Posted by jump on Sunday, September 30, 2012 at 2:04pm.
A window consists of a rectangular part of height h surmounted by a semicircle of radius r. The perimeter of the window is held constant at 10 feet, but h and r are allowed to vary. Find an expression for the rate of change of h with respect to r.

calc  Reiny, Sunday, September 30, 2012 at 3:12pm
I radius of semicircle is r, then the length of the rectangle is 2r
let the height of the rectangle be h
so 2r + 2h + (1/2)2πr = 10
2r+2h+πr=10
2h = 10  2r  πr
2 dh/dr = 2  π
dh/dr = 1  π/2