express the area A as a function of the width X
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 22 ft, express the area A of the window as a function of the width x of the window.
I will label 2 sides as y and base as x
π is pi
Perimeter = 2y + x + ((2πr)/2)
since there isn't really a base (x) at the top of the window I will remove x from the equation above.
I will then plug in Radius as (x/2)
p= 2y + ((2π(x/2))/2)
= 2y + (πx)/2
22 = 2y + (πx)/2
Solving for y in above equation I came up with:
y = 11 - [(πx)/4]
Now for the Area, A(x)
A(x) = xy + (πr^2)/2
Plugging in Y and Radius obtained before my answer to this problem came to:
A(x) = x[11 - ((πx)/4)] + [(π (x/2)^2)/2]
Re: express the area A as a function of the width X
All your calculations are OK.
Originally Posted by NeoSonata
Now expand the bracket and collect like terms:
... that's all!