Posted by Z32 on Monday, June 22, 2009 at 12:59am.
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?

Calculus  drwls, Monday, June 22, 2009 at 6:17am
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.

Calculus  Anonymous, Monday, March 30, 2015 at 11:05pm
34.288

Calculus  DNM, Wednesday, November 4, 2015 at 9:54pm
what the hell, this answer above provided absolutely no help!

Calculus  Anonymous, Wednesday, June 1, 2016 at 1:16am
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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