Let S be the graph of the plane z = 3x + 4y + 2 over the rectangle [0,2)] x [1,5). Assuming that the plane has a density of p(x,y,2) = y, find the center of mass. As usual, to find the mass, integrate P(x, y,2) over S. To find &, integrate x p(x, y,2) over S, then divide the result by the mass, and similarly for y and 2.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Let S be the graph of the plane z = 3x + 4y + 2 over the rectangle [0,2] × [1,5). Assuming
that the plane has a density of p(x, y, 2) = y, find the center of mass.
As usual, to find the mass, integrate p(x, y,2) over S. To find 8, integrate x p(x, y,2) over S,
then divide the result by the mass, and similarly for y and 2.
Transcribed Image Text:1. Let S be the graph of the plane z = 3x + 4y + 2 over the rectangle [0,2] × [1,5). Assuming that the plane has a density of p(x, y, 2) = y, find the center of mass. As usual, to find the mass, integrate p(x, y,2) over S. To find 8, integrate x p(x, y,2) over S, then divide the result by the mass, and similarly for y and 2.
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