Unformatted text preview: dy dt = ky ( M & y ) where y ( t ) is the population at time t , M is the maximum sustainable population, and k is a growth constant. Use separation of variables to &nd the general solution. 5. A thin plate occupies the region in the &rst quadrant of the coordinate plane and is bounded by the curves x = 0 , y = x; and y = p 2 & x 2 : (a) (10 pts) Find the x coordinate of its centroid. (b) (5 pts) Use the Theorem of Pappus to &nd the volume swept out if the plate is revolved around the line x = & 1 . 1...
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 Spring '09
 CHEUNG
 Math, Calculus, pts, Euclidean geometry, Polar coordinate system, …rst quadrant

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