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(2) Consider a thin plate, which occupies the region D in the xy-plane bounded by the curves = y² and x = 2y-y². Suppose that the density of the plate at the point (x, y) is p(x,y). (a) Find the mass M and the center of mass (7,5) of the plate if its density at the point (x, y) is p(x, y) = y + 1. Find the average density Paverage of the plate. Here Paverage (b) A thin plate of now constant density p(x, y) = c occupies the c so that it has the same mass M as the plate in part (a). Compare the value Paverage found in part (a) with c. = p(x, y)dxdy. Area (D) same region D. Find

(2) Consider a thin plate, which occupies the region D in the xy-plane bounded by the curves = y² and x = 2y-y². Suppose that the density of the plate at the point (x, y) is p(x,y). (a) Find the mass M and the center of mass (7,5) of the plate if its density at the point (x, y) is p(x, y) = y + 1. Find the average density Paverage of the plate. Here Paverage (b) A thin plate of now constant density p(x, y) = c occupies the c so that it has the same mass M as the plate in part (a). Compare the value Paverage found in part (a) with c. = p(x, y)dxdy. Area (D) same region D. Find

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) Consider a thin plate, which occupies the region D in the xy-plane bounded by the curves z = y² and x = 2y - y². Suppose that the density of the plate at the point (x, y) is p(x,y). (a) Find the mass M and the center of mass (7,5) of the plate if its density at the point (x, y) is p(x, y) = y + 1. Find the average density Paverage of the plate. Here Paverage (b) A thin plate of now constant density p(x, y) = c occupies the c so that it has the same mass M as the plate in part (a). Compare the value Paverage found in part (a) with c. = 1 Area (D) same region D. Find p(x, y)dady.
Transcribed Image Text:(2) Consider a thin plate, which occupies the region D in the xy-plane bounded by the curves z = y² and x = 2y - y². Suppose that the density of the plate at the point (x, y) is p(x,y). (a) Find the mass M and the center of mass (7,5) of the plate if its density at the point (x, y) is p(x, y) = y + 1. Find the average density Paverage of the plate. Here Paverage (b) A thin plate of now constant density p(x, y) = c occupies the c so that it has the same mass M as the plate in part (a). Compare the value Paverage found in part (a) with c. = 1 Area (D) same region D. Find p(x, y)dady.
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