<p>The diagram below shows a stream of water flowing out from the end of a drainage pipe into a larger canal. The vertical height, \(y\) metres, of the stream above the surface level of the canal is measured at various horizontal distances, \(x\) metres, from the end of the pipe. The results are recorded in the table:</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1775551806324-hmr6cepv504.png" style="max-width: min(350px, 100%); height: auto; display: block;" alt="Diagram of water stream from a drainage pipe" class="aligncenter custom-width" /></figure></div>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 490px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">\(x\)</th><th style="text-align: center; --cell-justify: center">\(1\)</th><th style="text-align: center; --cell-justify: center">\(2\)</th><th style="text-align: center; --cell-justify: center">\(3\)</th><th style="text-align: center; --cell-justify: center">\(4\)</th><th style="text-align: center; --cell-justify: center">\(5\)</th><th style="text-align: center; --cell-justify: center">\(6\)</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(y\)</td><td style="text-align: center; --cell-justify: center">\(1.20\)</td><td style="text-align: center; --cell-justify: center">\(1.14\)</td><td style="text-align: center; --cell-justify: center">\(1.04\)</td><td style="text-align: center; --cell-justify: center">\(0.90\)</td><td style="text-align: center; --cell-justify: center">\(0.86\)</td><td style="text-align: center; --cell-justify: center">\(0.50\)</td></tr></tbody></table></div></div>
<p>The motion of the water stream can be represented by the equation \(y = P + Qx^2\), where&nbsp;\(P\) and \(Q\) are constants. However, one of the \(y\)-values in the table have been recorded incorrectly.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Using graph paper, plot \(y\) against \(x^2\) and draw a straight line graph.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Based on your graph, identify which value of \(y\) is incorrect and estimate the correct value.</span></div></li><li><div class="list-item-content"><span class="list-item-text">estimate the values of \(P\) and \(Q\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Explain the meaning of the value of \(P\) in the context of the water stream.</span></div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1775549390753-ag7pmkj47wl.png" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

The diagram below shows a stream of water flowing out from the end of a drainage pipe into a larger canal. The vertical height, \(y\) metres, of the stream above the surface level of the canal is measured at various horizontal distances, \(x\) metres, from the end of the pipe. The results are recorded in the table:

The motion of the water stream can be represented by the equation \(y = P + Qx^2\), where \(P\) and \(Q\) are constants. However, one of the \(y\)-values in the table have been recorded incorrectly.

Using graph paper, plot \(y\) against \(x^2\) and draw a straight line graph.

Based on your graph, identify which value of \(y\) is incorrect and estimate the correct value.

Explain the meaning of the value of \(P\) in the context of the water stream.

Linear Law

Question b749f0f3