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Let H be a solid region given by z> Vx2 + y² and 2² + y? + z? < 6 whose density at any point is given by f (x, y, z) = Vr2 + y² + z² Use spherical coordinates to find the following. (a) Find the mass of the above region. (b) Find z, the z- coordinate of the center of mass of the above region. (ẽ and y are obviously 0, so we don't ask about them).

Let H be a solid region given by z> Vx2 + y² and 2² + y? + z? < 6 whose density at any point is given by f (x, y, z) = Vr2 + y² + z² Use spherical coordinates to find the following. (a) Find the mass of the above region. (b) Find z, the z- coordinate of the center of mass of the above region. (ẽ and y are obviously 0, so we don't ask about them).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer parts a & b and explain.

Let H be a solid region given by x² + y² and x2 + y? + 22 < 6 whose density at any point is given by f (x, y, z) = Vx² + y² + z² Use spherical coordinates to find the following. (a) Find the mass of the above region. (b) Find z, the z- coordinate of the center of mass of the above region. ( and ỹ are obviously 0, so we don't ask about them).
Transcribed Image Text:Let H be a solid region given by x² + y² and x2 + y? + 22 < 6 whose density at any point is given by f (x, y, z) = Vx² + y² + z² Use spherical coordinates to find the following. (a) Find the mass of the above region. (b) Find z, the z- coordinate of the center of mass of the above region. ( and ỹ are obviously 0, so we don't ask about them).
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