\

(a) Express the total area $\"\"$ enclosed by the pieces of wire as a function of the length $\"\"$ of a side of the square.

\

One piece will be shaped as a square, and the other piece will be shaped as a circle.

\

Total area $\"\"$ = Area of the square + Area of the circle.

\

Formula for the area of the circle is $\"\"$ .

\

Find the radius of the circle.

\

Circumference of the circle is $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Area of the circle is $\"\"$ .

\

Formula for the area of the square is $\"\"$ .

\

Side of the square is $\"\"$ .

\

Area of the square is $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

\

(b) Find the domain of $\"\"$ .

\

The length of two pieces $\"\"$ and $\"\"$ must be greater than $\"\"$ .

\

Domain of $\"\"$ in interval notation is $\"\"$ .

\

\

(c) Graph the function $\"\"$ .

\

$\"\"$

\

Locate the minimum point on the graph.

\

$\"\"$

\

$\"\"$ is smallest when $\"\"$ .

\

\

(a) The function is $\"\"$ .

\

(b) Domain of $\"\"$ in interval notation is $\"\"$ .

\

(c) Graph of the function $\"\"$ :

\

$\"\"$

\

$\"\"$ is smallest when $\"\"$ .