$\"\"$

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The function is $\"\"$ .

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(a).

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Graph:

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Graph of $\"\"$ where $\"\"$ .

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$\"\"$

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$\"\"$

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(b).

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The height of the arc at its center .

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The function is $\"\"$ .

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Substitue $\"\"$ in the above equation

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$\"\"$

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$\"\"$

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Observe the graph:

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The height of the arc at its center is $\"\"$ .

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$\"\"$

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(c).

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At what points the arc height is $\"\"$ .

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Substitue $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Since $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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(d).

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The function is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in the above equation

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$\"\"$

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$\"\"$

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The slope is $\"\"$ .

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$\"\"$

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(a).

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$\"\"$

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(b). $\"\"$ .

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(c). $\"\"$ .

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(d).The slope is $\"\"$ .