Max area - A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet.

Question

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Answer 1

let the radius of the circle be x ft
then the base of the rectangle is 2x ft
let the height of the rectangle be y ft

2x + 2y + pi x = 16
y = (16-2x- pix)/2

Area = pi x^2/2 + 2xy
= pi x^2/2 + 2x(16-2x-pix)/2
= pi x^2/2 + 16 - 2x - pix

d(Area)/dx = pix - 2 - pi
= 0 for a max of area.

etc.

Answer 2

My anus is leaking acid.