SOLUTION: Hey Guys, came across this problem in my maths homework and I can't seem to solve it. Can someone maybe help me out? A Norman window has the shape of a rectangle with a s

Question 1057214: Hey Guys,
came across this problem in my maths homework and I can't seem to solve it.
Can someone maybe help me out?
A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the width of the rectangle. Find the dimensions w * h of the Norman window whose perimeter is 500in. that has maximal area.
Answer in inches:
w=
h=
There is also a picture with it.
http://imgur.com/a/dr4ti
Thanks for the help!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the width of the rectangle. Find the dimensions w * h of the Norman window whose perimeter is 500in. that has maximal area.
-------
Perimeter P = w + w*pi/2 + 2h = 500
w*(pi/2 + 1) + 2h = 500
h = 250 - w*(pi/4 + 1/2)
----
Area = w*h + pi*(w/2)^2/2
Sub for h
Area = w*(250 - w*(pi/4 + 1/2)) + pi*w^2/8
Area = (pi/8)*w^2 -w^2*(pi/4 + 1/2) + 250w
Area = (-pi/8 - 1/2)*w^2 + 250w
dArea/dw = (-pi/4 - 1)w + 250 = 0
w = 250/(pi/4 + 1)
w =~ 140.025
h =~ 70.012
RELATED QUESTIONS
I am trying to help my son with his homework, and it might as well be in a foreign... (answered by colliefan)

I was doing my homework and came across a problem. Can you help me. Logarithmic... (answered by AnlytcPhil)

I've been working on a Thanksgiving break assignment, and just recently came across a... (answered by algebrahouse.com,MathTherapy)

Hey I cant seem to figure out this problem and I'm not very good at logarithms. Can you... (answered by Gogonati)

Im trying to help my son with his math basic algebra homework. We came across a question... (answered by solver91311)

Hey! I despratly need help!!!!! Math is my worst subject. I tried working out this word... (answered by stanbon)

This is driving me crazy. I finally solved my problem, but I can�t figure out why my... (answered by kensson,MathTherapy)

hey guys i need help with my algebra homework well its 9t^3+66t^2-48t and the answer (answered by stanbon)

I came across this problem in my homework and I am not sure how to approach it. We have... (answered by Cromlix)