Hello, Evan.Kimia!

Your answer is "close", so you're doing most of it Right.

You probably made a very simpler error.

A Norman window has the shape of a rectangle surmounted by a semicircle.

If the perimeter of the window is 20ft, find the value of

so that the greatest possible amount of light is admitted.

For my critical number, i get 80/(pi + 4) . It shoud be: . Code:

* * *
* *
* *
* *
* - - - - * - - - - *
| r r |
| |
y| |y
| |
| |
* - - - - - - - - - *
2r

The radius of the semicircle is

Hence, the width of the rectangle is

The height of the rectangle is

The perimeter of the semicircle is: .

The perimeter of the rectangle is: .

The total perimeter is 20:

. . .[1]

The area of the semicircle is: .

The area of the rectangle is: .

The total area is: . .[2]

Substitute [1] into [2]: .

. . And we have: .

Differentiate and equate to zero: .

. . .

Substitute into [1]: .