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3 a) Let W be the solid in R³ satisfying 0 ≤ z ≤ y², x² + y² ≤9, y ≥ 0 with density on the region given by p(x, y, z) = y g/cm². Set up the integral that computes the total mass on the region in two ways, (1) with differentials in the order dydzdx, and (2) using cylindrical coordinates. b) Compute the center of mass of the region W.

3 a) Let W be the solid in R³ satisfying 0 ≤ z ≤ y², x² + y² ≤9, y ≥ 0 with density on the region given by p(x, y, z) = y g/cm². Set up the integral that computes the total mass on the region in two ways, (1) with differentials in the order dydzdx, and (2) using cylindrical coordinates. b) Compute the center of mass of the region W.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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a) Let W be the solid in R³ satisfying 0 ≤ z≤ y², x² + y² ≤9, y ≥ 0 with density on the region given by p(x, y, z) = y g/cm². Set up the integral that computes the total mass on the region in two ways, (1) with differentials in the order dydzdx, and (2) using cylindrical coordinates. b) Compute the center of mass of the region W.
Transcribed Image Text:a) Let W be the solid in R³ satisfying 0 ≤ z≤ y², x² + y² ≤9, y ≥ 0 with density on the region given by p(x, y, z) = y g/cm². Set up the integral that computes the total mass on the region in two ways, (1) with differentials in the order dydzdx, and (2) using cylindrical coordinates. b) Compute the center of mass of the region W.
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