- #1
chaosblack
- 16
- 0
Hello, new here, first post. Just need some help with homework.
Question One
This norman window is made up of a semicircle and a rectangle. The total perimeter of the window is 16 cm. What is the maximum area?
**
* * <<< Semicircle
*****
| | <<< Rectangle
L | |
______
D
P (total) = 2L + D + (pi * d)
A (total) = D * L + (pi(d/2)^2)/2)
What I did was using this equation:
16 = 2L + D + ((pi * d)/2)
L = 8 - d/2 - ((pi * d)/4)
A = D (8 - d/2 - ((pi * d)/4)) + (pi (d/2)^2)/2)
A = 8d - (d^2)/2
A' = 8 - d
Let 0 = A' to find critical value
then 8 = d.
When I sub that back into the original equation, I get L as a value less than 8, which doesn't make sense. (I think it works out to be L = 4 - pi)
I'm pretty much lost, sorry if this is too messy to read, any help would be appreciated. Thanks
Question One
Homework Statement
This norman window is made up of a semicircle and a rectangle. The total perimeter of the window is 16 cm. What is the maximum area?
**
* * <<< Semicircle
*****
| | <<< Rectangle
L | |
______
D
Homework Equations
P (total) = 2L + D + (pi * d)
A (total) = D * L + (pi(d/2)^2)/2)
The Attempt at a Solution
What I did was using this equation:
16 = 2L + D + ((pi * d)/2)
L = 8 - d/2 - ((pi * d)/4)
A = D (8 - d/2 - ((pi * d)/4)) + (pi (d/2)^2)/2)
A = 8d - (d^2)/2
A' = 8 - d
Let 0 = A' to find critical value
then 8 = d.
When I sub that back into the original equation, I get L as a value less than 8, which doesn't make sense. (I think it works out to be L = 4 - pi)
I'm pretty much lost, sorry if this is too messy to read, any help would be appreciated. Thanks