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Find the center of mass of the solid region bounded above by the spere x² + y² +z² = 4 and below by the upper nappe of the cone 22 = 2² + y², and whose density is given by p(x, y, z) = z²(x² + y² + 22). (Use symmetry to avoid calculating moments when possible!)

Find the center of mass of the solid region bounded above by the spere x² + y² +z² = 4 and below by the upper nappe of the cone 22 = 2² + y², and whose density is given by p(x, y, z) = z²(x² + y² + 22). (Use symmetry to avoid calculating moments when possible!)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.3: Volume And Average Value
Problem 11E
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2. Find the center of mass of the solid region bounded above by the spere x2 + y² + 2² = 4 and below by the upper nappe of the cone 2 = ² + y², and whose density is given by p(x, y, z) = z²(x² + y² +2²). (Use symmetry to avoid calculating moments when possible!)
Transcribed Image Text:2. Find the center of mass of the solid region bounded above by the spere x2 + y² + 2² = 4 and below by the upper nappe of the cone 2 = ² + y², and whose density is given by p(x, y, z) = z²(x² + y² +2²). (Use symmetry to avoid calculating moments when possible!)
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