Calculus

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 22 feet?

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  1. Write equations for:
    (1) area of the window in terms of the semicircle diameter (x) and height (y) of the rectangle.

    (2) Perimeter = constant = 22 ft

    A = (pi/2)*x^2 + x*y= (pi +1)x + 2y
    P = (pi+1)x + 2y = 22

    Eliminate the variable y by making the substitution
    y = 11 - [(pi+1)/2]x into the first equation for (A), making it an equation in one variable, x.
    Solve dA/dx = 0 for the optimum x.

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  2. 34.288

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  3. what the hell, this answer above provided absolutely no help!

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  4. A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possibe Norman window with a perimeter of 21 feet?

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