# QUESTION 2

Find the average value of the function $f(x, y)=20-2 y$ over the rectangle $R=[0,3] imes[0,5]$.
$\bigcirc \mathrm{A} f_{ ext {ave }}=0$
$\bigcirc \mathrm{B} f_{ ext {ave }}=75$
$\bigcirc \mathrm{C} f_{ ext {ave }}=15$
$\bigcirc \mathrm{D} f_{ ext {ave }}=3$
$\bigcirc$ E None of these

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# QUESTION 2

Find the average value of the function $f(x, y)=20-2 y$ over the rectangle $R=[0,3] 	imes[0,5]$.
$\bigcirc \mathrm{A} f_{	ext {ave }}=0$
$\bigcirc \mathrm{B} f_{	ext {ave }}=75$
$\bigcirc \mathrm{C} f_{	ext {ave }}=15$
$\bigcirc \mathrm{D} f_{	ext {ave }}=3$
$\bigcirc$ E None of these

StudyXY · Accepted Answer

: Recall the formula for finding the average value of a function over a region. : In this case, the function is $f(x, y) = 20 - 2y$ and the region $R$ is a rectangle with bounds $0 \leq x \leq 3$ and $0 \leq y \leq 5$. : Now, compute the double integral of the function over the region $R$: : Integrate with respect to $x$: : Integrate with respect to $y$: : Plug the results back into the formula: The correct answer is $\bigcirc \mathrm{C}$.

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QuestionAnatomy and Physiology

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Step 1
: Recall the formula for finding the average value of a function over a region.

Step 2
: In this case, the function is $f(x, y) = 20 - 2y$ and the region $R$ is a rectangle with bounds $0 \leq x \leq 3$ and $0 \leq y \leq 5$.

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