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This repository was archived by the owner on Jul 30, 2024. It is now read-only.
Copy file name to clipboardExpand all lines: source/03-AD/03.ptx
+24-12Lines changed: 24 additions & 12 deletions
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@@ -279,30 +279,42 @@ recall that when <m>y</m> is a function of <m>x</m>, which in turn is a function
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<!-- Using triangles -->
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<remarkxml:id="right-triangles-sides-theorem">
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<activityxml:id="right-triangles-related-rates">
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<introduction>
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<p>Recall that in a right triangle with sides <m>a,b</m> and hypotenuse <m>c</m> we have the relationship </p>
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<me> a^2 + b^2 = c^2,</me>
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<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>
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</remark>
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</introduction>
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<activityxml:id="right-triangles-related-rates"><p> Notice that by differentiating each variable in the equation above with respect to <m>t</m>, we get a relationship between <m>\frac{da}{dt}, \frac{db}{dt}, \frac{dc}{dt}</m>. Find this related rates equation! </p></activity>
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<task>
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<statement>
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<p> Notice that by differentiating the equation above with respect to <m>t</m> we get a relationship between
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<m>a,b,c, \frac{da}{dt}, \frac{db}{dt}, \frac{dc}{dt}</m>. Find this related rates equation.
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</p>
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</statement>
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</task>
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<activityxml:id="rel-rates-right-triangles1">
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<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?
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<task>
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<statement>
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<p> A rectangle has one side of 8 cm. How fast is the diagonal of the rectangle changing at the instant when the other
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side is 6 cm and increasing at a rate of 3 cm per minute?
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</p>
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</activity>
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</statement>
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</task>
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<activityxml:id="rel-rates-right-triangles2">
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<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?
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<task>
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<statement>
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<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.
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When is the top of the ladder sliding the fastest down the wall?
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</p>
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<olmarker="A."cols="2">
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<li><p> When the bottom of the ladder is 4 meters from the wall. </p></li>
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<li><p> When the bottom of the ladder is 8 meters from the wall. </p></li>
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<li><p> The top of the ladder is sliding down at a constant rate. </p></li>
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