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.
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