7. Use cylindrical coordinates to find z for the solid bounded above by the paraboloid z = x² + y², bounded below by the xy-plane, and is inside the cylinder x2 + y? 8(x, y, z) find M). = 4. Take the density to be 8T8 (that means you don't need to = constant. You may assume the mass is M = Answer. 7 = 4/3.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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7. Use cylindrical coordinates to find \( \bar{z} \) for the solid bounded above by the paraboloid \( z = x^2 + y^2 \), bounded below by the \( xy \)-plane, and is inside the cylinder \( x^2 + y^2 = 4 \). Take the density to be \( \delta(x, y, z) = \text{constant} \). You may assume the mass is \( M = 8\pi \delta \) (that means you don't need to find \( M \)).

**Answer:** \( \bar{z} = \frac{4}{3} \).
Transcribed Image Text:7. Use cylindrical coordinates to find \( \bar{z} \) for the solid bounded above by the paraboloid \( z = x^2 + y^2 \), bounded below by the \( xy \)-plane, and is inside the cylinder \( x^2 + y^2 = 4 \). Take the density to be \( \delta(x, y, z) = \text{constant} \). You may assume the mass is \( M = 8\pi \delta \) (that means you don't need to find \( M \)). **Answer:** \( \bar{z} = \frac{4}{3} \).
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