Finding the function

[Madi1316]

I started but got stuck...

A Norman Window has the shape of a rectangle surmounted by a semicircle. It has a perimeter of 40 ft.
A) find the function that models the area of the window
I ended up with this function, but I'm not sure it's right.
x²(-3╥ -4)
----------- +20x
8

B) find the dimensions, to two decimal places, that admits the greatest amount of light.

 

[phoenix9124]

The perimeter would be:
2h + w + 0.5w*pi = 40 (Equation 1)

With 'h' as height, 'w' as width.
The perimeter of the semi circle is 0.5*pi*w since the perimeter of a circle is pi*diameter (and w = d in this case).

The area is the area of the rectangle + the semi circle:
A = h*w + (0.5(0.25*pi*w^2)) (Equation 2)

Using these 2 equations you can make an equation of the area only dependant of the height (or width).

If this is not the approach as intended, I'm confused by OP

 

[DrPhil]

I started but got stuck...

A Norman Window has the shape of a rectangle surmounted by a semicircle. It has a perimeter of 40 ft.
A) find the function that models the area of the window
I ended up with this function, but I'm not sure it's right.
x²(-3╥ -4)
----------- +20x
8

B) find the dimensions, to two decimal places, that admits the greatest amount of light.

I would like to see your intermediate steps - we have to see your work to know where you got stuck!
We also need to see how you defined variables - looks like "x" is the width of the window?

Can't say that I agree with your answer - please repost showing how you did it. Another reason we need to see your work is to know what procedure you use for the second part - maximizing the Area.