Q5QKIBB/Aa8FNxcsWMBMzvh3PS0MSIBw0wurASd7wc0nnnhCWHAzoCOPYhFAIEOAiQ4ZHHyDwIgECDcuPjOLwT2Cw30oXEA8RACBQAUGCjhMdAiUnsJjJkC4yepQE3C8pmmy4GYWFt8igIDvAhpwWHDTd1YKTJjAqIS1N6fmmmmaZ599tugqvrrpCM7UqVOdOxzrhw8bAvkW6OzslKNHj6arcfDgQenq6kp/rw9effVVeffddzOey+WbSZMmyZgxYzJeeuGFF8oFF1yQfk5nG7IFI2CuA9TT4vrZo5teB6ibnj7Xzyg2BBDoX4Bw07+Ns1yD/tgEHH2s96HQJRwIOAPA8aMRC7S1tcmJEydk//79TlkmpLzzzjvpX3LZO9HTqeedd17G0x/72Mfksssuy3gul2+eeeaZPi9rampK/6J1/1BXvC4vL3eeMqHIBKGSkhLRZQfYhi5AwBm6Ge9AwAgUpFKplPlmqF9ramqkrq7OeVt9fb1z8e1Qy7Dh9Vu2bJGqqqqMqm7fvl0qKioynuMbBIYiYEZeNMC0t7fLG2+8IdkBYt68ec79mDSkjB071ileA4RuRUVFzky/oezTr9fq9R966kS3I0eOyNtvv+08NqEoux0meF199dVigs9IR34KCgoymjOCj7KMcqL2jVovX748I9RqoNSp4hqA2BBAoK8A4aavieczelMtHbVxb2vXrk2P7rif5zEC2QKtra2ip43eeustZzTG/FGgr/P6xR+XEQ/3CJSeMtMg5w4+Jrxp6LnkkktEQ1yuIz1JCTd6jBBwsv9F8T0CAwtwWmpgn/RPzSwGd8Axp6v0JlxsCBgBHZF55ZVX5MCBAxlBxpy+0V/kL7zwgmiAiftf3qZ92aM0ZuRHA58GPx3x0fu66OZ20lGq7Pca5yR9NRMdtM3m2hszk5MRnCQdCbQ1VwFGbnKV6n0dIzhDBEvAyzXMNDc3O//t2bNH9P5IulVXV8twRiQSQNZvE3Wk5+WXX3YCz4svvpj+Ra6jW5/97GfliiuukLKyMueC2iSN3BgwDYUbNmzIuA5Qw+Dq1au5DtAg8RUBESHcDOMw0A9g9ywGLUI/fJnFMAxMC9+iv2Cef/55Z/TlqaeecsKM/oKZP3++XHnllfLJT34y9iMyYXWbWusCt7/73e/kt7/9bUbYMSMYpi5xvebGtM/9dd26dRkBR3/GRAe3EI+TLsB9boZxBJhZDPoLzWz6QasX/emHMVv8BDTQNjY2iq4arxfy6ulJvQD429/+tnNhrY7Y6CrPepG5ORUTP4XwW6SnY6ZMmSK6PMH69eudGWR6Sk9HcbI3HVVNyr8/FtzM7n2+RyBTgHCT6ZHzdwScnKmsfaEGGp0ppyMy48ePlx/96EfOL1X95aqjBLW1tYSZkHvXHXayd62BU4PnypUrRYOOni6M86YBR2epujc1YMFNtwiPkypAuBlBz2vA2bZtm3NKyhSjIzgsuGk07PuaHWj0F4WegtRpz1u3bnVGEHQkgS16AnpfIA2eevPNW2+9Vc4//3zR21XEeURHj009HeXeWHDTrcHjpAoQbkbY8zptlQU3R4iY57frX/h6ysmM0JhA84c//CEdaDjVlOdOymH3ZlRHRzT0NKEGHZ1arkHHjOjEcQkVM5PTTaQzOfW6HDYEkipAuPGh5800Tb2o2GxmmqaOBLBFU+lTh78AACAASURBVEB/0ekpDP0L/+677+4zQpPr/Vai2TpqpSNsGnSefvrp9OiGLqEyffp053RjnE5bmYDjvg5QA44e30m5DokjHgG3AOHGrTGCxybgeC24qcPibNEQ0A96HZnRURr9RaebDuvrX/p60SojNNHoJz9rof829Ze/XvCto3F33HGHcwyY01ZxGc3RNuqx7Q44d911FxMd/DyYKMsaAcKNj12lH6L6Aap3LjabjuDoRX4EHCOSn686gqbD9Hp64r777nNGafQXnfaX/lJgS4aAjsbpdSp6/ZSetjr33HOdkKthV09N2j7KwUSHZBzHtHJwAcLN4EZDfgXTNIdMFtgb9O63elGpznbSe9K4R2k47RQYuxUF62krM5qjgUdPTc6cOdMZ/bD5lNVAAcfmdllxUFHJyAgQbgLqCg04mzdvziidaZoZHIF+o6caNNTo3Wx10xvB6V/rjNIEym5l4Rpy9ZSkXpujp6x0+r+estKRPlvDgAYcbY/7OkCdyTl37lzhOkArD1MqPUQBws0QwYbycv3AZJrmUMRG/lodqTHX0+hMGQ01ej8a1icauW3cS9DTyuaUlf671ZE+m0OOuQ7QHXCY6BD3o5j2GQHCjZEI6KuOFGQHHKZp+o9tTj/pSI3OhtHraXT0jFDjv3USStR/tzrS5w45OqJj2zU5BJwkHK200UuAcOOl4vNzAwUc2z4sfaYZcXF62kCnu7pPP+l1FFxPM2JaChBxTmNqyNm+fbtzmspck2MTjgk42RMd9Do0JjrY1JPUdSgChJuhaI3gtRpw9C637mmaOoLDelTDQ9VQaK6N0GncnH4aniPvyk1A1wwz1+TobDs99WnTFHINOEx0yK2veVU8BAg3IfbjQLMYGMHJvSP0l4r+Ba0XfOpf1PqXNaefcvfjlcMT0ICg1+Tokit66lPvk6QXrdt00TEBZ3h9z7vsEyDchNxnBJzhg+svEf1lor9UzOwW/YuaDYEwBfSUp5761NFCvdZLZyDpzfNs2TTgeC24qSOhbAjERYBwk4ee1IDjteCmjkYwTdO7Q/QGa/pL5J133nF+qegHtP4lzYZAvgR0tFBHDXX6uC5WuXTpUmv+/eoIVPZEh6qqKmc0NF+e7BcBPwUIN35qDqEs/esve8FNpmn2BTSjNXPmzHF+iaxfv55TUH2ZeCaPAhoU9Ho63fQiXVtGcQaa6JBHTnaNgC8ChBtfGIdXiJnFwH0ovP302hodrdGhf/3lob9E2BCIooCOxmrw1tM9Oopjy7U4JuBkT3Rgwc0oHmXUaSgChJuhaAXwWhNwsqdp6i/yJE/T1IuF9doaPf302GOPsaBlAMceRfovYEZxzLU4Nsyo0oDDgpv+HwuUmF8Bwk1+/Z29a8DJnsWQ1AU39TSUXrugFzfqwoZ64TDX1kTgIKUKOQvoKI4Gcj12NaDbcJqKiQ45dy8vtESAcBOhjsoOOFq1JK0obv7a1XbrLwRd2JANARsFzB8setGunqay4TSPCTjz5s1Lk+t6VHovLpumu6crz4NECxBuItb9GnC8pmna8NffSCj1FJzeZVhvjqYXWusHLRsCtguYm3fqrCobQoIZdXJfB8iCm7YfhcmsP+Emgv2u5+2zp2nqX396HUocNz0FpSNUGur0/iGchopjLye3TRoY9NYPutmwKrf++2MmZ3KP17i0nHAT0Z40sxjc1Yvjgpsa2PT+GhrmmA3l7m0ex0nA3PqhvLzcOc71FGyUNwJOlHuHuuUiQLjJRSlPrzEBJ3uapgaCOCzXoO3QURsNNtpWNgTiLKCBoba21rnQWE/BRn02pNZXp7dnz+Rkwc04H6XxaRvhJuJ9qb/0s6dpxmHBTRNstG0Em4gfhFTPVwEzccCWyQKmvm4EW+rurjOPkyVAuLGgv80sBvcIjpnFYOMIjjvYcOGwBQcgVfRdwAQGW0KCqa8bwpa6u+vM4+QIEG4s6eu4BByCjSUHHNUMXMAEBg0JNqwpp/Xdvn17hovWnQU3M0j4JiIChJuIdEQu1dCA8/TTT0v2NE1bFtzUD0E9pfbjH/+Yqd65dDivib2ACTh6Mb0NAaeioqLPTE4W3Iz9YWplA0dZWesEV9rMYlACPTWlm97NWC/ys2XTu7ayIeC3QEFBgd9FhlqeTf+Gs2H0jxbdNKyxIRAFAUZuotALQ6yDCTjuEZwhFsHLEUAAAV8FNOA0Njb6WiaFITBcAcLNcOXy/D4TcNzTNPNcJXaPAAIJF+jq6kq4AM2PigDhJio9MYx6aMDRc+BsCCCAAAIIIHBagGtuTlvE4lEqlYpFO2gEAgjYIVBTUyN1dXV2VJZaJkaAkZvEdDUNRQABBBBAIBkChJtk9DOtRCCWAjp9WkcO2BBAAAG3AOHGrcFjBBCwSuDEiROcErGqx6gsAuEIEG7CcWYvCCCAAAIIIBCSAOEmJGh2gwAC/guUlJRIfX29/wVTIgIIWC1AuLG6+6g8AskWKC4uFl26gA0BBBBwCxBu3Bo8RgABBBBAAAHrBQg31nchDUAguQKdnZ3S0NCQXABajgACngKEG08WnkQAARsEjh49KgsWLLChqtQRAQRCFCDchIjNrhBAAAEEEEAgeAHCTfDG7AEBBAISKCoqkurq6oBKp1gEELBVgHBja89RbwQQkHHjxkltbS0SCCCAQIYA4SaDg28QQAABBBBAwHYBwo3tPUj9EUiwALOlEtz5NB2BAQQINwPg8CMEEIi2ALOlot0/1A6BfAkQbvIlz34RQAABBBBAIBABwk0grBSKAAJhCDBbKgxl9oGAfQKEG/v6jBojgECvALOlOBQQQMBLgHDjpcJzCCCAAAIIIGCtAOHG2q6j4gggwGwpjgEEEPASINx4qfAcAghYIcBsKSu6iUoiELoA4SZ0cnaIAAIIIIAAAkEKEG6C1KVsBBBAAAEEEAhdgHATOjk7RAABvwQmTpwoqVTKr+IoBwEEYiJAuIlJR9IMBBBAAAEEEOgRINxwJCCAgLUCJ0+elNbWVmvrT8URQCAYAcJNMK6UigACIQgcPnxYysrKQtgTu0AAAZsECDc29RZ1RQABBBBAAIFBBQg3gxLxAgQQQAABBBCwSYBwY1NvUVcEEMgQYLZUBgffIIBArwDhhkMBAQQQQAABBGIlQLiJVXfSGASSJcBsqWT1N61FIFcBwk2uUrwOAQQiJ8Bsqch1CRVCIBIChJtIdAOVQAABBBBAAAG/BAg3fklSDgIIIIAAAghEQoBwE4luoBIIIDAcgfHjx0tLS8tw3sp7EEAgxgKEmxh3Lk1DIO4Co0ePFp0OzoYAAgi4BQg3bg0eI4AAAggggID1AoQb67uQBiCQXAFdNLOgoCC5ALQcAQQ8BQg3niw8iQACCCCAAAK2ChBubO056o0AAggggAACngKEG08WnkQAARsEmC1lQy9RRwTCFyDchG/OHhFAwCcBZkv5BEkxCMRMgHATsw6lOQgggAACCCRdgHCT9COA9iNgsQCzpSzuPKqOQIAChJsAcSkaAQQQQAABBMIXINyEb84eEUAAAQQQQCBAAcJNgLgUjQACwQowWypYX0pHwFYBwo2tPUe9EUBAmC3FQYAAAl4ChBsvFZ5DAAEEEEAAAWsFCDfWdh0VRwCBtrY2qampAQIBBBDIECDcZHDwDQII2CRw4sQJqaurs6nK1BUBBEIQINyEgMwuEEAAAQQQQCA8AcJNeNbsCQEEfBYoKSmR+vp6n0ulOAQQsF2AcGN7D1J/BBIsUFxcLJWVlQkWoOkIIOAlQLjxUuE5BBBAAAEEELBWgHBjbddRcQQQYLYUxwACCHgJEG68VHgOAQSsEGC2lBXdRCURCF2AcBM6OTtEAAEEEEAAgSAFCDdB6lI2AggEKsBsqUB5KRwBawUIN9Z2HRVHAAFmS3EMIICAlwDhxkuF5xBAAAEEEEDAWgHCjbVdR8URQKCzs1MaGhqAQAABBDIECDcZHHyDAAI2CRw9elQWLFhgU5WpKwIIhCBAuAkBmV0ggAACCCCAQHgChJvwrNkTAgj4LFBUVCTV1dU+l0pxCCBguwDhxvYepP4IJFhg3LhxUltbm2ABmo4AAl4ChBsvFZ5DAAEEEEAAAWsFCDfWdh0VRwABZktxDCCAgJcA4cZLhecQQMAKAWZLWdFNVBKB0AUIN6GTs0MEEEAAAQQQCFKAcBOkLmUjgECgAsyWCpSXwhGwVoBwY23XUXEEEGC2FMcAAgh4CRBuvFR4DgEEEEAAAQSsFSDcWNt1VBwBBJgtxTGAAAJeAoQbLxWeQwABKwSYLWVFN1FJBEIXINyETs4OEUAAAQQQQCBIAcJNkLqUjQACCCCAAAKhCxBuQidnhwgg4JfAxIkTJZVK+VUc5SCAQEwECDcx6UiagQACCCCAAAI9AoQbjgQEELBW4OTJk9La2mpt/ak4AggEI0C4CcaVUhFAIASBw4cPS1lZWQh7YhcIIGCTAOHGpt6irggggAACCCAwqADhZlAiXoAAAggggAACNgkQbmzqLeqKAAIZAsyWyuDgGwQQ6BUg3HAoIIAAAggggECsBAg3sepOGoNAsgSYLZWs/qa1COQqQLjJVYrXIYBA5ASYLRW5LqFCCERCgHATiW6gEggggAACCCDglwDhxi9JykEAAQQQQACBSAgQbiLRDVQCAQSGIzB+/HhpaWkZzlt5DwIIxFiAcBPjzqVpCMRdYPTo0aLTwdkQQAABtwDhxq3BYwQQQAABBBCwXoBwY30X0gAEkiugi2YWFBQkF4CWI4CApwDhxpOFJxFAAAEEEEDAVgHCja09R70RQAABBBBAwFOAcOPJwpMIIGCDALOlbOgl6ohA+AKEm/DN2SMCCPgkwGwpnyApBoGYCRBuYtahNAcBBBBAAIGkCxBukn4E0H4ELBZgtpTFnUfVEQhQgHATIC5FI4AAAggggED4AoSb8M3ZIwIIIIAAAggEKEC4CRCXohFAIFgBZksF60vpCNgqQLixteeoNwIICLOlOAgQQMBLgHDjpcJzCCCAAAIIIGCtAOHG2q6j4ggg0NbWJjU1NUAggAACGQKEmwwOvkEAAZsETpw4IXV1dTZVmboigEAIAoSbEJDZBQIIIIAAAgiEJ0C4Cc+aPSGAgM8CJSUlUl9f73OpFIcAArYLEG5s70Hqj0CCBYqLi6WysjLBAjQdAQS8BAg3Xio8hwACCCCAAALWChBurO06Ko4AAsyW4hhAAAEvAcKNlwrPIYCAFQLMlrKim6gkAqELEG5CJ2eHCCCAAAIIIBCkAOEmSF3KRgCBQAWYLRUoL4UjYK0A4cbarqPiCCDAbCmOAQQQ8BIg3Hip8BwCCCCAAAIIWCtAuLG266g4Agh0dnZKQ0MDEAgggECGAOEmg4NvEEDAJoGjR4/KggULbKoydUUAgRAECDchILMLBBBAAAEEEAhPgHATnjV7QgABnwWKioqkurra51IpDgEEbBcg3Njeg9QfgQQLjBs3TmpraxMsQNMRQMBLgHDjpcJzCCCAAAIIIGCtAOHG2q6j4gggwGwpjgEEEPASINx4qfAcAghYIcBsKSu6yaOSH0pHw7ekoKBACgrGyqxVe6TLeVW3HNu5QsaOXSYNb37g8T6eQiA3AcJNbk68CgEEEEDAN4FRUlr5kKROvSIbKkSantwv7d1aeKGM+cQsuaHsHXn3j84Tvu2RgpIlQLhJVn/TWgRiJcBsKcu7s3CcTP5CmciBTjnem2UKLxwvEy75tEwee4bljaP6+RQg3ORTn30jgMCIBJgtNSK+CLx5lJxVfIHIgdfk0JEPReQDeXPrT2TPdfNk6hh+PUWgg6ytAkePtV1HxRFAAAHbBUbJWecWn25E1z75WfNn5J75Fwu/nE6z8GjoAhw/QzfjHQggEBEBZktFpCOGXY1C+ci5xVIqLfL64ddkZ+2TcvHN18pF/GYatihv7BHgEOJIQAABawWYLWVt1/VWvFCKzimWIjkqLzz4kDSV3yDzL+JaG9t7NQr1J9xEoReoAwIIIJBQgcKziuVSERk180apmX0Rp6MSehz43WzCjd+ilIcAAgggMASBv5Bxdz4g990wScYM4V28FIGBBAg3A+nwMwQQiLTAxIkTJZVKRbqOVG4Aga498sMNhVK94nNSym+jAaD40VAFRg31DbweAQQQQACBYQt07ZFVX7pVOq6/Vca1HJW/vucmuYxp38Pm5I3eAmRlbxeeRQABCwROnjwpra2tFtSUKqYFurvkSMvv5fmWk/LX/2OxTCPYpGl44J8AIzf+WVISAgiELHD48GEpKyvj1FTI7iPa3dmz5f729hEVwZsRGEyAkZvBhPg5AggggAACCFglQLixqruoLAIIIIAAAggMJkC4GUyInyOAQGQFmC0V2a6hYgjkVYBwk1d+do4AAggggAACfgsQbvwWpTwEEAhNgNlSoVGzIwSsEiDcWNVdVBYBBNwCZraU+zkeI4AAAoQbjgEEEEAAAQQQiJUA4SZW3UljEEAAAQQQQIBwwzGAAALWCowfP15aWlqsrT8VRwCBYAQIN8G4UioCCIQgMHr0aNHp4GwIIICAW4Bw49bgMQIIIIAAAghYL0C4sb4LaQACyRXQRTMLCgqSC0DLEUDAU4Bw48nCkwgggAACCCBgqwDhxtaeo94IIIAAAggg4ClAuPFk4UkEELBBgNlSNvQSdUQgfAHCTfjm7BEBBHwSYLaUT5AUg0DMBAg3MetQmoMAAggggEDSBQg3ST8CaD8CFgswW8rizqPqCAQoQLgJEJeiEUAAAQQQQCB8AcJN+ObsEQEEEEAAAQQCFCDcBIhL0QggEKwAs6WC9aV0BGwVINzY2nPUGwEEhNlSHAQIIOAlQLjxUuE5BBBAAAEEELBWgHBjbddRcQQQaGtrk5qaGiAQQACBDAHCTQYH3yCAgE0CJ06ckLq6OpuqTF0RQCAEAcJNCMjsAgEEEEAAAQTCEyDchGfNnhBAwGeBkpISqa+v97lUikMAAdsFCDe29yD1RyDBAsXFxVJZWZlgAZqOAAJeAoQbLxWeQwABBBBAAAFrBQg31nYdFUcAAWZLcQwggICXAOHGS4XnEEDACgFmS1nRTVQSgdAFCDehk7NDBBBAAAEEEAhSgHATpC5lI4BAoALMlgqUl8IRsFaAcGNt11FxBBBgthTHAAIIeAkQbrxUeA4BBBBAAAEErBUg3FjbdVQcAQQ6OzuloaEBCAQQQCBDgHCTwcE3CCBgk8DRo0dlwYIFNlWZuiKAQAgChJsQkNkFAggggAACCIQnQLgJz5o9IYCAzwJFRUVSXV3tc6kUhwACtgv4Fm6eeeYZOXnypO0e1B8BBCwSGDdunNTW1lpUY6qKAAJhCPgWburq6kT/ijIBp6CgQLL/Mw2K2/PaHrPlq23Z+8/+3tRrqM9HoW2m7ubrUNvQ3+tpW+a/0f6cova8V7/phcXms8fUl68IIJBcgRGFm+XLl8tVV12VoafP6YdMKpXq8595YfbPbH9e22O2fLUte//Z35t6DfX5KLTN1N18HWob+ns9bcv8N9qfU9Se9+q3xYsXi/nsMfXlKwIIJFdgROFGh4R1GqY74Dz88MPOh4z+JcWGAAIIhCHw2GOPObtZuHCh8NkThjj7QCDaAiMKN9o0DThPP/203HjjjemWasCZO3eu6Iq9bAgggEDQAqNHj5Y1a9ZIZWWl6F2L2RBAINkCIw43ymc+WNwB57nnnnM+aAg4yT7AaD0CYQno59CiRYvSu+ManDQFDxBInIAv4UbVCDiJO3ZoMAKRFWhtbZWZM2fK7t27I1tHKoYAAsEJ+BZutIoacNavXy9r165N11hHcMaPH8+HTFqEBwggELTAxIkTnVGcGTNm8NkTNDblIxBBgVFB1GnZsmVOsbfccku6eP2Q2bVrl1xzzTXp53iAAAIIBCWgn0Nnn312UMVTLgIIRFjA15Ebdzv1g8U9gqM/468otxCPEUAgaAG9Boc/qIJWpnwEoicQWLjRpmrA2b59e0arNeBs2bIl4zm+QQABBIIWWLp0qaxbty7o3VA+AghEQCDQcKPtq6iocE5HudtaVVXFh4wbhMcIIBC4wA033CB6qpyAEzg1O0Ag7wKBhxttoQ4L6/U27o0PGbcGjxFAIGgB8zn01FNPsVRD0NiUj0CeBUIJN9pG/WB54YUXMu5mrAFn5cqVfNDk+SBg9wgkRUA/h7Zu3erM7ExKm2knAkkUCC3cKO6UKVP6LNdw1113sSZMEo882oxAngX0BqM1NTX8cZXnfmD3CAQhEGq40QYMtB4VdxQNoospEwEE+hNoamrij6v+cHgeAYsFQg83amUCzrx589J0LLiZpuABAgiEIGDWxdNdPf744yHskV0ggEBYAnkJN9o4/WDRlXzd61Gx4GZY3c5+EEBABcyyMe41qZBBAAH7BfIWbpTOfLC4Aw4Lbtp/UNECBGwS0M8hs+k9uFjs12jwFQF7BfIabpRtoICji9+xIYAAAmEJHDt2TCorK1mPKixw9oNAQAJ5DzfaLg04XgtulpWV8SETUMdTLAII9BXQu6rrKSq9k3pnZ2ffF/AMAghYIRCJcGOkWI/KSPAVAQTyJaCfQ4cPH5bi4uJ8VYH9IoDACAUiFW60LQScEfYob0cAgREL6IQH3fT2FI2NjSMujwIQQCBcgciFG22+BhyvBTdZEybcg4O9IZB0gZaWFpkzZw7rUSX9QKD91glEMtyooteCm6xHZd3xRYURsFpA76qu6+LpZ09DQ4PVbaHyCCRJILLhRjvBLHTn7hACjluDxwggELSAWRfv2muvDXpXlI8AAj4JRDrcaBvNB8tVV12VbrIGHNaESXPwAAEEAhbQERxzP5x9+/axHlXA3hSPwEgFIh9utIFeC27W1dWxJsxIe5/3I4DAkAVuuukmPnuGrMYbEAhXwIpwoyRmPSr3CI5Zj4oFN8M9aNgbAkkW0Gtvjhw5QsBJ8kFA2yMvYE24UUkTcLwW3OSW6ZE/1qggArEQMOvi6TU45lRVLBpGIxCIkYBV4UbdzQeLez0qHcHRW6YTcGJ0ZNIUBCIsoKFGP3PMxt2MjQRfEYiGgHXhRtn0g2XNmjUZK4qz4GY0DihqgUDSBPQmf3PnzuWPq6R1PO2NtICV4UZFTcCprq5OA5uAw4KbaRIeIIBAwAJ6Ty5dj2r8+PGiM6nYEEAg/wLWhhul04BTW1sra9euTUtqwGHBzTQHDxBAIAQBvav65s2bpaSkJIS9sQsEEBhMwOpwYxrHelRGgq8IIJAvAR290WsC2RBAIP8CsQg3ykjAyf/BRA0QQKBHYP78+bJlyxY4EEAgTwKxCTfqpwFH14FxbzNmzGDROzcIjxFAIHABvRawqqqKz57ApdkBAt4CsQo32kTWo/LuaJ5FAIHwBMzn0IsvvhjeTtkTAgikBWIXbrRl5oMl3UoRZ1XfdevWuZ/iMQIIIBCYgH4OrV+/PrDyKRgBBPoXiGW40ebqB0tLS4u4l2tgwc3+DwR+ggACwQnoFPGlS5ey4GZwxJSMQIZAbMONtnLixImi68C4Aw4Lbmb0P98ggEAIAjpFXE9RLV++nIATgje7QCDW4Ua716xH5Q44LLjJgY8AAmEKmM8hXXBTR5TZEEAgWIHYhxvlMx8s2etR6V9RrEcV7AFG6Qgg0COgn0Nbt26VKVOmQIIAAgELJCLcqKF+sGSvR8WCmwEfXRSPAAL9Cuh9cPjjql8efoDAiAQSE25UyaxH5R7BMetR8SEzouOINyOAwBAF9u/f76wszmfPEOF4OQI5CCQq3KiHCTheC26y6F0ORwwvQQABXwR0XTxdsqGystKX8igEAQROCyQu3GjT+1twc+rUqbJ79+7TOjxCAAEEAhTQu6pv27YtwD1QNALJFEhkuDFdzXpURoKvCCCQL4Hi4mJn13p6ij+u8tUL7DduAhaHmw+lo+FbUlBQIAUFY2XWqj3SJR9Ix54HpWpsgRRMWCV7Pxy8u/oLOI2NjYO/mVcggAACPgkcOnRIdC08Ftz0CZRiEi1gcbgZJaWVD0nq1EGpX3y+ND1QL41Prpf/vX+mPNiektRrt8m0Ubn1rdeCm3PmzGHRu9z4eBUCCPggYJaN0QU3GcHxAZQiEi1gcbjp7bfC8fL5b3xJSjtqZdm/lMryGybJmGF0qflgcb9Vl2tgPSq3CI8RQCBIAf0ceuGFF5zlY4LcD2UjEHcB+8ONFMrZV35eri8tlcuv+aSUjqBFBJy4H+60D4HoC7hv8qczOE+ePBn9SlNDBCImMIIoEJ2WdB9/V45KhzT+9P/Ka90jq5cGHK8FN1n0bmSuvBsBBIYmoKHmpptuYj2qobHxagQcAfvDTfch2fqDRilZWCHy0mvS1jXCdNPPgpusR8W/GAQQCFNAb1mhC/+aBTfD3Df7QsB2AcvDzQfy5tYfSWPFnXLvN78mFR2Nsr35Ndm7+j5pePODEfWNWY+KBTdHxMibEUBgBALmc+jmm28eQSm8FYHkCVgabrpk76pZUlDwJVkj/11WVV4so8ZOki+Ut0vtDzbJoeu+LZUXnTHi3jQfLO7lGnQEZ+HChawJM2JdCkAAgVwE9HPIXIejp6o6OztzeRuvQSDRAjlOlo6a0RiZdttvJHWbq15jpsttv2kX91Ounw77oX6w6IKbummw0e2JJ56Q9vZ2Z8hYf86GAAIIhCGwYcMG5z44erqKz54wxNmHrQKWjtyEy23Wo3KP4LDgZrh9wN4QQEBkyZIlUl5ezoKbHAwIDCJAuBkEyPzYBBwW3DQifEUAgbAFzLp4euPRoqKisHfP/hCwRoBwM4SuMh8sa9euTb9LR3BYcDPNwQMEEAhBQFcTN2tScR+cEMDZhXUChJthdFl/61Fxy/RhYPIWBBAYtoBeXDxz5kyWaxi2IG+MqwDhZpg9qwFn8+bNGe/WRe9YcDODhG8QQCBAAR29Wb16tbPgJkvFBAhNxI5vvgAAB7pJREFU0dYJEG5G0GU6NLxr166MElhwM4ODbxBAIGABr2VjAt4lxSMQeQHCzQi7yOuDhQU3R4jK2xFAYEgC+jmko8lsCCDQI0C48eFIIOD4gEgRCCDgi8CWLVukpqaGBTd90aQQWwUINz71nAacw4cPi3u5Bh3BYcFNn4ApBgEEchKYPXu2NDU1seBmTlq8KK4ChBsfe1bvGKp3DnUHHBbc9BGYohBAYFAB8zmkC262tLQM+npegEAcBQg3Pveq+WAh4PgMS3EIIJCzgH4O7dmzJ70mVc5v5IUIxESAcBNAR+oHy7Zt28S9XAMLbgYATZEIIDCogN7kb+XKlSz2O6gUL4iTAOEmoN7U+0/ogpvugKMLblZWVvIhE5A5xSKAgLfA73//ez57vGl4NqYChJsAO9asR+UOOCy4GSA4RSOAQB8B8zk0f/585w+uPi/gCQRiKEC4CbhTzQfLvffem96TCTgs15Am4QECCAQooJ9DK1askO9///sB7oWiEYiOAOEmhL4wHyzZC27qcg0EnBA6gF0ggIAjoJ9FuunnDp89HBRxFiDchNi7LLgZIja7QgCBfgXefvttZz0qAk6/RPzAcgHCTcgd2N+Cm3p/HDYEEEAgDAGd2KDr4jF6HIY2+8iHAOEmD+peC24uWLBAWNU3D53BLhFIqIC5q7p+ZUMgbgKEmzz1KOtR5Qme3SKAQFpA78llNk5RGQm+xkGAcJPHXhwo4OiNt9gQQACBMAQ6Ozvl1ltvZcHNMLDZRygChJtQmPvfiRkadi/XoAtuLl++nFV9+2fjJwgg4KOA3nRUr/vTBTe/973v+VgyRSGQH4FR+dkte3ULmPWo9CI/vQeObrpcg256l2MzfdN5gv8hgAACAQiYz6EAiqZIBEIXYOQmdHLvHZoPFvcIDiuKe1vxLAIIBCOgn0P6n25tbW0sFRMMM6WGIEC4CQE5113oh4rXgpszZ87kQyZXRF6HAAK+CGzdupX1qHyRpJB8CBBu8qE+wD69Ftw0yzXoX1JsCCCAQBgCS5YskcmTJzsBRy84ZkPAJgHCTQR7S6+xyV5RnIATwY6iSgjEWMB8DumNR7nuL8YdHdOmEW4i2rHmg4UFNyPaQVQLgQQI6OeQ3nTUhBtGcBLQ6TFpIuEmwh2pHyi6ki8Lbka4k6gaAgkR0NPi559/PgtuJqS/bW8m4caCHmTBTQs6iSoiEHMBnfCwefNm1qOKeT/HpXmEG0t6UgNOfX19Rm110bvGxsaM5/gGAQQQCErAa128oPZFuQiMRIBwMxK9kN9rVvJ171bvZsyGAAIIhCWgd1XX/9gQiLIAdyiOcu941M2sR6WjNl5ba2ur19M8hwACCPguoPfC2bVrl+/lUiACIxUg3IxUMA/vNwFHF7ozyzWYapSVlZmHfEUAAQQQQCCRApyWsrTbNeDoQndTp061tAVUGwEEEEAAgWAECDfBuIZSqs5e+MUvfiHu9ahC2TE7QQABBBBAIMICBalUKhXh+lG1HAT0xlpHjx7N4ZW8BAEEEAhOoKSkRHQJGTYE8i1AuMl3D7B/BBBAAAEEEPBVgNNSvnJSGAIIIIAAAgjkW4Bwk+8eYP8IIIAAAggg4KsA4cZXTgpDAAEEEEAAgXwLEG7y3QPsHwEEEEAAAQR8FSDc+MpJYQhEV6C7Y7esrrpcCgoKpGDWCmloPRbdylIzBBBAYAQChJsR4PFWBKwR6HpRtjb+hfzXn7wkqVPt8uyX35Rl5ffJzmPd1jSBiiKAAAK5ChBucpXidQhYK/C+HGg+KZ++/mop1X/xhaUyfUmVXC+Nsr2509pWUXEEEECgPwHCTX8yPI9AbATOlEvLr5aLXP/au986KPvKviF/M50brsWmm2kIAgikBVwfd+nneIAAArEVOCatOzfKnfd2yO2P3izTxvR+BHQ0SJVei+Ncj7Na9nZ1y+lrdGbJqr1dsRWhYQggED8B7lAcvz6lRQh4CxzbKbdf9jmp7dAfV0hN/Q/lnsrLZEz61R/Imw3flasWPCPX198jH332mFx7zzfkMhOA0q/jAQIIIBBtAUZuot0/1A4B/wTOni33t6fkVPuzsqlGpHbBV+U7DYfk9CXFZ8hFn6+U60v3Su2yJ+Xi5V8j2PinT0kIIBCiAOEmRGx2hUAUBApLp0vVP/xQNlT8QX797AHJOOF09hUy5/ppIpd/SiaVnhGF6lIHBBBAYMgChJshk/EGBGIgUPhxmfG1GX0b0v1Heffon0Qat8mu197v+3OeQQABBCwQINxY0ElUEQH/BbqkreU9ufbTl2Zec7P1R/KrkplSLq9LS1vGmI7/VaBEBBBAICABwk1AsBSLQGQEug9Jw5IrZdbtj8jejg9E5APp2Pmg3P/W16W6YryYD4HuN38pP2j8tPyve5fJ9RXt8sj2F+TNvQ/JiozrciLTKiqCAAII9CtgPtf6fQE/QAABywUKz5NPXjNZWmoXyZVj/5MUjF0q//zuF2XTT6qcC4Y/3LtKJhSMlc+tEfnuqvly0aiPyuQvfEo6alfJmkPlsqLy4nQAslyC6iOAQEIEmAqekI6mmQgggAACCCRFgJGbpPQ07UQAAQQQQCAhAoSbhHQ0zUQAAQQQQCApAoSbpPQ07UQAAQQQQCAhAv8fz/l7s5pZjeYAAAAASUVORK5CYII="></p>
<p style="text-align: left;">The volume of Nanako’s bag is 3888 cm<sup>3</sup>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the area of cloth, in cm<sup>2</sup>, needed to make Haruka’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the volume, in cm<sup>3</sup>, of the bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this value to write down, and simplify, the equation in<em> x</em> and <em>y</em> for the volume of Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down and simplify an expression in <em>x</em> and <em>y</em> for the area of cloth, <em>A</em>, used to make Nanako’s bag.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answers to parts (c) and (d) to show that</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = 3{x^2} + \frac{{10368}}{x}">
  <mi>A</mi>
  <mo>=</mo>
  <mn>3</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mfrac>
    <mrow>
      <mn>10368</mn>
    </mrow>
    <mi>x</mi>
  </mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}x}}">
  <mfrac>
    <mrow>
      <mrow>
        <mtext>d</mtext>
      </mrow>
      <mi>A</mi>
    </mrow>
    <mrow>
      <mrow>
        <mtext>d</mtext>
      </mrow>
      <mi>x</mi>
    </mrow>
  </mfrac>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your answer to part (f) to show that the width of Nanako’s bag is 12 cm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="question">
<p>The derivative of a function <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>'</mo><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><msup><mtext>e</mtext><mi>x</mi></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>. The graph of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math> passes through the point <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>4</mn><mo>)</mo></math> . Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>.</p>
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<p><strong>Note:</strong>     <strong>In this question, distance is in metres and time is in seconds.</strong></p>
<p> </p>
<p>A particle moves along a horizontal line starting at a fixed point A. The velocity <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
  <mi>v</mi>
</math></span> of the particle, at time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>, is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v(t) = \frac{{2{t^2} - 4t}}{{{t^2} - 2t + 2}}">
  <mi>v</mi>
  <mo stretchy="false">(</mo>
  <mi>t</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mfrac>
    <mrow>
      <mn>2</mn>
      <mrow>
        <msup>
          <mi>t</mi>
          <mn>2</mn>
        </msup>
      </mrow>
      <mo>−</mo>
      <mn>4</mn>
      <mi>t</mi>
    </mrow>
    <mrow>
      <mrow>
        <msup>
          <mi>t</mi>
          <mn>2</mn>
        </msup>
      </mrow>
      <mo>−</mo>
      <mn>2</mn>
      <mi>t</mi>
      <mo>+</mo>
      <mn>2</mn>
    </mrow>
  </mfrac>
</math></span>, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5">
  <mn>0</mn>
  <mo>⩽</mo>
  <mi>t</mi>
  <mo>⩽</mo>
  <mn>5</mn>
</math></span>. The following diagram shows the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v">
  <mi>v</mi>
</math></span></p>
<p><img src="images/Schermafbeelding_2017-08-15_om_08.18.11.png" alt="M17/5/MATME/SP2/ENG/TZ2/07"></p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
  <mi>t</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(0,{\text{ }}0)">
  <mo stretchy="false">(</mo>
  <mn>0</mn>
  <mo>,</mo>
  <mrow>
    <mtext> </mtext>
  </mrow>
  <mn>0</mn>
  <mo stretchy="false">)</mo>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(2,{\text{ }}0)">
  <mo stretchy="false">(</mo>
  <mn>2</mn>
  <mo>,</mo>
  <mrow>
    <mtext> </mtext>
  </mrow>
  <mn>0</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<p>Find the maximum distance of the particle from A during the time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0 \leqslant t \leqslant 5">
  <mn>0</mn>
  <mo>⩽</mo>
  <mi>t</mi>
  <mo>⩽</mo>
  <mn>5</mn>
</math></span> and justify your answer.</p>
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