SOLUTION: A wire 74 cm long is to be cut into two pieces. One piece will be shaped as a square, and the other will be shaped as a circle. (a )Express the total area A enclosed by the pie

Algebra ->  Surface-area -> SOLUTION: A wire 74 cm long is to be cut into two pieces. One piece will be shaped as a square, and the other will be shaped as a circle. (a )Express the total area A enclosed by the pie      Log On


   

Question 1098848: A wire 74 cm long is to be cut into two pieces. One piece will be shaped as a square, and the other will be shaped as a circle.
(a )Express the total area A enclosed by the pieces of wire as a function of x where x is the length of one side of the square A(x)=
(b) What is the domain of A? Answer in interval notation Domain:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, side length for one side of the square piece;
4x, the perimeter for the square;
74-4x, the circumference for the circle part.

Circle:
area is pi%2Ar%5E2
circumf is 2pi%2Ar=74-4x
-
r=%2874-4x%29%2F%282pi%29
r=%2827-2x%29%2Fpi


Total Area of Square plus Circle:
x%5E2%2Bpi%28%2827-2x%29%2Fpi%29%5E2

highlight%28x%5E2%2B%281%2Fpi%29%2827-2x%29%5E2%29

Looking for domain, use 27-2x%3E0, and solve this inequality for x.