Homework Help: Calculus

Posted by Anonymous on Friday, October 28, 2011 at 1:16pm.

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 47 feet?

Calculus - Steve, Friday, October 28, 2011 at 4:33pm
p = W + 2L + πW/2 = 47
2L = 47 - W - πW/2
L = 23.5 - 1.28W

A = WL + π(W/2)^2/2
= W(23.5 - 1.28W) + .327W^2
= 23.5W - 1.28W^2 + .327W^2
= 23.5W - .953W^2

max area at W = 23.5/1.906 = 12.3 ft
L = 7.756

perimeter = 12.3 + 2*7.756 + 1.57*12.3 = 47.1 (close enough)

area = 12.3*7.756 + 3.14*6.15 = 114.7 ft^2
Calculus - Anonymous, Friday, October 28, 2011 at 9:36pm
it says incorrect

Answer this Question

Related Questions

Calculus - A Norman window has the shape of a semicircle atop a rectangle so ...
Calculus - A Norman window has the shape of a semicircle atop a rectangle so ...
Calculus - A Norman window has the shape of a semicircle atop a rectangle so ...
Math (: - My answer doesn't make sense. It's too big. A Norman window ...
calculus - A Norman window has the shape of a semicircle atop a rectangle so ...
Math - A Norman window has the shape of a rectangle surmounted by a semicircle...
Calculus - A Norman window has the shape of a rectangle surmounted by a ...
Optimization - A Norman window has the shape of a semicircle atop a rectangle so...
calculus - A Norman window has the shape of a rectangle surmounted by a ...
cal - A Norman window has the shape of a rectangle surmounted by a semicircle (...

For Further Reading

First Name:
School Subject:
Answer: