# 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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