0003.qti

<item ident="D3-7994" title="D3 | Inverse Laplace transforms | ver. 7994">
  <itemmetadata>
    <qtimetadata>
      <qtimetadatafield>
        <fieldlabel>question_type</fieldlabel>
        <fieldentry>essay_question</fieldentry>
      </qtimetadatafield>
    </qtimetadata>
  </itemmetadata>
  <presentation>
    <material>
      <mattextxml>
        <div class="exercise-statement">
          <p>
            <strong>D3.</strong>
          </p>
          <p> Explain how to use convolution along with the formula <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\mathcal{L}\{e^{at})=\frac{1}{s-a}" alt="\mathcal{L}\{e^{at})=\frac{1}{s-a}" title="\mathcal{L}\{e^{at})=\frac{1}{s-a}" data-latex="\mathcal{L}\{e^{at})=\frac{1}{s-a}"/>to find the following inverse Laplace transform: </p>
          <p style="text-align:center;">
            <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\mathcal{L}^{-1}\left\{ \frac{3}{5 \, {\left(s + 7\right)} {\left(s - 4\right)}} \right\}" alt="\mathcal{L}^{-1}\left\{ \frac{3}{5 \, {\left(s + 7\right)} {\left(s - 4\right)}} \right\}" title="\mathcal{L}^{-1}\left\{ \frac{3}{5 \, {\left(s + 7\right)} {\left(s - 4\right)}} \right\}" data-latex="\mathcal{L}^{-1}\left\{ \frac{3}{5 \, {\left(s + 7\right)} {\left(s - 4\right)}} \right\}"/>
          </p>
        </div>
      </mattextxml>
      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;D3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Explain how to use convolution along with the formula &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cmathcal%7BL%7D%5C%7Be%5E%7Bat%7D)=%5Cfrac%7B1%7D%7Bs-a%7D" alt="\mathcal{L}\{e^{at})=\frac{1}{s-a}" title="\mathcal{L}\{e^{at})=\frac{1}{s-a}" data-latex="\mathcal{L}\{e^{at})=\frac{1}{s-a}"&gt;to find the following inverse Laplace transform: &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cmathcal%7BL%7D%5E%7B-1%7D%5Cleft%5C%7B%20%5Cfrac%7B3%7D%7B5%20%5C,%20%7B%5Cleft(s%20+%207%5Cright)%7D%20%7B%5Cleft(s%20-%204%5Cright)%7D%7D%20%5Cright%5C%7D" alt="\mathcal{L}^{-1}\left\{ \frac{3}{5 \, {\left(s + 7\right)} {\left(s - 4\right)}} \right\}" title="\mathcal{L}^{-1}\left\{ \frac{3}{5 \, {\left(s + 7\right)} {\left(s - 4\right)}} \right\}" data-latex="\mathcal{L}^{-1}\left\{ \frac{3}{5 \, {\left(s + 7\right)} {\left(s - 4\right)}} \right\}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext>
    </material>
    <response_str ident="response1" rcardinality="Single">
      <render_fib>
        <response_label ident="answer1" rshuffle="No"/>
      </render_fib>
    </response_str>
  </presentation>
  <itemfeedback ident="general_fb">
    <flow_mat>
      <material>
        <mattextxml>
          <div class="exercise-answer">
            <h4>Partial Answer:</h4>
            <p style="text-align:center;">
              <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?\frac{3}{55} \, e^{\left(4 \, t\right)} - \frac{3}{55} \, e^{\left(-7 \, t\right)}" alt="\frac{3}{55} \, e^{\left(4 \, t\right)} - \frac{3}{55} \, e^{\left(-7 \, t\right)}" title="\frac{3}{55} \, e^{\left(4 \, t\right)} - \frac{3}{55} \, e^{\left(-7 \, t\right)}" data-latex="\frac{3}{55} \, e^{\left(4 \, t\right)} - \frac{3}{55} \, e^{\left(-7 \, t\right)}"/>
            </p>
          </div>
        </mattextxml>
        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%5Cfrac%7B3%7D%7B55%7D%20%5C,%20e%5E%7B%5Cleft(4%20%5C,%20t%5Cright)%7D%20-%20%5Cfrac%7B3%7D%7B55%7D%20%5C,%20e%5E%7B%5Cleft(-7%20%5C,%20t%5Cright)%7D" alt="\frac{3}{55} \, e^{\left(4 \, t\right)} - \frac{3}{55} \, e^{\left(-7 \, t\right)}" title="\frac{3}{55} \, e^{\left(4 \, t\right)} - \frac{3}{55} \, e^{\left(-7 \, t\right)}" data-latex="\frac{3}{55} \, e^{\left(4 \, t\right)} - \frac{3}{55} \, e^{\left(-7 \, t\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext>
      </material>
    </flow_mat>
  </itemfeedback>
</item>