SOLUTION: A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 30 ft is to be constructed. Find a function t

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Question 1196270: A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 30 ft is to be constructed.
Find a function that models the area of the window.
A(x) =
Find the dimensions of the window that admits the greatest amount of light. (Round your answers to one decimal place.)
x = ft
height = ft
Found 3 solutions by math_tutor2020, josgarithmetic, ikleyn:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

The diagram is needed.

Take a screenshot of the figure, then upload it to your image hosting website of choice. Please share the link once the image is uploaded.

I tend to use imgur for image hosting, but you could use any similar service.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
........,
If the semicircle part is connected along one
of the x values, and h is the height, then A%28x%29=%281%2F2%29%28pi%29%28x%2F2%29%5E2%2Bhx, and 2%28pi%29%28x%2F2%29%2Bx%2B2h=30.

Your goal is to find the maximum A(x).

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

For a Norman form window,  see the solution in my lesson
    - Finding the maximum area of the window of a special form
in this site.

It was done for other input numbers/dimensions, but you can easily adopt/modify it for your data.

This solution is a TEMPLATE for you.