File "HL-paper3.html"

Path: /IB QUESTIONBANKS/4 Fourth Edition - PAPER/HTML/Physics/Option B HTML/HL-paper3html
File size: 304.84 KB
MIME-type: text/x-tex
Charset: utf-8

 
Open Back 
<!DOCTYPE html>
<html>


<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-212ef6a30de2a281f3295db168f85ac1c6eb97815f52f785535f1adfaee1ef4f.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-13d27c3a5846e837c0ce48b604dc257852658574909702fa21f9891f7bb643ed.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">

</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../index.html">Home</a>
</li>
<li class="active dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Questionbanks
<b class="caret"></b>
</a><ul class="dropdown-menu">
<li>
<a href="../../geography.html" target="_blank">DP Geography</a>
</li>
<li>
<a href="../../physics.html" target="_blank">DP Physics</a>
</li>
<li>
<a href="../../chemistry.html" target="_blank">DP Chemistry</a>
</li>
<li>
<a href="../../biology.html" target="_blank">DP Biology</a>
</li>
<li>
<a href="../../furtherMath.html" target="_blank">DP Further Mathematics HL</a>
</li>
<li>
<a href="../../mathHL.html" target="_blank">DP Mathematics HL</a>
</li>
<li>
<a href="../../mathSL.html" target="_blank">DP Mathematics SL</a>
</li>
<li>
<a href="../../mathStudies.html" target="_blank">DP Mathematical Studies</a>
</li>
</ul></li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">

<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>

<div class="page-content container">
<div class="row">
<div class="span24">



</div>
</div>

<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="images/ib-qb-46-logo-683ef0176708d789b2acbf6ece48c55de4cd5ddac781fb455afe3540d22d050e.jpg" alt="Ib qb 46 logo">
</div>
</div>
</div><h2>HL Paper 3</h2><div class="specification">
<p>The water supply for a hydroelectric plant is a reservoir with a large surface area. An outlet pipe takes the water to a turbine.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_15.42.28.png" alt="M18/4/PHYSI/HP3/ENG/TZ1/10"></p>
</div>

<div class="specification">
<p>The following data are available:</p>
<p>\[\begin{array}{*{20}{l}} {{\text{density of water}}}&amp;{ = 1.00 \times {{10}^3}{\text{ kg }}{{\text{m}}^{ - 3}}} \\ {{\text{viscosity of water}}}&amp;{ = 1.31 \times {{10}^{ - 3}}{\text{ Pa s}}} \\ {{\text{diameter of the outlet pipe}}}&amp;{ = 0.600{\text{ m}}} \\ {{\text{velocity of water at outlet pipe}}}&amp;{ = 59.4{\text{ m}}{{\text{s}}^{ - 1}}} \end{array}\]</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the difference in terms of the velocity of the water between laminar and turbulent flow.</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>The water level is a height <em>H </em>above the turbine. Assume that the flow is laminar in the outlet pipe.</p>
<p>Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by <em>v</em> = \(\sqrt {2gH} \).</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>Calculate the Reynolds number for the water flow.</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>Outline whether it is reasonable to assume that flow is laminar in this situation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>An air bubble has a radius of 0.25 mm and is travelling upwards at its terminal speed in a liquid of viscosity 1.0 &times; 10<sup>&ndash;3</sup> Pa s.</p>
<p>The density of air is 1.2 kg m<sup>&ndash;3</sup> and the density of the liquid is 1200 kg m<sup>&ndash;3</sup>.</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>Explain the origin of the buoyancy force on the air bubble.</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>With reference to the ratio of weight to buoyancy force, show that the weight of the air bubble can be neglected in this situation.</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>Calculate the terminal speed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Two tubes, A and B, are inserted into a fluid flowing through a horizontal pipe of&nbsp;diameter 0.50 m. The openings X and Y of the tubes are at the exact centre of the pipe.&nbsp;The liquid rises to a height of 0.10 m in tube A and 0.32 m in tube B. The density of the&nbsp;fluid = 1.0 &times; 10<sup>3</sup> kg m<sup>&ndash;3</sup>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_09.34.50.png" alt="M18/4/PHYSI/HP3/ENG/TZ2/10"></p>
</div>

<div class="specification">
<p>The viscosity of water is 8.9 &times; 10<sup>&ndash;4</sup> Pa s.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the velocity of the fluid at X is about 2 ms<sup>–1</sup>, assuming that the flow is laminar.</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>Estimate the Reynolds number for the fluid in your answer to (a).</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>Outline whether your answer to (a) is valid.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph below represents the variation with time <em>t </em>of the horizontal displacement <em>x </em>of a mass attached to a vertical spring.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_15.49.15.png" alt="M18/4/PHYSI/HP3/ENG/TZ1/11"></p>
</div>

<div class="specification">
<p>The total mass for the oscillating system is 30 kg. For this system</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the motion of the spring-mass system.</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>determine the initial energy.</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>calculate the Q at the start of the motion.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A solid sphere A suspended by a string from a fixed support forms a simple pendulum.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoYAAAIcCAYAAABrd29cAAAKqGlDQ1BJQ0MgUHJvZmlsZQAASImVlwdUU1kax+976Y0WiHRCDb13pNdQBOkgKiGhhBJCIKjYlUEFx4KKCFhAhqrAqBRRERHFwiCg2HVABhF1HSyIipp9yBJ2ds/unv2f8533y/fu++73bu495/8AIF9j8fmpsBQAabwsQbC3Gz0yKpqOGwEQwAACIAJ1FjuT7xoU5A8QzV//qo93kdGIbhvN1vr3+/9V0pz4TDYAUBDCcZxMdhrCZ5BoYvMFWQCgOEhec1UWf5a3IywrQBpEuGyWE+e4aZbj5rj7x5jQYHeE7wOAJ7NYgkQASH8geXo2OxGpQ0YjbMrjcHkIWyLsxE5iIfOQkXvAMC0tfZaPIawb9091Ev9SM05ck8VKFPPcu/wQ3oObyU9lrfk/l+N/Ky1VOD+HBhLkJIFP8Ox8yJrVpKT7iZkXtyRwnrmcuZ5mOUnoEzbP7Ez36HnmsDz85lmYEuY6zyzBwrPcLGboPAvSg8X1ealL/MX145lijs/0DJnnBK4Xc55zkkIj5jmbG75knjNTQvwWxriL8wJhsLjnBIGX+B3TMhd6Y7MW5spKCvVZ6CFS3A8n3sNTnOeFicfzs9zENfmpQQv9p3qL85nZIeJns5ANNs/JLN+ghTpB4vUBXBAAWICdFb96dl8B93T+GgE3MSmL7oqckng6k8c2NqSbm5rZADB75ub+0ve0H2cJot1YyG1tBsCxQyQSnVvI+e0B4DQDAGL/Qo6xFwBJJQCulbOFguy53OxWR04yEUgCWaAAVIEm0AVGwBxYAwfgAjyBLwgEoSAKrABskATSgACsAuvAZpAHCsAecACUgKPgOKgBJ8Ep0ArOg0vgKrgJ+sEQeASGwRh4BSbBRzADQRAOokBUSAFSg7QhA8gcsoWcIE/IHwqGoqBYKBHiQUJoHbQVKoAKoRKoHKqFfoXOQpeg69AA9AAagSagd9AXGAWTYVlYBdaBTWBb2BX2g0Ph5XAinAHnwLnwLrgYroBPwC3wJfgmPAQPw6/gKRRAkVA0lDrKCGWLckcFoqJRCSgBagMqH1WEqkA1oNpRPajbqGHUa9RnNBZNRdPRRmgHtA86DM1GZ6A3oHeiS9A16BZ0N/o2egQ9if6OoWCUMQYYewwTE4lJxKzC5GGKMFWYZswVzBBmDPMRi8XSsAysDdYHG4VNxq7F7sQexjZiO7ED2FHsFA6HU8AZ4BxxgTgWLguXhzuEO4G7iBvEjeE+4Ul4Nbw53gsfjefht+CL8HX4Dvwgfhw/Q5AiaBPsCYEEDmENYTehktBOuEUYI8wQpYkMoiMxlJhM3EwsJjYQrxAfE9+TSCQNkh1pKYlL2kQqJjWRrpFGSJ/JMmR9sjs5hiwk7yJXkzvJD8jvKRSKDsWFEk3Jouyi1FIuU55SPklQJYwlmBIciY0SpRItEoMSbyQJktqSrpIrJHMkiyRPS96SfC1FkNKRcpdiSW2QKpU6K3VPakqaKm0mHSidJr1Tuk76uvQLGZyMjoynDEcmV+a4zGWZUSqKqkl1p7KpW6mV1CvUMVmsLEOWKZssWyB7UrZPdlJORs5SLlxutVyp3AW5YRqKpkNj0lJpu2mnaHdpXxapLHJdFL9ox6KGRYOLpuWV5F3k4+Xz5Rvlh+S/KNAVPBVSFPYqtCo8UUQr6isuVVyleETxiuJrJVklByW2Ur7SKaWHyrCyvnKw8lrl48q9ylMqqireKnyVQyqXVV6r0lRdVJNV96t2qE6oUdWc1Lhq+9Uuqr2ky9Fd6an0Yno3fVJdWd1HXahert6nPqPB0AjT2KLRqPFEk6hpq5mguV+zS3NSS00rQGudVr3WQ22Ctq12kvZB7R7taR2GToTONp1WnRcMeQaTkcOoZzzWpeg662boVuje0cPq2eql6B3W69eH9a30k/RL9W8ZwAbWBlyDwwYDhhhDO0OeYYXhPSOykatRtlG90YgxzdjfeItxq/EbEy2TaJO9Jj0m302tTFNNK00fmcmY+ZptMWs3e2eub842LzW/Y0Gx8LLYaNFm8dbSwDLe8ojlfSuqVYDVNqsuq2/WNtYC6wbrCRstm1ibMpt7trK2QbY7ba/ZYezc7Dbanbf7bG9tn2V/yv5PByOHFIc6hxeLGYvjF1cuHnXUcGQ5ljsOO9GdYp2OOQ07qzuznCucn7lounBcqlzGXfVck11PuL5xM3UTuDW7Tbvbu6937/RAeXh75Hv0ecp4hnmWeD710vBK9Kr3mvS28l7r3emD8fHz2etzj6nCZDNrmZO+Nr7rfbv9yH4hfiV+z/z1/QX+7QFwgG/AvoDHS7SX8Ja0BoJAZuC+wCdBjKCMoHNLsUuDlpYufR5sFrwuuCeEGrIypC7kY6hb6O7QR2G6YcKwrnDJ8Jjw2vDpCI+IwojhSJPI9ZE3oxSjuFFt0bjo8Oiq6KllnssOLBuLsYrJi7m7nLF89fLrKxRXpK64sFJyJWvl6VhMbERsXexXViCrgjUVx4wri5tku7MPsl9xXDj7ORPxjvGF8eMJjgmFCS8SHRP3JU4kOScVJb3munNLuG+TfZKPJk+nBKZUp4hSI1Ib0/BpsWlneTK8FF53umr66vQBvgE/jz+cYZ9xIGNS4CeoyoQyl2e2Zcki5qZXqCv8STiS7ZRdmv1pVfiq06ulV/NW967RX7NjzXiOV84va9Fr2Wu71qmv27xuZL3r+vIN0Ia4DV0bNTfmbhzb5L2pZjNxc8rm37aYbinc8mFrxNb2XJXcTbmjP3n/VJ8nkSfIu7fNYdvR7ejt3O19Oyx2HNrxPZ+Tf6PAtKCo4OtO9s4bP5v9XPyzaFfCrr7d1ruP7MHu4e25u9d5b02hdGFO4ei+gH0t++n78/d/OLDywPUiy6KjB4kHhQeHi/2L2w5pHdpz6GtJUslQqVtpY5ly2Y6y6cOcw4NHXI40HFU5WnD0yzHusfvl3uUtFToVRcexx7OPP68Mr+z5xfaX2irFqoKqb9W86uGa4JruWpva2jrlut31cL2wfuJEzIn+kx4n2xqMGsobaY0FTaBJ2PTy19hf757yO9V12vZ0wxntM2XN1Ob8FqhlTctka1LrcFtU28BZ37Nd7Q7tzeeMz1WfVz9fekHuwu4OYkduh+hizsWpTn7n60uJl0a7VnY9uhx5+U730u6+K35Xrl31unq5x7Xn4jXHa+ev218/e8P2RutN65stvVa9zb9Z/dbcZ93XcsvmVlu/XX/7wOKBjkHnwUu3PW5fvcO8c3NoydDA3bC79+/F3Bu+z7n/4kHqg7cPsx/OPNr0GPM4/4nUk6Knyk8rftf7vXHYevjCiMdI77OQZ49G2aOv/sj84+tY7nPK86JxtfHaF+Yvzk94TfS/XPZy7BX/1czrvL9J/63sje6bM3+6/Nk7GTk59lbwVvRu53uF99UfLD90TQVNPf2Y9nFmOv+Twqeaz7afe75EfBmfWfUV97X4m9639u9+3x+L0kQiPkvA+mEFUEjACQkAvKsGgBIFALUf8Q8Sc574h6A5H/+DwH/iOd/8Q9YANCCXWSvk3glAExI6LgBIIL9nLVGoC4AtLMTxD2UmWJjP1SIjzhLzSSR6rwIArh2AbwKRaOawSPStEmn2AQCdGXNefFZY5AulAefE9lg20G6yCfyL/g6ASgOXEKUHbQAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAAxppVFh0WE1MOmNvbS5hZG9iZS54bXAAAAAAADx4OnhtcG1ldGEgeG1sbnM6eD0iYWRvYmU6bnM6bWV0YS8iIHg6eG1wdGs9IlhNUCBDb3JlIDUuNC4wIj4KICAgPHJkZjpSREYgeG1sbnM6cmRmPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5LzAyLzIyLXJkZi1zeW50YXgtbnMjIj4KICAgICAgPHJkZjpEZXNjcmlwdGlvbiByZGY6YWJvdXQ9IiIKICAgICAgICAgICAgeG1sbnM6dGlmZj0iaHR0cDovL25zLmFkb2JlLmNvbS90aWZmLzEuMC8iCiAgICAgICAgICAgIHhtbG5zOmV4aWY9Imh0dHA6Ly9ucy5hZG9iZS5jb20vZXhpZi8xLjAvIj4KICAgICAgICAgPHRpZmY6T3JpZW50YXRpb24+MTwvdGlmZjpPcmllbnRhdGlvbj4KICAgICAgICAgPHRpZmY6WVJlc29sdXRpb24+MTQ0PC90aWZmOllSZXNvbHV0aW9uPgogICAgICAgICA8dGlmZjpSZXNvbHV0aW9uVW5pdD4yPC90aWZmOlJlc29sdXRpb25Vbml0PgogICAgICAgICA8dGlmZjpDb21wcmVzc2lvbj4xPC90aWZmOkNvbXByZXNzaW9uPgogICAgICAgICA8dGlmZjpQaG90b21ldHJpY0ludGVycHJldGF0aW9uPjI8L3RpZmY6UGhvdG9tZXRyaWNJbnRlcnByZXRhdGlvbj4KICAgICAgICAgPHRpZmY6WFJlc29sdXRpb24+MTQ0PC90aWZmOlhSZXNvbHV0aW9uPgogICAgICAgICA8ZXhpZjpQaXhlbFhEaW1lbnNpb24+NjQ2PC9leGlmOlBpeGVsWERpbWVuc2lvbj4KICAgICAgICAgPGV4aWY6UGl4ZWxZRGltZW5zaW9uPjU0MDwvZXhpZjpQaXhlbFlEaW1lbnNpb24+CiAgICAgIDwvcmRmOkRlc2NyaXB0aW9uPgogICA8L3JkZjpSREY+CjwveDp4bXBtZXRhPgpieF+tAABAAElEQVR4Ae3dDXhU1Z348R++/Nfa2HZw+zS2tCUE2toXl4G+4MMSIUjrBqwgKmBbUl94ycZUeTeAgBjAEEDbyIb3bbCaRIugltSKBCFrtV0hXdptrSRAW5W4rcSXrLUPdfnP78LEEJOZO3Nn7tx77vc+j2Uyc8655/c5Q/PjnHvP7XUycggHAggggAACCCCAQOAFzgq8AAAIIIAAAggggAAClgCJIV8EBBBAAAEEEEAAAUuAxJAvAgIIIIAAAggggIAlQGLIFwEBBBBAAAEEEEDAEiAx5IuAAAIIIIAAAgggYAmQGPJFQAABBBBAAAEEELAESAz5IiCAAAIIIIAAAghYAiSGfBEQQAABBBBAAAEELAESQ74ICCCAAAIIIIAAApYAiSFfBAQQQAABBBBAAAFLgMSQLwICCCCAAAIIIICAJUBiyBcBAQQQQAABBBBAwBIgMXThi9Da2ip3Ll4i9TvrXTgbp0AAAQQQQCDYAvo7d9PGjdLe3h5siCSiJzFMAs1ulWhCOHTIpbK1utpuNcohgAACCCCAgAOBN998Q1YsWy7D8/JIEBN07HUyciRYh+JxBDQhXF+1riMZnFxYKNOKpkt2dnacmnyMAAIIIIAAAqkQaGpqkrWV98mehgYJ9Q7J9KIimThpkmRlZaWieWPbIDFM4dCSEKYQk6YQQAABBBBIgQAJYmKIJIaJeXVbmoSwWxbeRAABBBBAwDMCJIj2hoLE0J5Tt6VICLtl4U0EEEAAAQQ8K0CCGHtoSAxj+3T7KQlhtyy8iQACCCCAgG8ESBC7HyoSw+5dun2XhLBbFt5EAAEEEEDAtwIkiGcOHYnhmR7d/kRC2C0LbyKAAAIIIGCMAAniqaEkMYzzldYNMnUvJA4EEEAAAQQQMF/gh1u3yozbbpW2423WNjcbN2+WcDhsfuCnIyQxjDPUumv6P33xS3FK8TECCCCAAAIImCCgex5qUjgiP1+KS24JVFKo40diaPNbrAlibU2NrKuqsr4w/XL7yYyZs6RgdIHNFiiGAAIIIIAAAl4T6Pr7PagJYXRcSAyjEjb/7PoFIkG0CUcxBBBAAAEEPCTQ9fd50BPC6NCQGEYlEvyz6xeKBDFBQIojgAACCCCQAYGuv79JCM8cBBLDMz0S/qnrF4wEMWFCKiCAAAIIIJB2ga6/r0kIuycnMezeJeF3u37hSBATJqQCAggggAACKRfo+vuZhDA2MYlhbJ+EP+36BSRBTJiQCggggAACCDgW6Pr7mITQHimJoT2nhEt1/UJqgrhy1arA3faeMBwVEEAAAQQQcChQV1snFSvLA73tTLKEJIbJytms1zlBvP5b35aZs2barEkxBBBAAAEEEEhGYNTIkfLpT/cN5D6EyXh1rkNi2FmD1wgggAACCCCAQIAFzgpw7ISOAAIIIIAAAggg0EngnE6veYkAAggESuBEwzwZeOND8k4CUZ97yXUy48ovyWcuv0ZG5JyXQE2KIoAAAt4XYMbQ+2NEDxFAwEMCJw4+JCuX3SE3j/iqjJ1fL0ff9VDn6AoCCCDgUIDE0CEg1RFAIKgCb8mvH7xNvlW6S14PKgFxI4CAcQIsJRs3pASEAAJJCVwyX3Y/NkX6xqz8mjRt2yT/VrFZGlpPREqekNaHVsmGSUNlbvj8mDX5EAEEEPCDADOGfhgl+ogAAh4RuFDC4+fJupoyGZV97uk+vShb7ntCXvNID+kGAggg4ESAxNCJHnURQCCQAmfnjJdlc4ZLNDU88cwv5KBOIHIggAACPhcgMfT5ANJ9BBDIhMDZcuGgr8jnoqd+54i0vERmGOXgTwQQ8K8AiaF/x46eI4AAAggggAACKRUgMUwpJ40hgEBQBN59/bi0BSVY4kQAgcAIkBgGZqgJFAEEUifwthx8skFeijbYZ7AM/lT0isPom/yJAAII+E+AxNB/Y0aPEUAgwwLvtjwgyza9eLoX50qfKy+XS87OcKc4PQIIIJACAfYxTAEiTSCAQBAE3pXXmx6XH//iWfnJ6ofk19F7Tc4dLN+55gtCXhiE7wAxImC+AImh+WNMhAggYEfg4HIZ2Xe5nZKdyvSRUXeXyQ25PDO5EwovEUDAxwIsJft48Og6AghkUODcS2Tixq2ydnwus4UZHAZOjQACqRVgxjC1nrSGAAJGC/SR/KJvy9c++hm5vHCE9GX92OjRJjgEgihAYhjEUSdmBBB4v4CtZyW/vxrvIIAAAiYJsJRs0mgSCwIIIIAAAggg4ECAxNABHlURQAABBBBAAAGTBEgMTRpNYkEAAQQQQAABBBwIkBg6wKMqAggggAACCCBgkgCJoUmjSSwIIIAAAggggIADARJDB3hURQABBBBAAAEETBIgMTRpNIkFAQQQQAABBBBwIEBi6ACPqggggAACCCCAgEkCJIYmjSaxIIAAAggggAACDgR6nYwcDupTFQEEEEAAAQQQQMAQAWYMDRlIwkAAAQQQQAABBJwKkBg6FaQ+AggggAACCCBgiACJoSEDSRgIIIAAAggggIBTARJDp4LURwABBBBAAAEEDBEgMTRkIAkDAQQQQAABBBBwKnCO0wZi1c/tmxPrYz5DAAEEEEAAAQQQSINAy9EjSbXKjGFSbFRCAAEEEEAAAQTMEyAxNG9MiQgBBBBAAAEEEEhKgMQwKTYqIYAAAggggAAC5gmQGJo3pkSEAAIIIIAAAggkJUBimBQblRBAAAEEEEAAAfMESAzNG1MiQgABBBBAAAEEkhIgMUyKjUoIIIAAAggggIB5AiSG5o0pESGAAAIIIIAAAkkJkBgmxUYlBBBAAAEEEEDAPIFeJyOHeWEREQIIIIAAAggggECiAswYJipGeQQQMF5ga/VWuXb8NdLU1GR8rASIAAIIdBZgxrCzBq8RQCDwAq2trTJ0yKVyzrnnyKc+9SnZtXt34E0AQACB4AgwYxicsSZSBBCwIVBRXm6V+vuJv8vhlsOyaeNGG7UoggACCJghwIyhGeNIFAggkAIBXTq+ZtzVHS0NGjxIjhw5Ik/v2ydZWVkd7/MCAQQQMFWAGUNTR5a4EEAgYYHlZWUS6h3qqDd/4UJpO94mqytWdbzHCwQQQMBkARJDk0eX2BBAwLZAXW2dHNh/QObMnddRJxwOy+TCQtlaXS3Nh5o73ucFAgggYKoAS8mmjixxIYCAbYH29nYZnpcnoVDIutkkt2+OVbfl6BHRm1HGFBTIwIFh2bRls+02KYgAAgj4UYAZQz+OGn1GAIGUCmxYv8FaMl656v1LxtnZ2TK9qEj2NDRI477GlJ6XxhBAAAGvCZzjtQ7RHwQQQMBtgRH5I6xT6tJxd8fESZPk5ZdelgGfGdDdx7yHAAIIGCPAUrIxQ0kgCCCQKoHOS8mpapN2EEAAAT8IsJTsh1GijwgggAACCCCAgAsCJIYuIHMKBBBAAAEEEEDADwIkhn4YJfqIAAIIIIAAAgi4IEBi6AIyp0AAAQQQQAABBPwgQGLoh1GijwgggAACCCCAgAsCJIYuIHMKBBBAAAEEEEDADwIkhn4YJfqIAAIIIIAAAgi4IEBi6AIyp0AAAQQQQAABBPwgQGLoh1GijwgggAACCCCAgAsCJIYuIHMKBBBAAAEEEEDADwIkhn4YJfqIAAIIIIAAAgi4IEBi6AIyp0AAAQQQQAABBPwgQGLoh1GijwgggAACCCCAgAsCJIYuIHMKBBDInEBra6urJ3f7fK4Gx8kQQMB4ARJD44eYABEIrkD9znoZOuRSadzX6ApCXW2ddT6SQ1e4OQkCCKRBgMQwDag0iQACmRdob2+XRXcslH65/WRY3jBXOnTZ8Mus8yycv8CV83ESBBBAINUCJIapFqU9BBDwhEBtTY20HW+TlatWudaf7OxsKV0wX/Y0NLg2S+lacJwIAQQCIdDrZOQIRKQEiQACgRHQpVxdQh6Rny+btmxOOO7cvjlWnZajRxKuqzOVw/PyJBQKya7duxOuTwUEEEAgkwLMGGZSn3MjgEBaBCrKy612y5YvS0v7sRrNysqSpXeVyeGWw7Jp48ZYRfkMAQQQ8JwAiaHnhoQOIYCAE4GmpibZsX2HFJeUiC7tZuIoGF1gzVauq6oSnUHkQAABBPwiQGLol5GinwggYEtg7uzZEuodkqnTptoqn65CxSW3WNc4rq5w7xrHdMVCuwggEBwBEsPgjDWRImC8gG4Xo0u4c+bOE13SzeQRDodlcmGhbK2uluZDzZnsCudGAAEEbAtw84ltKgoigICXBaI3feTk5MjD27Y56qqTm086n1hvghlTUCADB4aTugmmc1u8RgABBNwQYMbQDWXOgQACaRfYsH6DtXQ7f+HCtJ/L7gn0GsfpRUXW9jW62TYHAggg4HUBEkOvjxD9QwCBuAK6VLu2slLGjhsruoTrpWPipEnWJtv3rFnNjSheGhj6ggAC3QqQGHbLwpsIIOAngbtXrLC6O2fePM91W691XLR4iXXto266zYEAAgh4WYDE0MujQ98QQCCugD4HWZ80ok8cydT2NPE6qY/k0822dfsanqMcT4vPEUAgkwIkhpnU59wIIOBYYOmdS6ylWl2y9fJxe2mpdQ1kdPNtL/eVviGAQHAFSAyDO/ZEjoDvBfTJIro9zYyZszK+PU08zP4D+lvb1+jm27oJNwcCCCDgRQESQy+OCn1CAAFbAro0q0u0+qQRPxyz5pzafHtt5X1+6C59RACBAAqcE8CYCRkBBAwR2Lh5s1yQdYFvotEbUe659/sy4DMDfNNnOooAAsESYIPrYI030SKAgA2BVG1wbeNUFEEAAQQ8JcBSsqeGg84ggAACCCCAAAKZEyAxzJw9Z0YAAQQQQAABBDwlQGLoqeGgMwgggAACCCCAQOYESAwzZ8+ZEUAAAQQQQAABTwmQGHpqOOgMAggggAACCCCQOQESw8zZc2YEEEAAAQQQQMBTAiSGnhoOOoMAAggggAACCGROgMQwc/acGQEEEEAAAQQQ8JQAiaGnhoPOIIAAAggggAACmRMgMcycPWdGAAEEEEAAAQQ8JUBi6KnhoDMIIIAAAggggEDmBEgMM2fPmRFAAAEEEEAAAU8JkBh6ajjoDAIIIIAAAgggkDkBEsPM2XNmBBDoQaD5ULM0NTX18Gkw3q7fWS+tra3BCJYoEUDAMwIkhp4ZCjqCAAJRgaLp02TKTTdFfwzcn5oYlxQXy/qqdYGLnYARQCCzAiSGmfXn7Agg0EWgrrZODrcclqV3lXX5JDg/9h/QXyYXFsrW6urAz5wGZ9SJFAFvCPQ6GTm80RV6gQACQRdob2+X4Xl5kpOTIw9v25Yxjty+Oda5W44eyVgfohYDB4Zl05bNGesHJ0YAgWAJMGMYrPEmWgQ8LbC6YpW0HW+T+QsXerqfbnQuKytLphcVyZ6GBtHrDTkQQAABNwRIDN1Q5hwIIBBXQK+r06XTsePGSjgcjls+CAVunjJF+uX2k3vWrBadQeRAAAEE0i1AYphuYdpHAAFbAnevWCGh3iGZM2+erfJBKbRo8RLrmsvampqghEycCCCQQQESwwzic2oEEDgl0Liv0Voy1aXT7OxsWDoJDMsbJiPy82XFsuVsX9PJhZcIIJAeARLD9LjSKgIIJCCw9M4l1pLpxEmTEqgVnKK3l5ZawVaUlwcnaCJFAIGMCJAYZoSdkyKAQFRg08aN1lLpjJmzRG+44Hi/gG5fU1xSIju272D7mvfz8A4CCKRQgO1qUohJUwggkJiAPtljTEGBeG1LFi9sV9NVMrp9Taa38unaL35GAAGzBJgxNGs8iQYBXwnokz10e5riklt81e9MdFZnU+fMnScH9h9g+5pMDADnRCAgAiSGARlowkTAawL6LGTdnkaf8MH2NPZGZ8LECda1mIvuWMj2NfbIKIUAAgkKkBgmCEZxBBBIjcDayvus7WlmzZmdmgYD0srKVac2Ad+wfkNAIiZMBBBwU4DE0E1tzoUAApaAPslDn+ih29Nww0liXwqdXdXta9ZWVrJ9TWJ0lEYAARsC3HxiA4kiCCCQOgG9iWLcVVdZDe7avTt1DaewJS/efNI5PL1pZ+iQS60Ekecod5bhNQIIOBVgxtCpIPURQCAhgaYDTdb2NPpED47kBHQT8NIF8+VXv2pi1jA5QmohgEAPAswY9gDD2wggkD4BnfHy8hNOvD5jqCMTfXYyS/Hp+57SMgJBFDgniEETMwIIZFbAy0lhZmXsn52E0L4VJRFAwL4AS8n2rSiJAAIIIIAAAggYLUBiaPTwEhwCCCCAAAIIIGBfgMTQvhUlEUAAAQQQQAABowVIDI0eXoJDAAEEEEAAAQTsC5AY2reiJAIIIIAAAgggYLQAiaHRw0twCCCAAAIIIICAfQESQ/tWlEQAAQQQQAABBIwWIDE0engJDgEEEEAAAQQQsC9AYmjfipIIIIAAAggggIDRAiSGRg8vwSGAAAIIIIAAAvYFSAztW1ESAQQQQAABBBAwWoDE0OjhJTgEEEAAAQQQQMC+AImhfStKIoAAAggggAACRguQGBo9vASHgLsCa1avkaamJndPytliCtTvrJe62rqYZfgQAQQQiAqQGEYl+BMBBBwJNO5rlLWVlbL/+ecdtUPl1Ao8sm2bzL/9dmltbU1tw7SGAAJGCpAYGjmsBIWAuwLt7e2y9M4l0i+3n0ycNMndk3O2mAJly5dZn1eUl8csx4cIIICACpAY8j1AAAHHArU1NXK45bDMmDlLsrKyHLdHA6kTyM7OluKSEtmxfQfL/KljpSUEjBXodTJyGBsdgSGAQNoFdIlyTEGBDBwYlk1bNqf9fG6cILdvjnWalqNH3Dhd2s+hM7rD8/IkJydHHo4sLXMggAACPQkwY9iTDO8jgIAtgfVV66TteJvcXlpqqzyF3BfQWdw5c+fJgf0HuBHFfX7OiICvBEgMfTVcdBYBbwnoHchbq6tlcmGh9B/Q31udozdnCEyYOMG6BrRiZbnoDCIHAggg0J0AiWF3KryHAAK2BNZW3ieh3iGZNWe2rfIUyqzAylWrrNndDes3ZLYjnB0BBDwrQGLo2aGhYwh4W0D3x9vT0CDTi4q44cTbQ9XRu3A4LGPHjbW2FWL7mg4WXiCAQCcBbj7phMFLBBCwJxC9mSEUCsmu3bvtVfJRKdNuPulMrwnh0CGXyoj8fGNuFuocH68RQMCZADOGzvyojUAgBXR7Gr3hZNHiJYGM389B6/Y1pQvmW7O9PKXGzyNJ3xFIjwAzhulxpVUEjBUIwoyTyTOG+sU0fcbX2L98BIaACwLMGLqAzCkQMEkg+gSN6BM1TIotKLHo9jVL7yqzNiXftHFjUMImTgQQsCFAYmgDiSIIIHBKQJce9Qka+iQNXZLk8K9AwegCGTR4kKyrqmL7Gv8OIz1HIOUCJIYpJ6VBBMwVmDt7trU9zdRpU80NMkCRzV+40LpWdHXFqgBFTagIIBBLgMQwlg6fIYBAh0BdbZ219KhP0OB5yB0svn6h29fo5uS6SXnzoWZfx0LnEUAgNQIkhqlxpBUEAiGgS4/6BA0OcwSmFU23nojyVvtb5gRFJAggkLQAdyUnTUdFBBAwVcD0u5JNHTfiQgAB5wLMGDo3pAUEEEAAAQQQQMAIARJDI4aRIBBAAAEEEEAAAecCJIbODWkBAQQQQAABBBAwQoDE0IhhJAgEEEAAAQQQQMC5AImhc0NaQAABBBBAAAEEjBAgMTRiGAkCAQQQQAABBBBwLkBi6NyQFhBAAAEEEEAAASMESAyNGEaCQAABBBBAAAEEnAuQGDo3pAUEEEAAAQQQQMAIARJDI4aRIBBAAAEEEEAAAecCJIbODWkBAQQQQAABBBAwQoDE0IhhJAgEEEAAAQQQQMC5AImhc0NaQAABBBBAAAEEjBAgMTRiGAkCAQQQQAABBBBwLkBi6NyQFhDwtUBTU5OMGjlS9E8OBHoSaNzXaH1P2tvbeyrC+wggYIAAiaEBg0gICDgRWF5WJm1tbTJgwAAnzVDXcIGsC7LkcMth2bB+g+GREh4CwRYgMQz2+BN9wAXqd9bLgf0HZHpRkWRlZQVcg/BjCYTDYRk7bqysrayU1tbWWEX5DAEEfCzQ62Tk8HH/6ToCCCQpoEuCw/PyJBQKya7du5NsxcxquX1zrMBajh4xM8Ako9KEcOiQS2VEfr5s2rI5yVaohgACXhZgxtDLo0PfEEijQG1NjbQdb5OVq1al8Sw0bZJAdna2lC6YL3saGkSvOeRAAAHzBJgxNG9MiQiBuALM/MQmYsawZx9mmnu24RMETBBgxtCEUSQGBBIUWDh/gVWjbPmyBGtSPOgCei3q0rvKrBtRNm3cGHQO4kfAOAESQ+OGlIAQiC2g29LoUmBxSYno0iAHAokKFIwusK4zXFdVJWxfk6ge5RHwtgCJobfHh94hkHKBubNnS6h3SKZOm5rytmkwOALFJbdY16iuruAa1eCMOpEGQYDEMAijTIwInBaoq62zlgB1KZDtafhaOBHQ7WsmFxbK1upqNkd3AkldBDwmQGLosQGhOwikS0CX/CpWlsugwYNElwI5EHAqMK1oujX7vLbyPqdNUR8BBDwiQGLokYGgGwikW0CfWKHb08xfuDDdp6L9gAjoNaq6Obpes6qbpXMggID/Bdiuxv9jSAQIxBVoPtQs3xg1ynpyxep77olbPugF2K4msW+APmtbj+2PPsolConRURoBzwkwY+i5IaFDCKRe4O4VK6xG58ybl/rGaTHwAosWL7GuXdVN0zkQQMDfAiSG/h4/eo9AXAF9QoUu9ekTK9ieJi4XBZIQGJY3rGP7Gp6jnAQgVRDwkACJoYcGg64gkA6BpXcukX65/WTipEnpaJ42EbAEbi8tta5hrSgvRwQBBHwscI6P+07XEUDAhsCEiRPls5/9HNd+2bCiSPIC/Qf0t2al9bvGgQAC/hXg5hP/jh09RwCBNAlw80maYGkWAQQ8L8BSsueHiA4igAACCCCAAALuCJAYuuPMWRBAAAEEEEAAAc8LkBh6fojoIAIIIIAAAggg4I4AiaE7zpwFAQQQQAABBBDwvACJoeeHiA4igAACCCCAAALuCJAYuuPMWRBAAAEEEEAAAc8LkBh6fojoIAIIIIAAAggg4I4AiaE7zpwFAQQQQAABBBDwvACJoeeHiA4igAACCCCAAALuCJAYuuPMWRBAAAEEEEAAAc8LkBh6fojoIAIIIIAAAggg4I4AiaE7zpwFAQQQQAABBBDwvACJoeeHiA4igAACCCCAAALuCJAYuuPMWRBIuUB7e7vofxwI+E2gtbXVb12mvwgERoDEMDBDTaCmCdz2vVtl3FVXmRYW8Rgu0HyoWcYUFMimjRsNj5TwEPCnAImhP8eNXgdcoKmpSfY0NMiEiRMDLkH4fhPoP6C/DBwYlnVVVcLMod9Gj/4GQYDEMAijTIzGCcydPVtCvUMycdIk42IjIPMFiktukbbjbbK+ap35wRIhAj4TIDH02YDRXQTqauvkcMthWXpXmWRlZQGCgO8EwuGwTC4slK3V1aKz3xwIIOAdgV4nI4d3ukNPEEAgloDebDI8L09ycnLk4W3bYhXlMwcCuX1zrNotR484aIWqsQSi32VdVt60ZXOsonyGAAIuCjBj6CI2p0LAqcDqilXWEtz8hQudNkV9BDIqoLPd04uKrGtl63fWZ7QvnBwBBN4TIDF8z4JXCHhaQO/m1KW3sePGii7FcSDgd4Gbp0yRfrn95J41q9l6ye+DSf+NESAxNGYoCcR0gbtXrLBuOJkzb57poRJfgAQWLV5iXTNbW1MToKgJFQHvCpAYends6BkCHQKN+xqtJTddesvOzu54nxcI+F1gWN4wGZGfLyuWLWf7Gr8PJv03QoDE0IhhJAjTBZbeucRacmN7GtNHOpjx3V5aagVeUV4eTACiRsBDAiSGHhoMuoJAdwL6hAjdnmbGzFlsT9MdEO/5XkA3vS4uKZEd23ewfY3vR5MA/C7AdjV+H0H6b7SAPhlCHx/Glh7uDjPb1bjrrWeLbl/DVkzu23NGBDoLMGPYWYPXCHhMQJ8MoU+I0CdFcCBgsoBuXzNn7jw5sP+AsH2NySNNbF4XIDH0+gjRv8AK6BMhdHsafUIE29ME9msQqMAnTJxgXUu76I6FbF8TqJEnWC8JkBh6aTToCwKdBNZW3mdtTzNrzuxO7/ISAbMFVq46tYn7hvUbzA6U6BDwqACJoUcHhm4FW0CX0vY0NFhPhuB5yMH+LgQtep0d1+1r1lZWsn1N0AafeD0hwM0nnhgGOoHA+wU0OSwYXfD+D3gn7QLcfJJ24pgn0Juujh07xiUUMZX4EIH0CJAYpseVVhFAwMcCJIY+Hjy6jgACjgRYSnbER2UEEEAAAQQQQMAcARJDc8aSSBBAAAEEEEAAAUcCJIaO+KiMAAIIIIAAAgiYI0BiaM5YEgkCCCCAAAIIIOBIgMTQER+VEUAAAQQQQAABcwRIDM0ZSyJBAAEEEEAAAQQcCZAYOuKjMgIIIIAAAgggYI4AiaE5Y0kkCCCAAAIIIICAIwESQ0d8VEYAAQQQQAABBMwRIDE0ZyyJBAEEEEAAAQQQcCRAYuiIj8oIIIAAAggggIA5AiSG5owlkSCAAAIIIIAAAo4ESAwd8VEZAQQQQAABBBAwR4DE0JyxJBKfCDTua5T29naf9JZuIuBdgdbWVmlqavJuB+kZAj4UIDH04aDRZf8KNB9qlu9OniyrK1b5Nwh6joBHBL7zrW/JlJtu4h9aHhkPumGGAImhGeNIFD4RuHvFCgn1Dsm0ouk+6THdRMC7AosWL5G2421SW1Pj3U7SMwR8JkBi6LMBo7v+FdAl5D0NDTK9qEiys7P9Gwg9R8AjAsPyhsmI/HxZsWy56LIyBwIIOBcgMXRuSAsIxBXQawqX3rlE+uX2k4mTJsUtTwEEELAnULZ8mVWworzcXgVKIYBATAESw5g8fIhAagR0qetwy2GZMXOWZGVlpaZRWkEAAWv2vbikRHZs38GNKHwfEEiBQK+TkSMF7dAEAgj0IKBLXGMKCmTgwLBs2rK5h1K87SWB3L45Vndajh7xUrfoSw8COiM/PC9PcnJy5OFt23ooxdsIIGBHgBlDO0qUQcCBwPqqddYF8reXljpohaoIINCTgM7Cz5k7Tw7sPyB1tXU9FeN9BBCwIUBiaAOJIggkK6B7rG2trpbJhYXSf0D/ZJuhHgIIxBGYMHGCdQ1vxcpytq+JY8XHCMQSIDGMpcNnCDgUWF5WZm1PM2vObIctUR0BBOIJrFy1ypqd37B+Q7yifI4AAj0IkBj2AMPbCDgVqN9Zby1t6fY03HDiVJP6CMQXCIfDMnbcWFlbWcn2NfG5KIFAtwLcfNItC28i4EwgejF8KBSSXbt3O2uM2q4LcPOJ6+QpO6He7DV0yKXW/obc7JUyVhoKkAAzhgEabEJ1T0C3p9EnMujSFgcCCLgnoJvHly6Yb20mr5vKcyCAQGICzBgm5kVpBOIKMGMRl8jzBZgx9PwQxewgM/YxefgQgZgCzBjG5OFDBBIXiD6BIfpEhsRboAYCCDgR0Gt6l95VZm0qv2njRidNUReBwAmQGAZuyAk4nQK6PY0+gUGfxMDzkNMpTdsIxBYoGF1gXWe4rqqK7WtiU/EpAmcIkBiewcEPCDgTeGzHo9b2NFOnTXXWELURQMCxQHHJLda1vvv27nPcFg0gEBQBrjEMykgTp2sCzYea2czaNe30nIhrDNPjmolW9ZpfZu8zIc85/SrAjKFfR45+e1aAJ5x4dmjoWAAFSAoDOOiE7EiAxNARH5URQAABBBBAAAFzBEgMzRlLIkEAAQQQQAABBBwJkBg64qMyAggggAACCCBgjgCJoTljSSQIIIAAAggggIAjARJDR3xURgABBBBAAAEEzBEgMTRnLIkEAQQQQAABBBBwJEBi6IiPyggggAACCCCAgDkCJIbmjCWRIIAAAggggAACjgRIDB3xURkBBBBAAAEEEDBHgMTQnLEkEgQQQAABBBBAwJEAiaEjPiojgAACCCCAAALmCJAYmjOWRIIAAggggAACCDgSIDF0xEdlBBBAAAEEEEDAHAESQ3PGkkjSKNDa2ip3Ll4i+icHAgiYJdB8qNn6+21WVESDQHICJIbJuVErYAIV5eWytbpa2t9qD1jkhIuA+QIvvvii9fe7rrbO/GCJEIE4AiSGcYD4GIGmpibZsX2HTC4slP4D+gOCAAKGCRSMLpBBgwdJxcpyaW/nH3+GDS/hJChAYpggGMWDJ7C8rExCvUMya87s4AVPxAgERGD+woXSdrxNNqzfEJCICROB7gVIDLt34V0ELIH6nfVyYP8BmTN3nmRlZaGCAAKGCoTDYRk7bqysrawUveaQA4GgCvQ6GTmCGjxxIxBLQJeUhuflSSgUkl27d8cqymeGCeT2zbEiajl6xLDICCeWgN5cNnTIpTIiP182bdkcqyifIWCsADOGxg4tgTkVqK2psZaWVq5a5bQp6iOAgA8EsrOzpXTBfNnT0CCN+xp90GO6iEDqBZgxTL0pLRogwMyBAYPoIARmDB3g+byqrhSMu+oqKwpWCnw+mHQ/KQFmDJNio5LpAgvnL7BCLFu+zPRQiQ8BBDoJ6LXEM2bOksMth2XTxo2dPuElAsEQIDEMxjgTZQICuj2NLiUVl5SILi1xIIBAsAR0+xq9znBdVRXb1wRr6Ik2IkBiyNcAgS4Cc2fPtranmTptapdP+BEBBIIiUFxyi3WN8eoKrjEOypgT5ykBEkO+CQh0EtAnH+gS0tK7ytieppMLLxEImoBuX6Ob2usTj3QVgQOBoAiQGAZlpIkzroBedK5PPtAnIOhSEgcCCARbYFrRdGv1YG3lfcGGIPpACZAYBmq4CTaWgD7xQJ98oE9A4EAAAQT0GuPpRUXWNce62T0HAkEQYLuaIIwyMcYV0CcdfGPUKOvJB6vvuSdueQqYLcB2NWaPb6LRjRo50qqy/dFHucQkUTzK+06AGUPfDRkdTofA3StWWM3OmTcvHc3TJgII+Fhg0eIl1rXHuuk9BwKmC5AYmj7CxGdbQJ94wPY0trkoiEBgBIblDbO2r3nzzbcCEzOBBleApeTgjj2RI4BADwIsJfcAw9sIIGC8ADOGxg8xASKAAAIIIIAAAvYESAztOVEKAQQQQAABBBAwXoDE0PghJkAEEEAAAQQQQMCeAImhPSdKIYAAAggggAACxguQGBo/xASIAAIIIIAAAgjYEyAxtOdEKQQQQAABBBBAwHgBEkPjh5gAEUAAAQQQQAABewIkhvacKIUAAggggAACCBgvQGJo/BATIAIIIIAAAgggYE+AxNCeE6UQQAABBBBAAAHjBUgMjR9iAkQAAQQQQAABBOwJkBjac6IUAggggAACCCBgvACJofFDTIAIIIAAAggggIA9ARJDe06UQgABBBBAAAEEjBcgMTR+iIMd4JrVa2TWjBnBRiB6BBBwRaC1tVWuHT9eGvc1unI+ToJAOgRIDNOhSpueEND/k15bWSlvvPGmJ/pDJxBAwGyBrKwsef3112XpnUvMDpTojBYgMTR6eIMd3ML5CyyAsuXLgg1B9Agg4IqAJoYzZs6Swy2HZdPGja6ck5MgkGoBEsNUi9KeJwSamppkT0ODlC6YL9nZ2Z7oE51AAAHzBQpGF8iI/HxZV1UlumrBgYDfBEgM/TZi9NeWwNzZsyXUOyQTJ02yVZ5CCCCAQKoEiktukbbjbbK+al2qmqQdBFwTIDF0jZoTuSVQV1tnLeUsvatMdGmHAwEEEHBTIBwOy+TCQtlaXS26esGBgJ8Eep2MHH7qMH1FIJZAe3u7DM/Lk5ycHHl427ZYRfkMgR4FcvvmWJ+1HD3SYxk+QCCWQPT/iwYODMumLZtjFeUzBDwlwIyhp4aDzjgVWF2xylrCmb9wodOmqI8AAggkLaCrFdOLiqxrnet31ifdDhURcFuAxNBtcc6XNoHmQ83W0s3YcWNFl3I4EEAAgUwK3DxlivTL7Sf3rFktOoPIgYAfBEgM/TBK9NGWwN0rVlg3nMyZN89WeQohgAAC6RZYtHiJdc1zbU1Nuk9F+wikRIDEMCWMNJJpAX3SgG5Po0s3bE+T6dHg/AggEBUYljfM2r5mxbLlbF8TReFPTwuQGHp6eOicHQFdotEnDeiSDdvT2BGjDAIIuClwe2mpdbqK8nI3T8u5EEhKgMQwKTYqeUlAl2j0SQP6xAG2p/HSyNAXBBBQgf4D+ktxSYns2L6D7Wv4SnhegO1qPD9EdDCWgD5ZYExBgbAlRCwlPktUgO1qEhWjfDyB6PY1bKUVT4rPMy3AjGGmR4DzOxLQJwvoEwaiSzWOGqMyAgggkCYBXc2YM3eeHNh/QNi+Jk3INJsSARLDlDDSSCYE9IkC+mQBfcKALtVwIIAAAl4WmDBxgnUt9KI7FrJ9jZcHKuB9Oyfg8RO+jwUuuugiKymcNWe2j6Og6wggECSBlatWyf7nnw9SyMTqMwGuMfTZgNFdBBBIvwDXGKbfmDMggIA3BVhK9ua40CsEEEAAAQQQQMB1ARJD18k5IQIIIIAAAggg4E0BEkNvjgu9QgABBBBAAAEEXBcgMXSdnBMigAACCCCAAALeFCAx9Oa40CsEEEAAAQQQQMB1ARJD18k5IQIIIIAAAggg4E0BEkNvjgu9QgABBBBAAAEEXBcgMXSdnBMigAACCCCAAALeFCAx9Oa40CsEEEAAAQQQQMB1ARJD18k5IQIIIIAAAggg4E0BEkNvjgu9QgABBBBAAAEEXBcgMXSdnBMigAACCCCAAALeFCAx9Oa40CsEEEAAAQQQQMB1ARJD18k5oR2B1tZWO8UogwACCBgrwP8PGju0ng6MxNDTwxPMzrW3t8uYggJZs3pNMAGIGgEEAi9w7fjxsnD+gsA7AOC+AImh++acMY7A6opV0na8TUbkj4hTko8RQAABMwW+ccUVsqehQep31psZIFF5VoDE0LNDE8yONR9qlq3V1TK5sFDC4XAwEYgaAQQCL3DzlCnSL7efLLpjoegqCgcCbgmQGLolzXlsCdy9YoWEeodkWtF0W+UphAACCJgqsGjxEmv1pLamxtQQicuDAiSGHhyUoHZJl0x06WR6UZFkZ2cHlYG4EUAAAUtgWN6wyCU1+bJi2XLhRhS+FG4JkBi6Jc15YgroUsk9a1ZbSycTJ02KWZYPEUAAgaAIlC1fZoVaUV4elJCJM8MCJIYZHgBOf0pAl0oOtxwWXTrJysqCBQEEEEAgIqCrJ8UlJbJj+w5pamrCBIG0C5AYpp2YE8QT0CWSdVVV1pKJLp1wIIAAAgi8JzB12lTr2uvlZWXvvckrBNIkQGKYJliatS+wvmqddYH17aWl9itREgEEEAiIgK6izJk7Tw7sPyB1tXUBiZowMyVAYpgpec5rCejSSHR7mv4D+qOCAAIIINCNwISJE6xrsCtWlrN9TTc+vJU6ARLD1FnSUhICujSi29PMmjM7idpUQQABBIIjsHLVqc3/N6zfEJygidR1ARJD18k5YVRAt6fRpRHdnoYbTqIq/IkAAgh0L6Cb/o8dN1bWVlayfU33RLybAoFeJyNHCtqhCQQSEtDtaYbn5UkoFJJdu3cnVJfCCKRbILdvjnWKlqNH0n0q2kcgIQG9WW/okEutm/U2bdmcUF0KI2BHgBlDO0qUSbmAbk+jz0PWpREOBBBAAAF7Arp9TemC+dbDABr3NdqrRCkEEhBgxjABLIqmRoB/8abGkVbSJ8CMYfpsadm5ACsuzg1poWcBZgx7tuGTNAno9jR6RHf0T9NpaBYBBBAwUkCvyV56V5n1UAC2rzFyiDMaFDOGGeUP5sn1X7v79u6TgtEFwQQgas8LMGPo+SGigxEBvYEv77I8bt7j25BSARLDlHLSGAIImCBAYmjCKBIDAggkI8BScjJq1EEAAQQQQAABBAwUIDE0cFAJCQEEEEAAAQQQSEaAxDAZNeoggAACCCCAAAIGCpAYGjiohIQAAggggAACCCQjQGKYjBp1EEAAAQQQQAABAwVIDA0cVEJCAAEEEEAAAQSSESAxTEaNOggggAACCCCAgIECJIYGDiohIYAAAggggAACyQiQGCajRh0EEEAAAQQQQMBAARJDAweVkBBAAAEEEEAAgWQESAyTUaMOAggggAACCCBgoACJoYGDSkgIIIAAAggggEAyAiSGyahRBwEEEEAAAQQQMFCAxNDAQc1USO3t7VK/sz5Tp+e8CCCAAAJdBPj/5S4g/BhXgMQwLhEF7ArU1tRISXGxNDU12a1COQQQQACBNArs/MlO/n85jb4mNk1iaOKoZiCm1tZWWVdVJSPy8yUcDmegB5wSAQQQQKCrwOgxoyXUOyRzZ8/u+hE/I9CtAIlhtyy8mahARXm5tB1vk9tLSxOtSnkEEEAAgTQJZGVlydK7yuRwy2Gpq61L01lo1iQBEkOTRjNDsejS8Y7tO2RyYaH0H9A/Q73gtAgggAAC3QkUjC6QQYMHScXKctFrDjkQiCVAYhhLh89sCSwvK7OWKmbNYanCFhiFEEAAAZcF5i9caK3qbFi/weUzczq/CZAY+m3EPNZfvQv5wP4DMmfuPNElCw4EEEAAAe8J6LXfY8eNlbWVldJ8qNl7HaRHnhHodTJyeKY3dMRXArokMTwvT0KhkOzavdtXfaezCMQSyO2bY33ccvRIrGJ8hoCvBPQmwaFDLrVuEty0ZbOv+k5n3RNgxtA9a+POpNvT6A0nK1etMi42AkIAAQRME8jOzpbSBfNlT0ODNO5rNC084kmRADOGKYIMWjP8yzNoIx6seJkxDNZ4BylaXekZd9VVVsis9ARp5O3HyoyhfStKdhJYOH+B9VPZ8mWd3uUlAggggICXBfRa8BkzZ1nb12zauNHLXaVvGRIgMcwQvJ9Pq9vT6FJEcUmJ6NIEBwIIIICAfwR0+xp9GIE+lIDta/wzbm71lMTQLWmDzqM76OtO+lOnTTUoKkJBAAEEgiNQXHKLdY346gquEQ/OqNuLlMTQnhOlTgvozvm6g77upM/2NHwtEEAAAX8K6PY1+lCCrdXVPN/en0OYtl6TGKaN1ryGdclBd87XHfR1KYIDAQQQQMC/AtOKplurP2sr7/NvEPQ85QIkhiknNbdBXXLQ7Wl0B30OBBBAAAF/C+g14tOLiqxrxvVhBRwIqACJId8D2wKPP/6YtXO+LkFwIIAAAgj4X+DmKVOkX24/2f3ULv8HQwQpEWAfw5QwBqOR6N1rXFsYjPEOcpTsYxjk0Q9e7LovLTtMBG/ce4r4nJ4+4H0EugqQEHYV4WcEEEDA/wIkhf4fw1RGwFJyKjVpCwEEEEAAAQQQ8LEAiaGPB4+uI4AAAggggAACqRQgMUylJm0hgAACCCCAAAI+FiAx9PHg0XUEEEAAAQQQQCCVAiSGqdSkLQQQQAABBBBAwMcCJIY+Hjy6jgACCCCAAAIIpFKAxDCVmrSFAAIIIIAAAgj4WIDE0MeDR9cRQAABBBBAAIFUCpAYplKTthBAAAEEEEAAAR8LkBj6ePDoOgIIIIAAAgggkEoBEsNUatIWAggggAACCCDgYwESQx8PHl1HAAEEEEAAAQRSKUBimEpN2kIAAQQQQAABBHwsQGLo48FLVdcb9zVKXW1dqpqjHQQQQAABwwTa29tlzeo10nyo2bDICKerAIlhV5GA/ax/2Wfcdqts2rghYJETLgIIIICAXQH9XfHgAz+Su1essFuFcj4VIDH06cClqtsb1m+QtuNtsnLVqlQ1STsIIIAAAoYJZGdny/SiItnT0CC6ysRhrkCvk5HD3PCILJZAa2urDB1yqYzIz5dNWzbHKspnCARKILdvjhVvy9EjgYqbYBGIJaCzhuOuusoqsmv37lhF+czHAswY+njwnHZ94fwFVhNly5c5bYr6CCCAAAKGC2RlZcmMmbPkcMvhyOVHGw2PNrjhkRgGdOybmpqsJYHSBfNFlwg4EEAAAQQQiCdQMLrAWmVaV1UluurEYZ4AiaF5Y2orormzZ0uod0gmTppkqzyFEEAAAQQQUIHiklusa9PXV60DxEABEkMDBzVeSLoEoEsBS+8qE10a4EAAAQQQQMCuQDgclsmFhbK1ulp09YnDLAFuPjFrPONGoxcPD8/Lk5ycHHl427a45SmAQBAFuPkkiKNOzIkIRH+XDBwY5ubFROB8UJYZQx8MUiq7uLpilbUEMH/hwlQ2S1sIIIAAAgES0NWm6PY19TvrAxS5+aGSGJo/xh0R6o71OvWvSwC6FMCBAAIIIIBAsgI3T5ki/XL7yT1rVovOIHKYIUBiaMY42opCd6zXG06mFU23VZ5CCCCAAAIIxBJYtHiJdc16bU1NrGJ85iMBEkMfDZaTrupO9bpjvU79sz2NE0nqIoAAAghEBYblDbO2r1mxbDnb10RRfP4niaHPB9BO93WKf+mdS6wpf7ansSNGGQQQQAABuwK3l5ZaRSvKy+1WoZyHBUgMPTw4qeqaTvHr9jS6Yz3b06RKlXYQQAABBFSg/4D+kb0NS2TH9h1sX2PAV4LtagwYxFgh6M70YwoKhC0FYinxGQJnCrBdzZke/IRAPIHo9jVshRZPyvufM2Po/TFy1MNjx45JKBSS6FS/o8aojAACCCCAQDcCuho1Z+486xMeldcNkI/eYsbQR4NFVxFAwB0BZgzdceYsCCDgPQFmDL03JvQIAQQQQAABBBDIiACJYUbYOSkCCCCAAAIIIOA9ARJD740JPUIAAQQQQAABBDIiQGKYEXZOigACCCCAAAIIeE+AxNB7Y0KPEEAAAQQQQACBjAiQGGaEnZMigAACCCCAAALeEyAx9N6Y0CMEEEAAAQQQQCAjAiSGGWHnpAgggAACCCCAgPcESAy9Nyb0CAEEEEAAAQQQyIgAiWFG2DkpAggggAACCCDgPQESQ++NCT1CAAEEEEAAAQQyIkBimBF2TooAAggggAACCHhPgMTQe2NCjxBAAAEEEEAAgYwIkBhmhJ2TIoAAAggggAAC3hMgMfTemNju0bXjx0tdbZ3t8hREAAEEEEAg0wJ3Ll4i+h+HNwVIDD04Lprw5fbNsf67+cabOnrY2toqzYearZ83bdwoB/YfkAsuuKDjc14ggAACCCDgB4Gt1dXS1NRkdbVxX+MZXY7+/tM/16xec8Zn/JB+ARLD9BvHPIP+xdDkL/oXpL29Xf7hvA901Hn77bflTy+9LK+//obsfXqvfGPUKBk5YoT84N7vy4j8fCkYXdBRlhcIIIAAAgh4XWDWnNnykY98RObOniNfHjRIvjt5srzwwgvW77kjR/5wRvfPOvtseeedd6z3dEJk1owZopMkHOkTOCd9TdNyLAFNABffcYfs2L7DKtarVy/5duEN8ve//10+/ok+HVX7fOrT8uKLp2YJH3vsMev9o0eOWn9Oun5SRzleIIAAAggg4AeBrKws+cYVV0Quhart6O6WLT+MvPcv1s9fvOQS+c3Bg9brD37wAnnm57+Q8847T350/4/kT3/8o/V7s7ikRGbOmtlRnxepEyAxTJ1lQi3pX4w33nizo07D7t3yjYLREgr1lgEDPiO3zpwlH/jA+RLqHeoo89zPf97x+nMXXyyXDR/e8TMvEEAAAQQQ8IvAoiWLIwnedvnb3/5mdfn3L/yuIzG85rqJMubKq+T48dc6fgf+R+M+KymMxvehD3EZVdQi1X+ylJxqUZvt6czgd757g3wwkiDqUTDmSvnA6SXkfrm58oUvfkn0T00Uo8cP1lbJx7Kz5ayzzpIbbp4iv/jlftGZR72IN3rtYbQsfyKAAAIIIOAlAb1Zsn5nvRxrfdX6/fWtwkKre18bcql877b3Zv8+/vGPW7//vvyVr3b8Dszt31++Gimnh/5uHPrPedZr/if1Ar1ORo7UN0uL3QloEjfuqqukcu1aefOt/5W33mqXwy0t1r+IOieA3dXV957/z1/Khqp/k/HXTej4l1Xtgw9Iw1O7rDae3rdPdCaSAwEEnAnoRe96tBw94qwhaiOAgCWg19FfM+5q6/XUon8VTfr0+MG9a6xl4/LITSZ2fg92/p350Y/+o7z0xz/II9u2yaYtm632+B/nAswYOje03cJt37s1kggeltGR6yj2NDRY9brOCvbU2Dt//as8uv0Ra8bwssuGW8U0UdSkUI+2421yw+l/fVlv8D8IIIAAAgh4QEBvFply03s7bOgER1vbcatn3yn8rvXntocfttXTzr8zN65fLyXFxdbvU70xhSM1AiSGqXGM24rejh9NBrXwU0/+LG6dzgX27n1aXo385Zp4/bfkvA+cumtZ/8WlF+nqccGHPiTfu/W2zlV4jQACCCCAQMYFsiOXQE2dNq2jH7rqFZ0d1D/1UqpfPvestYLWUSjOC50s2fv0no5S66qquFu5Q8PZCxJDZ362aw/4zAC5/tvf6ig/+Yb3/vXU8WYPL/RfVk/U77SSQL32sPMxdVqRtbS8bEW5fOl0ktj5c14jgAACCCCQaYFRX79CdLm486VQ0T5d8S8F1vX2/77Z/qyfTpDcPPVUspkV2c93elERl1JFQR3+yTWGDgETqf673/1e/vu3v5VXXn7ZurnEbt0Hf3S/PN2wW5aULRe9KLenQ6+3uORLX7BuSOFaw56UeB+B+AJcYxjfiBII2BHQa+v199Hefc9Y27H1VKdx7165v/rf5TuRbduGXXZZT8Xe975eUvXFyITJoMFhuSj7Y+/7nDcSF2DGMHGzpGv8z5//Yk2fd531i9WgXmirSeHw/JExk8JXXnlF9HqLyyPldH9EDgQQQAABBDItoDdcjv3mVbInsiVb9LrC7vqkyaBeP/jItodFl4ntHnpJlc4e/jny+5UjNQLsY5gax5it6E7tJ078XXpf+NHIcvCXOq6tiFnp9IcP1T5oTbFfPf6amMX1+oz6nzxulXn99baYZfkQAQQQQACBdAvoTSd6w6Uev45sWN35buTuzn3dxOvl7mV3yRM/rZexV4/vrki37+nEyM+e+Kkc/8ufZcilQ+TmKVO6Lceb9gRIDO05OSoVfbqJNtLd9RU9Na5T5DpjqHWiN5z0VLbPJz/Z8ZHeoRydvu94kxcIIIAAAgi4KHDs2LEzzqZ7EcY6dMZQ9yrUSY7LIo9+jd6gEquOfvbjh2o7npSiP5MYqkLyB0vJydslVfPCCy+0VU+n0h+4f6u1PU30MUGxKupj9PQO5cIbb5TSBfOtxDBWeT5DAAEEEEAg3QL6+2hMZClZfz/ZSfTGX3ut1aX7q39ou2ufijw6liN1AswYps7SVku9e9tLDHV7mv+NXLRbcusMW+3qTSm6c3wo9BEZFP4nW3UohAACCCCAQLoEwuGw6H+7G/baPoUmj7pKtu2hOvnv3/za1o2aHzj/fNvtUzC+AIlhfKOMlOjTp491w4lOrXMggAACCCDgV4Fzzjkn5h3JXePShzj86Y9/jDzRy95EStf6/OxMgMTQmV9CtfW5yH/969u26uidy4nevfyTxx+V3EgieeD5i7nGwpYyhRBAAAEE0iWgN5/85PHH5T/+45nIHcltkU2ui+JeL6996bxHod2+6e9XXWXjcC7APobODeO20HyoWXSq+4XfH4pbNtkCOx7Z1nFXcqh3SJ4/cCDZpqiHQOAF2Mcw8F8BAFIgoL/7vjFqVEdLt86cldCER0dFmy++8PnPSvtb7dJ/QH+bNSjWnQA3n3SnkuL39Ev6iU/0vDF1Kk73wu9+29HMZQlsDtpRiRcIIIAAAgikUEB/9+lERfT4r1/9Kvoy5X/q9fX66D2SQue0LCU7N7TdQusrL8tDkQtqw+HBCe3sbucE0/61WJ79+TOyd0+DjLz8vX+h2alLGQQQQAABBNIhcOWV35TGxkbJGz5CBg/+cspPXH/NyQAADV1JREFUsWnDejk/siI36fpJKW87qA2ylOzSyN98402yp6HBOpteC7GivMLWtRaJdO/zn/+c9Ugg9jBMRI2yCLxfgKXk95vwDgLJCER/H+kjYV851ppMEz3W0X1+dUPs6KFb47CHYVQj+T9ZSk7eLqGaV49/bxd3vUD2N5Hb8FNx6LWF+t955/2/judE8pzkVMjSBgIIIICAU4Ho76MBA3IjTwA7IT+4d43owxtScTz37M/PaGbMlVee8TM/JCdAYpicW8K1CkYXRB7yPciqV1RcIvp8R6eH/uXSHeL1v9UrV4pe6MuBQDAEXpFHbgqLzuxZ//1zuTS9G4zIiRIBPwo8+/NnZf7c2dYTSvThDfoYO6fH9d/+jlx9ekPs4pIS6xpDp21SX4TE0MVvwYq7y+Vnu3bJ9KKpovs66dNNdLYvkQeGd+7uU0/+rOPHdF7U23ESXiDgFYHXnpOf7nv9vd681CC7DtrbCuq9SrxCAAG3BN566y154403rNPpqtkvn3s2qVO3tR2XB390v1X3ggsil2WtWC4/3Lo1shXO1KTao9L7BUgM32+Stnf0bin9T6fWP/fZ/vL9e1Zbs33L7rrT2uHdzon1X1nRRHLW3Nvlwx/+sFWtcu1a7sayA0gZAwTelqZN66XhROdQjsijNc9Ip1Sx84e8RgCBDAvoqtnkwkKrF18bMkTGXn3q8ipN9PQ/O8fPnvipLF28SJ5u2G09H1mf8qWTLMPyhlm/V+20QZn4AtyVHN8oLSUe+NED0tJ8aun31cgmoH+NzB5GD72gVg99zJ1u9KlH49698uTPfipaVh8XdE1k+vzzF39WHvrxj+XFF18U/UvHgUAgBN79nex6/MipUL9wmeS/8XNpeOmEtG5/WBrm5cvVF54dCAaCRMBvAovvXCKf6PMJmThpkvz1nb/Jb3/7gugzkX9z8KDoU76um3i99afGpRMg0eXm6BPAXvvLXzo2sX7yiSciO3E8ayWFfnPwen+ZMczQCH3zm9+M/AXoZ5390337yqivf916Hb3LSu+0unfNqo7evfbaX6ykUN946mdPWEmhzjzqDCRJYQcTLwIg8O7Bp2RnJBEUOVf65N0o06/MORX1iefkwUcOCZcaBuBLQIi+FdC7hvV310f/8UL54Pn/YCWFGoz+7uv8ZLDvFRdZdxx3vuv4uzfc0BH3iPx8CQ8Kd/zMi9QJMGOYOsuEWtKEbvujj0ptTU1kZvATolPi77zzjvxX0/6OdvQvim7aeUHkL9GI/BEdTzbR6zSaDjTxL6UOKV4ER+AVefS+WnnJCvhCufQrl8jAUL70qXox8t5b0lT9qBy88XMSZtIwOF8JIvWtwK+ams7o+8iRI+Wss86Sl15++Yz3z+p1UoYN+2dr2Vi3pNHfmUyInEGU0h9IDFPKmVhj+q+mznsunXfeefLyS386oxFNGPW46KKPSX3kX0g6szh6zGiupzhDiR8CI9D5ppNzvyRf/acL5OyPXC6j+2yW9TqLaN2EUhLZRP78wJAQKAJ+FdDff7rFzIMPPChvvfmmfOELF1uhvPPOmTeS/c+rr1pJoX7Y+XemX+P2er/Z4NqDI6QPHj927JjVs3CYqXIPDhFdyojAu/LatiIZOmuXnIgsI2dft1Z2rhwlH5F3pGXjDTJ62XOR9yMLzCNXyzObr5YLHfSRDa4d4FEVAYcCuin2oUOHrFYGDBjARIhDz0Src41homIulNfnPWpCSFLoAjan8I/Au4dk+wOnkj+RHLlq0tBIUqjHeZJ79bUy7NxToZzY94TsfY0rDU9p8L8I+E9AV9OivwP1NYe7AiSG7npzNgQQSFLg3YOPyv0H3jpVu0/ksopLOi0XXzhE/iXvVJooJ56W72/6FTehJOlMNQQQCLYAiWGwx5/oEfCJwNty8MmG0zedRO5GvvJyueSMG0w+JpcVfCWywKzHCXnp8afkIJOGPhlbuokAAl4SIDH00mjQFwQQ6F7g9WekbvvpvQvPHS633jxQzsgLIz9dOHaa3Njn9HrySz+Vur1/7r4t3kUAAQQQ6FGAxLBHGj5AAAFvCERuOtn9sOxo1VtLIjeX5F0hl3W3ifXZF8uo6J6G8gfZ8UCjvOaNAOgFAggg4BsBEkPfDBUdRSCoAq/K3vr/tO44lsjtJsMKhvRwx/H5csnXI3sanmbiJpSgfl+IGwEEnAiwXY0TPeoigED6BV57RKYMmdXl2ch2Thu5FrGoJvKYvMFdlp3j12W7mvhGlEAAATMFmDE0c1yJCgFDBN6Wpk3rk0gKNXxuQjHkS0AYCCDgogCJoYvYnAoBBBIUePd3suvx0zedJFjVKv5SrfzbjleSqUkdBBBAIJACPBIvkMNO0Aj4Q+Ddg0/JTn3UnR59psuP986z8RzkV+SRm0bLnN2vRyq9Lo31z8lr4509CcU6P/+DAAIIBECAGcMADDIhIuBPgT/Lvpqfxti7sKeoOu9pGFlQ3vewbG95p6fCvI8AAggg0EmAxLATBi8RQMBDAq81yoPb/3C6Qzky+usX27yJJLKn4chrZWx29Bl5++X+H/83T0Lx0NDSFQQQ8K4AiaF3x4aeIRBggcjehU8/IY2nV5Gl6yPw4sl8ZKhMGJdzuhQ3ocTj4nMEEEAgKkBiGJXgTwQQ8I7Au4dk+wPPnd67sLtH4MXr6pl7Ggo3ocQD43MEEEDAEiAx5IuAAAKeE3j34KNy/4G3TvcrkWXk90I5+5LLZXT0EXnRm1De+5hXCCCAAALdCJAYdoPCWwggkEmBt+Xgkw2nbzqJPAJv5DS5KXx+4h06e6DcNGO4nL7SUE7sXi+bm95OvB1qIIAAAgESIDEM0GATKgK+EDhj78JYj8CLF03kJpThV8iwaGYoR2Tnk7/jJpR4bHyOAAKBFuCReIEefoJHAIHuBHgkXncqvIcAAkEQYMYwCKNMjAgggAACCCCAgA0BnnxiA4kiCCBgvkBTU5Psf/55ee7Z5zqCvfnGm+STn/ykfO7ii+Wy4ZdJdnZ2x2e8QAABBEwUYCnZxFElJgQQsCXQ3t4utTU1UldbK4dbDsetMyI/X4pLbpFwOBy3LAUQQAABPwqQGPpx1OgzAgg4FtAZwrmzZ9tKCLuebOy4sXLnXXdJVlZW14/4GQEEEPC1AImhr4ePziOAQDIC9TvrpaS4OJmqHXVCvUNSW/eQ9B/Qv+M9XiCAAAJ+F+DmE7+PIP1HAIGEBFKRFOoJ2463ycQJ10nzoeaEzk9hBBBAwMsCJIZeHh36hgACKRVYe99axzOFnTukyWHR9Gmi1ypyIIAAAiYIkBiaMIrEgAACcQVeffVVuXfNmrjlEi2gN61sWL8h0WqURwABBDwpQGLoyWGhUwggkGqBB3/0gPzf//1fqpu12ltbWSmtra1paZtGEUAAATcFSAzd1OZcCCCQMYH6+p1pPff6qnVpbZ/GEUAAATcESAzdUOYcCCCQUQHdmsbOPoVOOvn44485qU5dBBBAwBMCJIaeGAY6gQAC6RTQJ5qk+9AbUbhDOd3KtI8AAukWIDFMtzDtI4BAxgU6P+YunZ05duxYOpunbQQQQCDtAiSGaSfmBAggEBSB3//+haCESpwIIGCoAImhoQNLWAgggAACCCCAQKICJIaJilEeAQQQQAABBBAwVIDE0NCBJSwEEHhP4MMf/tB7P6Tx1eAvfzmNrdM0AgggkH4BEsP0G3MGBBDIsMBXvzbElR5cdNFFrpyHkyCAAALpEiAxTJcs7SKAgGcEBg8enPa+DBo8SLKzs9N+Hk6AAAIIpFOAxDCdurSNAAKeEOg/oL9o4pbO45prr0tn87SNAAIIuCJAYugKMydBAIFMC3zv1tvS1oVQ75CMHjM6be3TMAIIIOCWAImhW9KcBwEEMiowLG+YjMjPT0sf7rn3+5KVlZWWtmkUAQQQcFOAxNBNbc6FAAIZFbj3B98Xnd1L5TG5sFA06eRAAAEETBAgMTRhFIkBAQRsCeisXm3dQylLDvW6xVlzZts6N4UQQAABPwiQGPphlOgjAgikTEBvRNHksF9uP0dt6kzhv1dXs4TsSJHKCCDgNYFeJyOH1zpFfxBAAIF0C7S3t8uG9RtkbWVlQqfSpeg5c+fJhIkTEqpHYQQQQMAPAiSGfhgl+ogAAmkTaG1tlfVV6+Txxx+TtuNtPZ5Hl411Sxq9+5gbTXpk4gMEEPC5AImhzweQ7iOAQOoEmg81y7Fjx+T3v3+ho1F9zJ0+0YTNqztIeIEAAgYLkBgaPLiEhgACCCCAAAIIJCLAzSeJaFEWAQQQQAABBBAwWIDE0ODBJTQEEEAAAQQQQCARARLDRLQoiwACCCCAAAIIGCxAYmjw4BIaAggggAACCCCQiACJYSJalEUAAQQQQAABBAwWIDE0eHAJDQEEEEAAAQQQSESAxDARLcoigAACCCCAAAIGC5AYGjy4hIYAAggggAACCCQiQGKYiBZlEUAAAQQQQAABgwVIDA0eXEJDAAEEEEAAAQQSESAxTESLsggggAACCCCAgMECJIYGDy6hIYAAAggggAACiQiQGCaiRVkEEEAAAQQQQMBggf8P4IgTT7bPQDQAAAAASUVORK5CYII=" alt></p>
<p>The <em>Q</em> factor for this system is 200 and the period of oscillation is approximately 0.4s.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The sphere A is displaced so that the system oscillates. Discuss, with reference to the <em>Q</em> factor, the subsequent motion of the pendulum.</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 support point P of the pendulum is now made to oscillate horizontally with frequency <em>f</em>.</p>
<p>Describe the amplitude of A and phase of A relative to P when</p>
<p>(i) <em>f</em> = 2.5 Hz.<br>(ii) <em>f</em> = 1 Hz.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The natural frequency of a driven oscillating system is 6 kHz. The frequency of the driver for&nbsp;the system is varied from zero to 20 kHz.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a graph to show the variation of amplitude of oscillation of the system with frequency.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxUAAAF/CAYAAAA/7eQfAAAgAElEQVR4Ae3dDXSV9Z0n8F9C12oX0fXYWRJs67qcRDvStYXitHUrggWdlhkWLc4oKRaOY61YWg6aFdGZVsSiDK5v66iHFAq1lVaWjuNYUHOgo32hxLGl00KW47E7QtwZx2MxZ8dyhtw9N29cklxINOD/n3xyTk5unue5z/39P7+bm+d7n5dbUSgUCuGLAAECBAgQIECAAAECb1Gg8i3ez90IECBAgAABAgQIECDQLiBUeCIQIECAAAECBAgQIPC2BISKt8XnzgQIECBAgAABAgQICBWeAwQIECBAgAABAgQIvC2Bd5Xeu6KiovRXtwkQIECAAAECBAgQINBLoOe1ng4JFcWZxWDRc6FeazGBAAECBAgQIECAAIFhJ1AuKzj8adg9FQyYAAECBAgQIECAwOAKCBWD62ltBAgQIECAAAECBIadgFAx7FpuwAQIECBAgAABAgQGV0CoGFxPayNAgAABAgQIECAw7ASEimHXcgMmQIAAAQIECBAgMLgCQsXgelobAQIECBAgQIAAgWEnIFQMu5YbMAECBAgQIECAAIHBFRAqBtfT2ggQIECAAAECBAgMOwGhYti13IAJECBAgAABAgQIDK6AUDG4ntZGgAABAgQIECBAYNgJCBXDruUGTIAAAQIECBAgQGBwBYSKwfW0NgIECBAgQIAAAQLDTkCoGHYtN2ACBAgQIECAAAECgysgVAyup7URIECAAAECBAgQGHYCQsWwa7kBEyBAgAABAgQIEBhcAaFicD2tjQABAgQIECBAgMCwExAqhl3LDZgAAQIECBAgQIDA4AoIFYPraW0ECBAgQIAAAQIEhp2AUDHsWm7ABAgQIECAAAECBAZXQKgYXE9rI0CAAAECBAgQIDDsBISKYddyAyZAgAABAgQIECAwuAJCxeB6WhsBAgQIECBAgACBYScgVAy7lhswAQIECBAgQIAAgcEVECoG19PaCBAgQIAAAQIECAw7AaFi2LXcgAkQIECAAAECBAgMroBQMbie1kaAAAECBAgQIEBg2AkIFcOu5QZMgAABAgQIECBAYHAFhIrB9bQ2AgQIECBAgAABAsNOQKgYdi03YAIECBAgQIAAAQKDKyBUDK6ntREgQIAAAQIECBAYdgJCxbBruQETIECAAAECBAgQGFwBoWJwPa2NAAECBAgQIECAwLATECqGXcsNmAABAgQIECBAgMDgCggVg+v5jq7tX//1X6OioiKKP30RIECAAAECBAgQOFYCQsWxkj4Gj/Pkk0+2P0rXz2PwkB6CAAECBAgQIECAQFQUCoVCqUPxne4ek0pnu52oQHHvxPnnnx8/+9nP4qMf/Whs3bo1TjjhhESrVRYBAgQIECBAgECOAuWygj0VOXazj5qLeycmTZrUPqf4096KPpBMIkCAAAECBAgQOCoC9lQcFdZju9KuvRTr1q2L2tra2LVrV8yePdveimPbBo9GgAABAgQIEBjyAvZUDOEWd+2lqKmpaR9l8ae9FUO44YZGgAABAgQIEEhMwJ6KxBoy0HJK91IUw0RXemxubra3YqCYlidAgAABAgQIEDisQNe2Zs+FnFPRUySz33vupegq396KLgk/CRAgQIAAAQIEjraAPRVHW/gorr/nXoriQ5WmR3srjiK+VRMgQIAAAQIEhqFA6bZm6fDtqSjVyOz2v/zLv8TnPve56DqXomf5xenF+cXlfBEgQIAAAQIECBA4WgL2VBwt2XdoveXS4ztUjoclQIAAAQIECBAYQgLltjXtqehscltzQ0yrmBUNzW9GxJvR3DArKqoXR+O+tohoi9bmTbFi8SPRXPz1bX21xb7GxVHd/Vhva2XuTIAAAQIECBAgQOAdFxAq+mzB8VEzd30U9i6LyaOKRK/FtlU3xfVNxcDhiwABAgQIECBAgACBUgGholTDbQIECBAgQIAAAQIEBiyQTqhoa4mmDStiTnVF+xWMKiqq44L6hmhs3tc5qFejsX5CVEz7emzYdNfB5S6ojzVNe2Jf8fCkOeM67ls9J+7a1hIdRyp13e/+aPzJ/T3u17VMT7fSw5/+KRrrL4opdzRFbJ4XtSMmRH3jP3UewlS8/WrJnTsfq/uwqeKRU4eOq3rOynjy+T0l9+m42dayLdbUTysz9l6Lm0CAAAECBAgQIEAgGYFEQsXr0bTyqpj+/RPi2qbfRaFQiMKBn8XNIx6NKVeviqbWkhMZNt8T9zZ+IG5qPhCFAy/HMx97Ia6ccFqcedvu+OTXm6JQ+G38eum74s4Zt8XGPfsPQm+eH7MfiM71/zZ2XTciVk+4KlY2vX5wmT5vnRqTl/8gnrlhfMTUVbHrwPZYPvnUPpfsPbFjXBPufS3+eMtvo1A4EM03nRHPP/FUtJQs3LZnQ1w1fl40jr4l9h4oRKGwMx6ofS5mT1ocG0rHUHIfNwkQIECAAAECBAikIpBGqNj3fKxf+UrUzbksJlYd12FTOSYmXXlZTN3y4/j53pJwUHVl3HzTjKgZWRlRWRUTLhwfVfHZWHrTvM77joqa8z4R41p+Ej/d1bWXIyKqro37ll11cJmZC+PmG16Jleufj5KlBrcvneO64eaFMbNmVERUxsiaGXHTzVdGVfcjvRpb7lkWDeO+Ejct+ERUtXdkVJw5d3msq/tJzL/n2aNXX3cNbhAgQIAAAQIECBB46wJphIpRk2P53u2xfOJr0bhhQ2wofjfUx5TaebH5rY/t0HuO+0ic3RVY2ueMjNNqz4iWtU/H9vYrPB26+Nv/rS32bX861racEbWnjSxZXWWMPG1sjOuasu8XsWltU1Sdc3qMPqQbR7u+rgL8JECAAAECBAgQIPD2BA7ZjH17q3o7994XOxvmRfWJtTHl3p9G+wFJJ18cD2x/KKbGi7Hr5daDKx83Nk4r7qUYrK+W3fHSKyV7QgZrvbE/Xnlp9yGHOR1u1S13TImTKrrOJyn+PCFq5333cHcxjwABAgQIECBAgEASAu9KoYq25u/Fgnnb4uLHXoqHZ34gOiJD8fMcNseOiDjnaBZZNTZOH31cxCuD/SDHxejTx0ZV7O7Hiqti6qrGeHLumZ1j78ddLEKAAAECBAgQIEAgEYFBfMv/rY6oLVpf3h074qz4xNn/sWSj+t/ijdcH8WyHHbvj5dITvqM1Xt71YlTVXRgT2j+LYiD19ziEqc+7VsaoCRdGXVWPPS3FD9JrH2/nnUZ9KKbVVceO534VLSXno0e8Hk0rPhMV0xoG4QP3+izQRAIECBAgQIAAAQKDIpBAqOja+H421q7+u84N6/3Rsu3hWDz//n4fPnREjZbVcettG6O5PVgUD7eqj9lr/yDu+9J5UTyF+vBfHec3dCzzZrS2/ltUjv14XDZ1b6xd80Ts7Fxn84aVcWvx0rNdX6POiy/d9wexdnZ9NOwsBqTiJ3NvjNtuXV0yrlNj0pcWx8VP/nksvvu5zvHvi+YNd8Si6yPuXDYzahLoUteQ/CRAgAABAgQIECDQUyCNzdVR58WXH18eE388J6pHFM8nGB///YenxpyN340bDl4mqWftA/t9Ul3UffTFuK1mRFRUnBSTt54da7Ysi5ljOq82ddi1HR9jL74qbty/JGpHnBGXrN8dbZU1Meveb8TCWBFnnVhc52dj1RtT4+aHPluypuNizMxlsWXN2bF18klRUTEiTrx6e3z0ui/F1JKlKsfMiLu33B3nv/K1zvGfFJO+f0pct/3hWDj+5JIl3SRAgAABAgQIECCQnkBFofihECVfFRUV7Z8TUTIp85vFD6S7KKa88MXY9eTcIf+u/9DrX+ZPP+UTIECAAAECBIaQQLltzTT2VAwhaEMhQIAAAQIECBAgMNwEhIrh1nHjJUCAAAECBAgQIDDIAsPg8KdBFkt8deV2SSVetvIIECBAgAABAgQyECi3rWlPRQbNUyIBAgQIECBAgACBlAWEipS7ozYCBAgQIECAAAECGQgIFRk0SYkECBAgQIAAAQIEUhYQKlLujtoIECBAgAABAgQIZCAgVGTQJCUSIECAAAECBAgQSFlAqEi5O2ojQIAAAQIECBAgkIGAUJFBk5RIgAABAgQIECBAIGUBoSLl7qiNAAECBAgQIECAQAYCQkUGTVIiAQIECBAgQIAAgZQFhIqUu6M2AgQIECBAgAABAhkICBUZNEmJBAgQIECAAAECBFIWECpS7o7aCBAgQIAAAQIECGQgIFRk0CQlEiBAgAABAgQIEEhZQKhIuTtqI0CAAAECBAgQIJCBgFCRQZOUSIAAAQIECBAgQCBlAaEi5e6ojQABAgQIECBAgEAGAkJFBk1SIgECBAgQIECAAIGUBYSKlLujNgIECBAgQIAAAQIZCAgVGTRJiQQIECBAgAABAgRSFhAqUu6O2ggQIECAAAECBAhkICBUZNAkJRIgQIAAAQIECBBIWUCoSLk7aiNAgAABAgQIECCQgYBQkUGTlEiAAAECBAgQIEAgZQGhIuXuqI0AAQIECBAgQIBABgJCRQZNUiIBAgQIECBAgACBlAWEipS7ozYCBAgQIECAAAECGQgIFRk0SYkECBAgQIAAAQIEUhYQKlLujtoIECBAgAABAgQIZCAgVGTQJCUSIECAAAECBAgQSFlAqEi5O2ojQIAAAQIECBAgkIGAUJFBk5RIgAABAgQIECBAIGUBoSLl7qiNAAECBAgQIECAQAYCQkUGTVIiAQIECBAgQIAAgZQFhIqUu6M2AgQIECBAgAABAhkICBUZNEmJBAgQIECAAAECBFIWECpS7o7aCBAgQIAAAQIECGQgIFRk0CQlEiBAgAABAgQIEEhZQKhIuTtqI0CAAAECBAgQIJCBgFCRQZOUSIAAAQIECBAgQCBlAaEi5e6ojQABAgQIECBAgEAGAkJFBk1SIgECBAgQIECAAIGUBYSKlLujNgIECBAgQIAAAQIZCAgVGTRJiQQIECBAgAABAgRSFhAqUu6O2ggQIECAAAECBAhkICBUZNAkJRIgQIAAAQIECBBIWUCoSLk7aiNAgAABAgQIECCQgYBQkUGTlEiAAAECBAgQIEAgZQGhIuXuqI0AAQIECBAgQIBABgJCRQZNUiIBAgQIECBAgACBlAWEipS7ozYCBAgQIECAAAECGQgIFRk0SYkECBAgQIAAAQIEUhYQKlLujtoIECBAgAABAgQIZCAgVGTQJCUSIECAAAECBAgQSFlAqEi5O2ojQIAAAQIECBAgkIGAUJFBk5RIgAABAgQIECBAIGUBoSLl7qiNAAECBAgQIECAQAYCQkUGTVIiAQIECBAgQIAAgZQFhIqUu6M2AgQIECBAgAABAhkICBUZNEmJBAgQIECAAAECBFIWECpS7o7aCBAgQIAAAQIECGQgIFRk0CQlEiBAgAABAgQIEEhZQKhIuTtqI0CAAAECBAgQIJCBgFCRQZOUSIAAAQIECBAgQCBlAaEi5e6ojQABAgQIECBAgEAGAkJFBk1SIgECBAgQIECAAIGUBYSKlLujNgIECBAgQIAAAQIZCAgVGTRJiQQIECBAgAABAgRSFhAqUu6O2ggQIECAAAECBAhkICBUZNAkJRIgQIAAAQIECBBIWUCoSLk7aiNAgAABAgQIECCQgYBQkUGTlEiAAAECBAgQIEAgZQGhIuXuqI0AAQIECBAgQIBABgJCRQZNUiIBAgQIECBAgACBlAWEipS7ozYCBAgQIECAAAECGQgIFRk0SYkECBAgQIAAAQIEUhYQKlLujtoIECBAgAABAgQIZCAgVGTQJCUSIECAAAECBAgQSFlAqEi5O2ojQIAAAQIECBAgkIGAUJFBk5RIgAABAgQIECBAIGUBoSLl7qiNAAECBAgQIECAQAYCQkUGTVIiAQIECBAgQIAAgZQFhIqUu6M2AgQIECBAgAABAhkICBUZNEmJBAgQIECAAAECBFIWECpS7o7aCBAgQIAAAQIECGQgIFRk0CQlEiBAgAABAgQIEEhZQKhIuTtqI0CAAAECBAgQIJCBgFCRQZOUSIAAAQIECBAgQCBlAaEi5e6ojQABAgQIECBAgEAGAkJFBk1SIgECBAgQIECAAIGUBYSKlLujNgIECBAgQIAAAQIZCAgVGTRJiQQIECBAgAABAgRSFhAqUu6O2ggQIECAAAECBAhkICBUZNAkJRIgQIAAAQIECBBIWUCoSLk7aiNAgAABAgQIECCQgYBQkUGTlEiAAAECBAgQIEAgZQGhIuXuqI0AAQIECBAgQIBABgJCRQZNUiIBAgQIECBAgACBlAWEipS7ozYCBAgQIECAAAECGQgIFRk0SYkECBAgQIAAAQIEUhYQKlLujtoIECBAgAABAgQIZCAgVGTQJCUSIECAAAECBAgQSFlAqEi5O2ojQIAAAQIECBAgkIGAUJFBk5RIgAABAgQIECBAIGUBoSLl7qiNAAECBAgQIECAQAYCQkUGTVIiAQIECBAgQIAAgZQFhIqUu6M2AgQIECBAgAABAhkICBUZNEmJBAgQIECAAAECBFIWECpS7o7aCBAgQIAAAQIECGQgIFRk0CQlEiBAgAABAgQIEEhZQKhIuTtqI0CAAAECBAgQIJCBgFCRQZOUSIAAAQIECBAgQCBlAaEi5e6ojQABAgQIECBAgEAGAkJFBk1SIgECBAgQIECAAIGUBYSKlLujNgIECBAgQIAAAQIZCAgVGTRJiQQIECBAgAABAgRSFhAqUu6O2ggQIECAAAECBAhkICBUZNAkJRIgQIAAAQIECBBIWUCoSLk7aiNAgAABAgQIECCQgYBQkUGTlEiAAAECBAgQIEAgZQGhIuXuqI0AAQIECBAgQIBABgJCRQZNUiIBAgQIECBAgACBlAWEipS7ozYCBAgQIECAAAECGQgIFRk0SYkECBAgQIAAAQIEUhZ4V8rFqe2tCVRUVLy1O7oXAQIECBAgQOAdEigUCu/QI3vYwRAQKgZDMbF1DOU/ymJgMr7EnnADKEf/BoCV4KL6l2BTBlCS/g0AK8FFh0P/EmRX0gAEHP40ACyLEiBAgAABAgQIECDQW0Co6G1iCgECBAgQIECAAAECAxAQKgaAZVECBAgQIECAAAECBHoLCBW9TUwhQIAAAQIECBAgQGAAAkLFALAsSoAAAQIECBAgQIBAb4GKQo9L6Qz1qwv0JhhaU/RvaPXTaAgQIECAAAECKQmU29a0pyKlLqmFAAECBAgQIECAQIYCQkWGTVMyAQIECBAgQIAAgZQEhIqUuvFWa2lriaY19XFB5ydpV1RMi/qGv4mmlv1vdY0J3a8tWpsbo6F+WhR3t7V/V8+JFU81R2tCVQ5aKW2/iQ3zxkV1fWPsG7SVvtMr2h8tTWuj/oLqzh5Oi/o126Kl7Z2ua5Aev+Tvr/35eUF9rGlqieyH17otVlzwiahvfLUHVM9+VscF9Q/H93Mbc9nx7YvmxoaS52tFVM+5K55qzuwvsuz4Dm1n254NMa96Qh99PnS55H473PiGwt/kYcbX1rIt1nT/Tyz+/a3N4/99a3M0NnRsq3T8Px8Xc1ZsiubW0lfLIfL6ktwfzLEpSKg4Ns5H8VH2x56Nt8X01RFXbt/b/jgH9t4So7feGNP/x7PZb5i27dkYCyYtiK2jb4m9BwpRKPwu9m6cGDvmXBILNvwm/w23Q54ZxV7eGfMbfnnI1Lx/2R97NiyM/3pPW3z+8ZejUDgQb+y6OmL15XHl6p1DoH+vR9PKq2L6D8+Nde3Pz0IcWHdu/HD6VbGy6fV8W9f6y1hz6+3xv7b8rtcY2vb8TSyZvi7iyo0df5MHmmL56Gfjmun3xpZ9pRsHve6azoSy4ys+XxfHpNlbY/TypjhQKEThwN7YeM4LMWfS4tiwJ5M3asqOr0cL2n4TG2/582ho6TE99V8PN77iGzNXXR73HKiLx4v9K/w2dl03IlZPWBCrm99MfWQd9R1ufK3bYuXlX4wfnvtQx/Oz8FKsO/enMf3y+6PpkI3zxIZa7MuCS2L21vfH8r2/i+LpvAf2/lWcs2NRTFqwMfZ0vnQMideXxOiPZTlCxbHUPhqP1fZibHrwBzGu7vNRN76q/REqqz4RC276Soxb+3Rsz+WffJ82b8buTd+Jhpgec+Z9LKran63HRdXEeXHT0rOiYf6D+WzE9Dm+0olt0brz27H4hr+P2o939LF0bra39z0b98z/SVwy59Nx5shiAytjZM2MuOnmWbFjyTfz79++52P9ylei7opPxpjOV9PKMZ+MK+peiZXrn88w1He+S3htY5w16w9jZK8nXuff5LjLYl7dxI6/ycqqmLjgxlg6bmts2v5ar3ukNeEI42t/Pd0QUTcn5k2sivaWdo9vQ8y/J/U3ao4wvkOasS92rv5a3PDiqfHxQ6an/MuRxtcW+7Y8GPOf/FjMufSDnc/fUVEzc2HcfMOLsWTVjxL/m+zH+LZtjJW7psYVF76v4/kZx8WYC2dG3a5vxfpt6f79te1+Jh5seHfUzbksJlYd1/4k695WaVgW92wp7hHN/fUl5b+dY1Nb57/BY/NgHuUoCLTujV07To5zTj+18wWm4zEqR58e58TmDP7JH87k+KiZuz4Ke5fF5FF9PFVbdsdLr2TyzuHhhlmc17o9/uqae+NdX78xLu+9JXekeyc6vy32bX861sbUmDbhlJIaK2PU5GWxt1xfS5bM+WbLCy/FK5m8cd/l3Na8Lq5c9GJM+/oXYsKJI7oml/xsjZd3vRhV55weo0v/JCtPjdPP+V2s3fSLpDfajji+yjNj7qa9sXf55BhVMuqum6n39Ijj6xpItEVr06q4ZskJ8fXFl/YRHrsXTOrGkcf3WmzftDmi7sKYcMj/jFNj8vLtZfuayiCPPL7DVbo3Xnjp1WT3/lbWzI1Nhe2xfPKpfQyiq/a8X1/6GNiwm1T6b2HYDX4oDLjtlZfihbK7rrv+UIfCSPsYw9SL4ryxx/cxI7dJr0fTX30tVp6xOL42Y2z0tSmX24g66t0fr7y0O1rG/ac4ae+Wg+fFDKVzYkZ9JGYtHB1rv/XDg7vvW/4+nt72vrhz2cyoyewVtrL6M7H68Ztjcuc7ib2ed22vxksvdBxm2WteRKS+0X3E8fU1qO5p74mpl308xibc036Pr/gmxqJvxRn3XR8zPnBC9whTv3HE8bU/P1+PcbXvib0l58Xkck7MEccXlTFq4oxYWLs5vvX0P3YGiP3Rsv3vYlvt9bFsVs0hby6m3s+D9Z0Xl513elRm/vpycDzD91bCL4/Dtyn9H3lbtL68O3b0/w5DYsm2PX8by5f8OuZePSXpf/D9wy6+Y/iNWPTElHj87hndh9D0776pL9XxrlO0PhKLFvxdnP7lx9uPoy00Xx+nrLt6iJwTc3KMX7gilr48P04b0XEhgRHVc6Kp7vZYOP7k1BvUu76RvxdV7Yep9Z7VPqV9z2jZdzHK3CmhyUcaX5+lFs91ui+W7Lgorp52Rtobbf0aX/FNjNvjiU//z7h75gfSHk/PfhxpfO3Pz/8XrWtvjAVPvy++/Mze9vO4mm88Jdb9YQbnxBxpfEWPkRNj4YNfjJcvOT1GtF+85N1RPeUfou7Ba2L84f52e1qm8HvxnJ7ld8WOuX8S04pvEOb++pKC6Ttcg1DxDjfAww9QoPWXsXrxsnjxypWxdEZm/xD7GGr7iejTn4lPr/h8fv8Q+hhPn5N+9N6ou7f+4LvfIz8Yl875WDw5FM6JKV6hZcrs2HrZ5nij/aTQQhTe2ByXbb0mPt/wy6F5hbI+mzxUJ3ae6zT/f8eV626MGWM6jgXPd7TFE9GXxPQnPhkrvjAhm8OeBubdEj86ri7uXfqpzvPwKmPkmZ+OOZf8JINzYo400uKbUHfFlEnPxWW//m3HmzTFi1/8+tOx9Q+vjYadOV2hrOOcnvkvXhrrln5miL2hdqQ+Dt35QkXWva2MkaeNjXFZj2EAxbf+Mhqu/dNYEtfFA4undP7DGMD9U1u0/cory+LFhbfEF3J8V7u/nlVj4/TRpRtjnc/b7M+JaYt9nSdNHjwptPhOYkdoemrJI7Et6wsl9NHgkdVRO24IXUigjyEenFQMFGvj2skrIpb+ZSyePCavd/UPDqT7VvHKOrfMfykWDuU3MSJ6n/MTI+O02jOSPzyvu1Flb7wW29Z/K3bVXRGXntl11k9XaPp5LPnG9qTPaTo4rH2xs+ErMXlJxNIHvlLyhtNwen05qDGUbgkVmXez/YTssv/jq3udwJ3rcNtanou72gPFomi8v67zSkK5jqaj7o6rYTTFluvPjRO7PoNjxFkxb3NLtNwxJU6qmBUNuVwCsc9WnBITpk2Nsk/PPu+T08SOk0J7HwzUFZpyv1BCH71oPyG7uo8ZHZN6ncBddsnUZ+yPlm0PdAaKb8f9c88eAu/qd15Zp+WJuH7Cf+j+3J8RtfNiczTFHVPeGxXTGqI5s4sLHPJMGvWhmFY3/pBJQ+qXfb+ITWub+hhSZ2jK4YqPbS2x7a7rOgJF410xtzscFS8OWLzgw3B4femjhUNkklCReyPb3zl8vddVHzpO4D4jak/L/VJC+6Ol8asxpfqz8dejvxpbhkigKD7tOq6GUbyOesn3gV/HqqlVUXXDM/HbwvqYW5PzieiVMbJ2Qlzc6ypknecCTfpY/Jfq0j0Yuf0xlgtNneOr6nnVq9zG11e9Zd7x7T5Btjr/je+2PdG4eHpUn/vXMfq+7w6RQFHsZefV9Epfb4qfFbBrVUyN8XHDM/8chU1zs7u4wKHP0lFRe+4fRPTauC6e37UnJn3q7KjOeaunbGjqvGpSr6teHarzTv/W1vJULJ4yPs796zFx35YegaK9uGHw+vJON+EoP37Of15HmSaT1VeeEdOuvih2LLkzVnceT1l8V//u2+6KHTd8IS7NeqO0ePzo/XH5lL+IXXPvi3W3z4ya3E5Ey+RpdLTKrBwzOb64cHTcceva7g9mamv5caxa8+O4+LqZ8ZjdYDgAABY3SURBVOGs+1m8EsvlsfRTu2PT97Yc/FTY1l/F99ZsjtqFM2LiIZe1PFrKx3K9x8fYaX8Sc3fcFbet7jxnpPjO4923x5Ids6L+0lyvPtNlWPwww6tjyu17Y+5jD8XtM8/MPyR1DW1Y/Dwuxkz9XCysXR+3PrS985ym4l6nR2PNYx+O6/70nMz7eUpM/Px18akXNsX3Gps7x1c8TO+JWLN2dCyc9ZE+L4WcROvbP7RvTty+a2Y8tu4vYmZN1+FbpdUN9deX0rEOzdtCRfZ9Lb6IfinWLT011p51UvtoRlR/IV4Y99V4/MvnpfsC0x/3tuZYv/jO2FK8VGXDJd1X16noOlSoYkLUNxY/MMdXugInx/hFj8SuxRH31IxoP+RixPiH4sDsB/O78kxfyCPPjrn3L41psSmuPrFjfBU1d8Zrsx+JxxdNzHwDpq8BR1SOuTDq130lRq+d2nHY3ojqmPHCuLjv8etiUuYhqq15Qyy+/omI+GU0dF9dp+OqXu2vO9WLo3GonSfTd5vznTpyYix6/G9jcdwfNZ1XRxp///6Y/bfLYmb2J9oXz5+oi/vvnRax6brOw2ZHRM3tr8XsLY/EomTPzXszmteviOu3tES03B+XnPbu7sPvuv6fV9c3tp8PMpRfX/L9o+p/5RWF4rEXJV/FBveYVDLXzdQF9C/1DqmPAAECBAgQIJCvQLltTXsq8u2pygkQIECAAAECBAgkISBUJNEGRRAgQIAAAQIECBDIV0CoyLd3KidAgAABAgQIECCQhIBQkUQbFEGAAAECBAgQIEAgXwGhIt/eqZwAAQIECBAgQIBAEgJCRRJtUAQBAgQIECBAgACBfAWEinx7p3ICBAgQIECAAAECSQgIFUm0QREECBAgQIAAAQIE8hUQKvLtncoJECBAgAABAgQIJCEgVCTRBkUQIECAAAECBAgQyFdAqMi3dyonQIAAAQIECBAgkISAUJFEGxRBgAABAgQIECBAIF8BoSLf3qmcAAECBAgQIECAQBICQkUSbVAEAQIECBAgQOBYCOyL5g2L44KKiqioqI5pDTuj7Vg87FB5jLad0TDtimhofrP3iNrnVUd1fWPs6z03ItpiX+PiqK6YEPWNr/axRNf8WX2vv497pDTpXSkVoxYCBAgQIECAAIGjJ9DW/L247pLH44zHXopnZn4gvLs8QOvWvbHr302JeWOPH+Adh/7inktDv8dGSIAAAQIECBAoEXh3nHryvxcoSkT6d7Mt9m3fEv8w8+Mx1hZ0LzIkvUhMIECAAAECBAgMNYE3o7lhVoyonReboynumPLeqKheHI3/+FTUV1fHBfX3xIo546KioqL78J22lm2xpn5a+7TioVIX1DdEY/OhB/a0tTTFhhVzorr9cKpxMWfFhtiw4r91rHtf8cCqV6OxfkLJ752u+xqjvvrgY7VPbWuJpjX1nYdmVUTFBfXR0NgcrV2taL9PdUx7+KnYVrJc9Zy74qledZXWXqxrUzS3tkXbng0xr7qvw4866ix/6FKxiNdi+6Z/ipnnnd7PQNYWrTvXxJzqcTHnrueiZcDHmXXatdsWD1cr/U7v0DWhouuJ6icBAgQIECBAYMgKHB81c9fHgV2rYmqMjxue+eco7F0Wk08aEREtsWXtz+OUG5+LwoH/G1v+bEKM3LMhrho/LxpH3xJ7DxSiUNgZD9Q+F7MnLY4Ne/Z3KLVui5WXXxb3/vMfx5Y3DkThwOa4dsT3Y/71Gweu2Pab2HDV1Jje+P5Yvvd3USgciDce+GBsnX1JLNjwm5LzPlpi85+tiMdO/Hw8XihE4cDLsW7MD2Lq1auiqbVjq70YHK4aPyNWx9Wxq1jXG9+O83csikkLNkZL1SfjirqItd/6Yewp3cjf94vYtDaibtqHYlS56ovL/MPEOK9fhz4VA8XauHbyioil3477v/KJqBrwVvepMXn59igUx9n1feDleObGqRGTro9ls2r6GW7KDWhwpw94eIP78NZGgAABAgQIECDwTgtU1V0Rl545KqLy96LmP++PLfcsi4ZxX4mbFnRtDI+KM+cuj3V1P4n59zwb+4onHW/bGCt3zYqbb5oRNSMrIyqrYuKCG2Pp1KoBDqct9m15MOY3nBVLb5oXE6uOi4jKGHlmXdy7bno8Of/B2NK+16NjtVU31MdNM8+MkcVfK6tiwoXjo2rLj+Pne4th583Yvek70RBXHqxr5Afj0jnTIxq+E5t2vycmzroiattvd51sXTys6elYG1Nj2oRTytTescxjv396jD7i1vOBeKM0UMw9u6PW7jV37ik6ZM9DcS/EiDhpyu3R0r1czxv7YufqW2L26tNi1QPzYnzRPKGvtKpJCEYpBAgQIECAAIFhKdD+rn1TVJ3TcwN6ZJxWe0a0rH06tu97NbZv2hwt48bGaaUbt5Wnx3mXnTdAtuJhRZujpWpsnD66GCi6vipj5GljY1zL5ti0/bWuiT1+di4TL8aul1sj2l6KZx99NuKQuipj1ORlsbewPubWvCdGfvjiqJv6fDz67Eude0A6Hj/qLowJo8ptGu+PV156LS453J6Mrspe+UGsvObG+GYxlF3ZM1AUF+rcU9S196H754H47TM3Rt+RrC1am1bFNfNejivXfS2uLAbAxL7KySVWpnIIECBAgAABAgSOpUDLHVPipEPeTT8haud99+iV0HJ7TDlpxCHnDnScAzLID1l5Rky7+qLYseSbHXtA2kPU6Fg46yPlD30qhpUNv3eYPRkHa2z55rfj+Y/8aXxux12xfGPpoVsHlxnorbY9G2PB9IZ4/6q/jMWTxyR12FPXWISKLgk/CRAgQIAAAQIEOgWqYuqqX8eB7nfRS47rL56LUfYd/bcBOHVV7Go/f6Pksdoff3ssn3zq21hxz7seF2MunBl1UdwD8mrHoU/jZsYfffjkngt2/962+0ex4fcnHWZPRveiUXXDuvj+X94WNy09Kxrm3xkbu85BObjIwG4Vz12ZPT+evPirsazPPR8DW93RWlqoOFqy1kuAAAECBAgQyFFg1IdiWl117HjuVz2uWPR6NK34TFRMa4jmtlNiwrSpUbXj+fhlS+eJ2+1jbY2Xd71YMuqOQ6ZKJvRxs9y6iof83BUXVAzgw+C6Dr/asTte7jxxu/iAbc0NMa30w/5GfSRmLRwda7/1nXj0ia0x7rLDXSb2zdj97Lb4/f4c+tQ9uuOjZtaiuLN2Q+c5KN0zBnajeAL7gnlxfVwfj989I8YkvOWecGkDM7c0AQIECBAgQIDAYAicGpO+tDgufvLPY/HdXZdCLX4S9x2x6PqIO5fNjJrKyhg16eq47+KtMX/xt2Nn+wZ8cZmVcesdTSVFHB9jz7soprY8Hmu+96uOy8O27owNty2PO7rPSC5d18OxrT2ktEVr88a4ddH9EXcuilk1/f2wueNj7MVXxY216+PWrz/TEYra9sSW1Y/G5kOumHRyfPiPZsa4hgXxZyvHxGWHvUxsMShF1J7Wfmp4ydiOcHPkhPjCiuuj9o6V8VDT60dYuK/ZxROzvxbznzw/Hlt3bXInZvesWKjoKeJ3AgQIECBAgMAwF6gcMyPu3nJ3nP/K16J6RPHKRCfFpO+fEtdtfzgWju88TKjyAzHz7sdi3fm/imtOLJ4LcWZc/dP3R90NUw/Rq6y5NO7dPDdiybg4sXiOxvRvxBuXLIqHSq8S1b2u/xP11e9uvxLSiZO+H++97tF4ZOHEHldPOmT1vX6prPpULH3kkbjywIqO2kd8NG49MDu2P3Lohnnl2Clx9dyzI6ZedPjLxA7oUrKl5VTGyA/PjOvm/iauX/SN7kveli5x2Nv7tsc3ljRES8v9cclpRZPSz6no8Rkfh13RsZlZUShe+Lbkq1hwj0klc91MXUD/Uu+Q+ggQIECAwFAWKH7I3ueidsnYeGbn0qNz7sVg8bXtjIaLZ8dzVz8WD8/8QJInPw/WUAdzPeW2Ne2pGExl6yJAgAABAgQIEMhAYH+0bHk01u6/Ir449X0CxSB0TKgYBESrIECAAAECBAgQyEOg46Ttd0f1rb+L6x5M70Pk8lDsXaXDn3qbZD2l3C6prAeleAIECBAgQIAAgSQEym1r2lORRHsUQYAAAQIECBAgQCBfAaEi396pnAABAgQIECBAgEASAkJFEm1QBAECBAgQIECAAIF8BYSKfHuncgIECBAgQIAAAQJJCAgVSbRBEQQIECBAgAABAgTyFRAq8u2dygkQIECAAAECBAgkISBUJNEGRRAgQIAAAQIECBDIV0CoyLd3KidAgAABAgQIECCQhIBQkUQbFEGAAAECBAgQIEAgXwGhIt/eqZwAAQIECBAgQIBAEgJCRRJtUAQBAgQIECBAgACBfAWEinx7p3ICBAgQIECAAAECSQgIFUm0QREECBAgQIAAAQIE8hUQKvLtncoJECBAgAABAgQIJCEgVCTRBkUQIECAAAECBAgQyFdAqMi3dyonQIAAAQIECBAgkISAUJFEGxRBgAABAgQIECBAIF8BoSLf3qmcAAECBAgQIECAQBICQkUSbVAEAQIECBAgQIAAgXwFhIp8e6dyAgQIECBAgAABAkkICBVJtEERBAgQIECAAAECBPIVECry7Z3KCRAgQIAAAQIECCQhIFQk0QZFECBAgAABAgQIEMhXQKjIt3cqJ0CAAAECBAgQIJCEgFCRRBsUQYAAAQIECBAgQCBfAaEi396pnAABAgQIECBAgEASAkJFEm1QBAECBAgQIECAAIF8BYSKfHuncgIECBAgQIAAAQJJCAgVSbRBEQQIECBAgAABAgTyFRAq8u2dygkQIECAAAECBAgkISBUJNEGRRAgQIAAAQIECBDIV0CoyLd3KidAgAABAgQIECCQhIBQkUQbFEGAAAECBAgQIEAgXwGhIt/eqZwAAQIECBAgQIBAEgJCRRJtUAQBAgQIECBAgACBfAWEinx7p3ICBAgQIECAAAECSQgIFUm0QREECBAgQIAAAQIE8hUQKvLtncoJECBAgAABAgQIJCEgVCTRBkUQIECAAAECBAgQyFdAqMi3dyonQIAAAQIECBAgkISAUJFEGxRBgAABAgQIECBAIF8BoSLf3qmcAAECBAgQIECAQBICQkUSbVAEAQIECBAgQIAAgXwFhIp8e6dyAgQIECBAgAABAkkICBVJtEERBAgQIECAAAECBPIVECry7Z3KCRAgQIAAAQIECCQhIFQk0QZFECBAgAABAgQIEMhXQKjIt3cqJ0CAAAECBAgQIJCEgFCRRBsUQYAAAQIECBAgQCBfAaEi396pnAABAgQIECBAgEASAkJFEm1QBAECBAgQIECAAIF8BYSKfHuncgIECBAgQIAAAQJJCAgVSbRBEQQIECBAgAABAgTyFRAq8u2dygkQIECAAAECBAgkISBUJNEGRRAgQIAAAQIECBDIV0CoyLd3KidAgAABAgQIECCQhIBQkUQbFEGAAAECBAgQIEAgXwGhIt/eqZwAAQIECBAgQIBAEgJCRRJtUAQBAgQIECBAgACBfAWEinx7p3ICBAgQIECAAAECSQgIFUm0QREECBAgQIAAAQIE8hUQKvLtncoJECBAgAABAgQIJCEgVCTRBkUQIECAAAECBAgQyFdAqMi3dyonQIAAAQIECBAgkISAUJFEGxRBgAABAgQIECBAIF8BoSLf3qmcAAECBAgQIECAQBICQkUSbVAEAQIECBAgQIAAgXwFhIp8e6dyAgQIECBAgAABAkkICBVJtEERBAgQIECAAAECBPIVECry7Z3KCRAgQIAAAQIECCQhIFQk0QZFECBAgAABAgQIEMhXQKjIt3cqJ0CAAAECBAgQIJCEgFCRRBsUQYAAAQIECBAgQCBfAaEi396pnAABAgQIECBAgEASAkJFEm1QBAECBAgQIECAAIF8BYSKfHuncgIECBAgQIAAAQJJCAgVSbRBEQQIECBAgAABAgTyFRAq8u2dygkQIECAAAECBAgkISBUJNEGRRAgQIAAAQIECBDIV0CoyLd3KidAgAABAgQIECCQhIBQkUQbFEGAAAECBAgQIEAgXwGhIt/eqZwAAQIECBAgQIBAEgJCRRJtUAQBAgQIECBAgACBfAWEinx7p3ICBAgQIECAAAECSQgIFUm0QREECBAgQIAAAQIE8hUQKvLtncoJECBAgAABAgQIJCEgVCTRBkUQIECAAAECBAgQyFdAqMi3dyonQIAAAQIECBAgkISAUJFEGxRBgAABAgQIECBAIF8BoSLf3qmcAAECBAgQIECAQBICQkUSbVAEAQIECBAgQIAAgXwFhIp8e6dyAgQIECBAgAABAkkICBVJtEERBAgQIECAAAECBPIVECry7Z3KCRAgQIAAAQIECCQhIFQk0QZFECBAgAABAgQIEMhXQKjIt3cqJ0CAAAECBAgQIJCEgFCRRBsUQYAAAQIECBAgQCBfAaEi396pnAABAgQIECBAgEASAkJFEm0YvCIKhcLgrcyaCBAgQIAAAQIECPRDQKjoB5JFCBAgQIAAAQIECBAoLyBUlLcxhwABAgQIECBAgACBfggIFf1AsggBAgQIECBAgAABAuUFhIryNuYQIECAAAECBAgQINAPAaGiH0gWIUCAAAECBAgQIECgvIBQUd7GHAIECBAgQIAAAQIE+iEgVPQDySIECBAgQIAAAQIECJQXECrK25hDgAABAgQIECBAgEA/BISKfiBZhAABAgQIECBAgACB8gJCRXkbcwgQIECAAAECBAgQ6IeAUNEPJIsQIECAAAECBAgQIFBeQKgob2MOAQIECBAgQIAAAQL9EBAq+oFkEQIECBAgQIAAAQIEygsIFeVtzCFAgAABAgQIECBAoB8CQkU/kCxCgAABAgQIECBAgEB5AaGivI05BAgQIECAAAECBAj0Q0Co6AeSRQgQIECAAAECBAgQKC8gVJS3MYcAAQIECBAgQIAAgX4ICBX9QLIIAQIECBAgQIAAAQLlBYSK8jbmECBAgAABAgQIECDQDwGhoh9IFiFAgAABAgQIECBAoLyAUFHexhwCBAgQIECAAAECBPohIFT0A8kiBAgQIECAAAECBAiUFxAqytuYQ4AAAQIECBAgQIBAPwSEin4gWYQAAQIECBAgQIAAgfICQkV5G3MIECBAgAABAgQIEOiHgFDRDySLECBAgAABAgQIECBQXkCoKG9jDgECBAgQIECAAAEC/RAQKvqBZBECBAgQIECAAAECBMoLCBXlbcwhQIAAAQIECBAgQKAfAkJFP5AsQoAAAQIECBAgQIBAeQGhoryNOQQIECBAgAABAgQI9ENAqOgHkkUIECBAgAABAgQIECgvIFSUtzGHAAECBAgQIECAAIF+CAgV/UCyCAECBAgQIECAAAEC5QWEivI25hAgQIAAAQIECBAg0A8BoaIfSBYhQIAAAQIECBAgQKC8QEWhUCh0za6oqOi66ScBAgQIECBAgAABAgT6FCiJEO3z31W6VM+ZpfPcJkCAAAECBAgQIECAQF8CDn/qS8U0AgQIECBAgAABAgT6LSBU9JvKggQIECBAgAABAgQI9CUgVPSlYhoBAgQIECBAgAABAv0W+P8EtOI7QkOpkQAAAABJRU5ErkJggg=="></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 <em>Q </em>factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A solid cube of side 0.15 m has an average density of 210 kg m<sup>&ndash;3</sup>.</p>
<p>(i) Calculate the weight of the cube.</p>
<p>(ii) The cube is placed in gasoline of density 720 kg m<sup>&ndash;3</sup>. Calculate the proportion of the volume of the cube that is above the surface of the gasoline.</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>Water flows through a constricted pipe. Vertical tubes A and B, open to the air, are located along the pipe.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Describe why tube B has a lower water level than tube A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A ball is moving in still air, spinning clockwise about a horizontal axis through its centre.&nbsp;The diagram shows streamlines around the ball.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-26_om_10.55.18.png" alt="M17/4/PHYSI/HP3/ENG/TZ2/10"></p>
</div>

<div class="specification">
<p>The surface area of the ball is 2.50 x&nbsp;10<sup>&ndash;2</sup> m<sup>2</sup>. The speed of air is 28.4 m\(\,\)s<sup>&ndash;1</sup> under the&nbsp;ball and 16.6 m\(\,\)s<sup>&ndash;1</sup> above the ball. The density of air is 1.20 kg\(\,\)m<sup>&ndash;3</sup>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the magnitude of the force on the ball, ignoring gravity.</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>On the diagram, draw an arrow to indicate the direction of this force.</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>State <strong>one</strong> assumption you made in your estimate in (a)(i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph below shows the displacement <em>y</em> of an oscillating system as a function of time <em>t</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>State what is meant by damping.</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 <em>Q</em> factor for the system.</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 <em>Q</em> factor of the system increases. State and explain the change to the graph.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A farmer is driving a vehicle across an uneven field in which there are undulations&nbsp;every 3.0 m.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The farmer&rsquo;s seat is mounted on a spring. The system, consisting of the mass of the farmer&nbsp;and the spring, has a natural frequency of vibration of 1.9 Hz.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed&nbsp;of 5.6 m s<sup>&ndash;1</sup>.</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>Outline what change would be required to the value of <em>Q</em> for the mass&ndash;spring system&nbsp;in order for the drive to be more comfortable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A reservoir has a constant water level. Q is a point inside the outlet pipe at 12.0m depth, beside the tap for the outlet.<br><img src="data:image/png;base64,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" alt><br>The atmospheric pressure is 1.05&times;10<sup>5</sup>Pa and the density of water is 1.00&times;10<sup>3</sup>kgm<sup>&minus;3</sup>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the pressure at Q when the tap is closed.</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>Explain what happens to the pressure at Q when the tap is opened.</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>The tap at Q is connected to an outlet pipe with a diameter of 0.10 m. The water flows steadily in the pipe at a velocity of 1.27ms<sup>&minus;1</sup>. The viscosity of the water is 1.8&times;10<sup>&minus;3</sup>Pas.</p>
<p>(i) Calculate the Reynolds number for this flow.</p>
<p>(ii) Explain the significance of this value.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A mass-spring system is forced to vibrate vertically at the resonant frequency of the system. The motion of the system is damped using a liquid.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>At time <em>t</em>=0 the vibrator is switched on. At time <em>t</em><sub>B</sub> the vibrator is switched off and the system comes to rest. The graph shows the variation of the vertical displacement of the system with time until <em>t</em><sub>B</sub>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>&nbsp;</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to energy in the system, the amplitude of oscillation between</p>
<p>(i) <em>t&nbsp;</em>= 0 and <em>t</em><sub>A</sub>.</p>
<p>(ii) <em>t</em><sub>A</sub> and <em>t</em><sub>B</sub>.</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 system is critically damped. Draw, on the graph, the variation of the displacement with time from <em>t</em><sub>B</sub> until the system comes to rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A driven system is lightly damped. The graph shows the variation with driving frequency <em>f</em> of&nbsp;the amplitude <em>A</em> of oscillation.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-26_om_11.02.12.png" alt="M17/4/PHYSI/HP3/ENG/TZ2/11"></p>
</div>

<div class="specification">
<p>A mass on a spring is forced to oscillate by connecting it to a sine wave vibrator.&nbsp;The graph shows the variation with time <em>t</em> of the resulting displacement <em>y</em> of the mass.&nbsp;The sine wave vibrator has the same frequency as the natural frequency of the&nbsp;spring&ndash;mass system.</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>On the graph, sketch a curve to show the variation with driving frequency of the&nbsp;amplitude when the damping of the system <strong>increases</strong>.</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>State and explain the displacement of the sine wave vibrator at <em>t</em> = 8.0 s.</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>The vibrator is switched off and the spring continues to oscillate. The <em>Q</em> factor&nbsp;is 25.</p>
<p>Calculate the ratio \(\frac{{{\text{energy stored}}}}{{{\text{power loss}}}}\) for the oscillations of the spring&ndash;mass system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows a simplified model of a Galilean thermometer. The thermometer consists&nbsp;of a sealed glass cylinder that contains ethanol, together with glass spheres. The spheres&nbsp;are filled with different volumes of coloured water. The mass of the glass can be neglected&nbsp;as well as any expansion of the glass through the temperature range experienced.&nbsp;Spheres have tags to identify the temperature. The mass of the tags can be neglected in all calculations.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Each sphere has a radius of 3.0 cm and the spheres, due to the different volumes of water&nbsp;in them, are of varying densities. As the temperature of the ethanol changes the individual&nbsp;spheres rise or fall, depending on their densities, compared with that of the ethanol.</p>
</div>

<div class="specification">
<p>The graph shows the variation with temperature of the density of ethanol.</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>Using the graph, determine the buoyancy force acting on a sphere when the&nbsp;ethanol is at a temperature of 25 &deg;C.</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>When the ethanol is at a temperature of 25 &deg;C, the 25 &deg;C sphere is just at&nbsp;equilibrium. This sphere contains water of density 1080 kg m<sup>&ndash;3</sup>. Calculate the&nbsp;percentage of the sphere volume filled by water.</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>The room temperature slightly increases from 25 &deg;C, causing the buoyancy force&nbsp;to decrease. For this change in temperature, the ethanol density decreases from&nbsp;785.20 kg m<sup>&ndash;3</sup> to 785.16 kg m<sup>&ndash;3</sup>. The average viscosity of ethanol over the temperature&nbsp;range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 &deg;C sphere falls.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>