A solid E lies within the cylinder 64x² + 64y² = 9, below the plane z = 16 and above the paraboloid z = 3 – x² – y² . The density at any point is in inversely proportional to the distance from the z-axis, with k the constant of proportionality.

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 25E
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A solid E lies within the cylinder 64x² + 64y? = 9, below the plane z = 16 and above the paraboloid z = 3 – x? – y² . The density at any point is in
inversely proportional to the distance from the z- axis, with k the constant of proportionality.
'n Soliede E lê binne die silinder 64x² + 64y? = 9, onder die vlak z = 16 en bo die paraboloïed z = 3 – x² – y². Die digtheid op enige punt is indirek
eweredig aan die afstand vanaf die z- as, met k die verhoudings-konstante.
т — kx
Transcribed Image Text:A solid E lies within the cylinder 64x² + 64y? = 9, below the plane z = 16 and above the paraboloid z = 3 – x? – y² . The density at any point is in inversely proportional to the distance from the z- axis, with k the constant of proportionality. 'n Soliede E lê binne die silinder 64x² + 64y? = 9, onder die vlak z = 16 en bo die paraboloïed z = 3 – x² – y². Die digtheid op enige punt is indirek eweredig aan die afstand vanaf die z- as, met k die verhoudings-konstante. т — kx
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