If E is the solid described below with density function p(x, y, z) = x² + y², find the following quantities, correct to three decimal places. E is bounded by the cylinder y2 + z² = 25 and the planes x = 0, y = 5x, and z = 0 in the first octant (a) the mass m m = 216.667 X (b) the center of mass 265 12 216/3 (x, y, z) = 9625 12 216 2 3 1625 3 216 2 (c) the moment of inertia about the z-axis 2708.333 X X

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If E is the solid described below with density function p(x, y, z) = x² + y², find the following quantities, correct to three decimal places.
E is bounded by the cylinder y2 + z² = 25 and the planes x = 0, y = 5x, and z = 0 in the first octant
(a) the mass m
m = 216.667 X
(b) the center of mass
265
12
216/3
(x, y, z) =
(5)
9625
12
216
2
3
1625
3
216
2
(c) the moment of inertia about the z-axis
2708.333 X
co/1
3
Transcribed Image Text:If E is the solid described below with density function p(x, y, z) = x² + y², find the following quantities, correct to three decimal places. E is bounded by the cylinder y2 + z² = 25 and the planes x = 0, y = 5x, and z = 0 in the first octant (a) the mass m m = 216.667 X (b) the center of mass 265 12 216/3 (x, y, z) = (5) 9625 12 216 2 3 1625 3 216 2 (c) the moment of inertia about the z-axis 2708.333 X co/1 3
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