$\"\"$

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The height of the kite is $\"\"$ .

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The horizontal positions of kite is $\"\"$ to $\"\"$ .

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Find the distance traveled by kite.

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Length of the curve $\"\"$ on the interval $\"\"$ is $\"\"$ .

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Find $\"\"$ .

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$\"\"$

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Length of the curve is $\"\"$ .

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Substitute $\"\"$ .

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Integrate between $\"\"$ to $\"\"$ .

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$\"\"$

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Let $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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When $\"\"$ , then $\"\"$ .

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When $\"\"$ , then $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ Apply formula: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The distance traveled by the kite is $\"\"$ . $\"\"$

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The distance traveled by the kite is $\"\"$ .