Question
Asked Nov 5, 2019
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Find the coordinates of the center of mass of the following solid with variable
density
The interior of the prism formed by z
x, X 2, y 3, and the coordinate planes with p(xy z)-4+y
The center of mass is located at
(Type exact answers.)
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Find the coordinates of the center of mass of the following solid with variable density The interior of the prism formed by z x, X 2, y 3, and the coordinate planes with p(xy z)-4+y The center of mass is located at (Type exact answers.)

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Step 1

Given,

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The density function is p(x, y,z) = 4+ y = x,x= 2, y = 3 and the coordinate planes. The region is interior to the prism The center of mass is given by (x,y,z),where 1 1 lxp(x, y.dV, y Sspcs.y. 2xdil and E E EР(х, у, -) := y E

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Step 2

From the given region, x varies from 0 to 2, y varies from 0 to 3 and z varies from 0 to x .

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2 3 x m =s(4+y)ddyd* 0 0 0 2 3 0 0 Intergrate with respect to z 2 3 m3D[[(4х + ух)dvdk 0 0 Integrate with respect to y 4ху + dx m 2 33 2

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Step 3

Integrate with respect...

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33 2 33r 1+1 0 33 2 2 J 33 22 2 2 33 (2) 2 =33

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Math

Calculus

Integration

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