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First attempt at addressing AD3 Activity #49 #110

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First attempt at addressing AD3 Activity #49 #110

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29 changes: 15 additions & 14 deletions calculus/source/03-AD/03.ptx
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Expand Up @@ -279,40 +279,41 @@ recall that when <m>y</m> is a function of <m>x</m>, which in turn is a function

<!-- Using triangles -->

<remark xml:id = "thm-right-triangles">
<p>Recall that in a right triangle with sides <m>a,b</m>, and hypotenuse <m>c</m> we have the relationship
</p>
<me> a^2 + b^2 = c^2. </me>
<p> You might know this as the Pythagorean theorem, even though this relationship was known by the Babylonians already a thousand years before his time!
</p>
</remark>


<activity xml:id="right-triangles-related-rates">
<introduction>
<p>Recall that in a right triangle with sides <m>a,b</m> and hypotenuse <m>c</m> we have the relationship </p>
<me> a^2 + b^2 = c^2,</me>
<p>also known in the western world as the Pythagorean theorem (even though this result was well know well before his time by other civilizations).</p>
</introduction>

<task>
<statement>
<p>Consider the relationship between the lengths of the sides of a right triangle given by <xref ref="thm-right-triangles"/>.
</p>
</introduction>
<task>
<p> Notice that by differentiating the equation above with respect to <m>t</m> we get a relationship between
<m>a,b,c, \frac{da}{dt}, \frac{db}{dt}, \frac{dc}{dt}</m>. Find this related rates equation.
</p>
</statement>
</task>

<task>
<statement>
<p> A rectangle has one side of 8 cm. How fast is the diagonal of the rectangle changing at the instant when the other
side is 6 cm and increasing at a rate of 3 cm per minute?
</p>
</statement>
</task>

<task>
<statement>
<p> A 10 m ladder leans against a vertical wall and the bottom of the ladder slides away at a rate of 0.5 m/sec.
When is the top of the ladder sliding the fastest down the wall?
<p> A 10 m ladder leans against a vertical wall whilst the bottom of the ladder is sliding away at a rate of 0.5 m/sec.
At which time is the top of the ladder sliding down the wall the fastest?
</p>
<ol marker="A." cols="2">
<li><p> When the bottom of the ladder is 4 meters from the wall. </p></li>
<li><p> When the bottom of the ladder is 8 meters from the wall. </p></li>
<li><p> The top of the ladder is sliding down at a constant rate. </p></li>
</ol>
</statement>
</task>
</activity>

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