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<quiz>
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    <name>
      <text>11.6.2.4 y' and y'' parametric</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>Find \( \dfrac{dy}{dx}\) and \( \dfrac{d^2y}{dx^2}\) where \( x = {@xt@}\) and \( y = {@yt@} \).
<ol class="HELM_parts">
<p></p>
  <li>
\( \dfrac{dy}{dx} = \) [[input:ans1]] [[validation:ans1]][[feedback:prt1]]
<p></p></li>
  <li>\( \dfrac{d^2y}{dx^2} = \) [[input:ans2]] [[validation:ans2]][[feedback:prt2]]<p></p>
<p></p></li></ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We have \(x = {@xt@} \quad \text{and} \quad y ={@yt@}\).</p>
<p>So \( \dfrac{dx}{dt} = {@ta1@}, \quad \dfrac{d^2x}{dt^2} = {@diff(ta1,t)@} \quad \text{and} \quad \dfrac{dy}{dt} = {@ta2@}, \quad \dfrac{d^2y}{dt^2} = {@diff(ta2,t)@}\).</p>
<p>Thus:</p>
<ol class="HELM_parts">
  <li><p>\(\displaystyle \frac{dy}{dx} = {@ta3@}\)</p></li>
  <li><p>\(\displaystyle \frac{d^2y}{dx^2} = {@ta4@}\)</p></li>
</ol>
<p>&nbsp;</p>]]></text>
    </generalfeedback>
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    <idnumber/>
    <stackversion>
      <text>2021120900</text>
    </stackversion>
    <questionvariables>
      <text>a1:rand([2,3,4,5]);
a2:rand([4,5,6,7]);

xt:4 - a1*t^2
yt:t^2 + a2*t;

ta1:diff(xt,t);
ta2:diff(yt,t)
ta3:ta2/ta1

ta4:( ta1*diff(ta2,t) - ta2*diff(ta1,t))/ta1^3;
ta4:simplify(ta4);


dydx(t):=(2*t + cos(pi*t) -t*pi*sin(pi*t))/(a1 - 4*pi*cos(pi*t));
Ta3:dydx(a2);</text>
    </questionvariables>
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      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\( x = {@xt@}, \,  y = {@yt@} \quad  \dfrac{dy}{dx} ={@ta3@}, \, \dfrac{d^2y}{dx^2} ={@ta4@} \)</text>
    </questionnote>
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      <text/>
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      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
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      <tans>ta3</tans>
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      <description/>
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        <value>ta3</value>
      </testinput>
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</quiz>
