Question: A \(1 \mathrm{~m} .\) long piece of wire is cut into 2 pieces. One piece is bent into the shape of a circle while the other piece is bent into the shape of an equilateral triangle. [See diagram.]

1. Let \(A_{1}\) represent the area of the circle and let \(x\) represent the length of the piece of wire used to make the circle. Find an equation giving the area \(A_{1}\) of the circle as a function of the length \(x\). What is the domain of this function?
2. Let \(\mathrm{A}_{2}\) represent the area of the triangle. Find an equation giving the area \(\mathrm{A}_{2}\) of the triangle as a function of \(x\). What is the domain of the function \(\mathrm{A}_{2}\) ?
3. Let A represent the sum of the area of the circle and the area of the triangle. Write A as a function of \(x\). What is the domain of \(A\) ?
4. Find the value of \(x\) that gives a minimum value for \(A\). For what value of \(x\) will A have a maximum value?

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