For the following exercises, consider a wire 4ft long cut into two pieces. One-piece forms a circle with radius r and the other forms a square of side x. A. Choose x to maximize the sum of their areas.
B. Choose x to minimize the sum of their areas.
1) What are the given variables?
2) If x is the side length of the square, what would be the perimeter of the square?
3) You cut out the part of the wire and made the square with it. What is the length of the remaining part of the wire?
4) You make the circle with the remaining part of the wire. What is the formula for the circumference of the circle?
5) Make an equation with answers to tasks 3 and 4.
6) Which variable would you maximize or minimize to solve the problems?
7) What is the equation for the sum (S) of the area of the square and the circle?
8) What constraint do you have? Your constraint should be the equation includes both variables x and r.
9) Write S in terms of one variable by using constraint
Solve your constraint for one variable in terms of the other variable
10) Use your previous answer to write the objective as a function of one variable.
11) Find the domain of S(x) in the context of the problem
What is the domain of S(x)? Write the answer as an inequality form.