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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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