$\"\"$

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(a).

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The wide of the rain gutter is $\"\"$ .

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Consider length of the gutter is $\"\"$

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Hence base of rain gutter is $\"\"$ .

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The area of gutter $\"\"$ is $\"\"$ .

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$\"\"$

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The general form of equation is $\"\"$ .

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Therefore $\"\"$ and $\"\"$ .

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The maximum area will occur at $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the equation $\"\"$ .

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$\"\"$

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$\"\"$

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The maximum cross sectional area will occur at $\"\"$ .

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$\"\"$

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(b).

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Find the length of the gutter when area is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ and $\"\"$

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$\"\"$ and $\"\"$

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The depth is in between $\"\"$ and $\"\"$ .

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$\"\"$

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(a).The maximum cross sectional area will occur at $\"\"$ .

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(b).The depth is in between $\"\"$ and $\"\"$ .