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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 -

    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

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