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(a)

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Express the total area $\"\"$ enclosed by the pieces of wire as a function of the length $\"\"$ of a side of the equilateral triangle.

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One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.

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

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Length of side of a equilateral traingle is $\"\"$ .

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So the perimeter of the equilateral traingle is $\"\"$ .

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

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Find the radius of the circle.

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

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$\"\"$ .

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$\"\"$ .

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

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Formula for the area of an equilateral triangle is $\"\"$ .

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

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Area of an equilateral triangle is $\"\"$ .

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$\"\"$ .

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

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

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

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

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$\"\"$

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Locate the minimum point on the graph.

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$\"\"$

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

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

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

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

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$\"\"$

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