SOLUTION: A 30-inch piece of wire is cut into two pieces, one of which measured x inches. The piece measuring x inches is bent to form a circle and the remaining piece is bent to form a squa

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Question 847480: A 30-inch piece of wire is cut into two pieces, one of which measured x inches. The piece measuring x inches is bent to form a circle and the remaining piece is bent to form a square. Express the total area of the circle and the square as a function of x. Find the domain of this function.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A 30-inch piece of wire is cut into two pieces, one of which measured x inches.
The piece measuring x inches is bent to form a circle and the remaining piece is bent to form a square.
Express the total area of the circle and the square as a function of x.
Find the domain of this function.
:
x = the circumference of the circle
find the radius
r = x%2F%282pi%29
Find the area
A = pi%2A%28x%2F%282pi%29%29%5E2
simplify
A = x%5E2%2F%284pi%29
:
Let s = the side of the square
4s = 30-x
s = %28%2830-x%29%29%2F4
Find the area of the square
A = %28%2830-x%29%2F4%29%5E2
:
Total area
A(x) = x%5E2%2F%284pi%29 + %28%2830-x%29%2F4%29%5E2
:
I think the domain would be: >0 and <30