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\textbf{Math 225: Calculus III}
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\textbf{Quiz 7}\quad \textsl{Mar.\ 26/28, 1996}
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\begin{enumerate}
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\item 
Find the centroid of the region inside the unit circle in the first
quadrant.
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\problemspace
\item 
Compute the average value of the function $f(x,y,z) = x^3 y$ over the solid
region bounded in the first quadrant by the planes $x + z = 2$ and
$y = 3$. The volume of the region is~6.
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