Find the dimensions of a Norman window of perimeter 20 ft

label Calculus
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

Jul 17th, 2015

Thank you for the opportunity to help you with your question!

The Perimeter is distance all round the shape and it is 20ft

The shape is in fom of a tectangle attached to a semi circle which means the perimeter can be given by

p=2y+2x +x *pi

remember the length of a curve is given by a half ( since its a semicircle)  times 2 times pi times the  radius and our radius is x

Let Pi be 3.14

20=2y+2x  + ( 3.14x)

20=2y + 5.14x

hight y= 20/2 - 5.14x/2

y=10 - 2.57x

Area= semicircle + rectangle

A= 1/2 pi * radius ^2 + y *2x

A=0.5 * 3.14 * x^2 + 2xy

Replace the y with 10-2.57x

A= 0.5 *3.14 * x^2 + 2x (10-2.57x)





I will finish the rest in 5 minutes
Jul 17th, 2015

I am working on the last part and will submit it shortly

Jul 17th, 2015

can you please provide a clear y= and x=

Jul 17th, 2015

Let Pi be 3.14

perimeter of semicircle= 1/2 pi * Diameter

=1/2  * 3.14 * 2x

20=2y+2x  + ( 3.14x)

20=2y + 5.14x

hight y= 20/2 - 5.14x/2

y=10 - 2.57x

Area= semicircle + rectangle

A= 1/2 pi * radius ^2 + y *2x

A=0.5 * 3.14 * x^2 + 2xy



A=2xy +1.57x^2

Replace the y with 10-2.57x

2.801122
A=20x -5.14x^2 + 3.14x^2

Group like terms together

A=20x - 3.57x^2


Find the max area by finding the axis of symmetry; x = -b/(2a)

x=-20/ 2(-3.57)

x= 2.80112 ft

y= 10 - 2.57x

y=10-(2.57 *2.80112)

y= 2.801122 ft

Area= 20x -5.14x^2 + 3.14x^2

A=20(2.80112) -5.14 (2.80112)^2 +3.14 (2.80112)^2

A= 56.0224 - 14.39776 + 7.846273


A= 49.47091 Square ft


Jul 17th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Jul 17th, 2015
...
Jul 17th, 2015
Jun 27th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer