$\"\"$

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The length of the rope is $\"\"$ .

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Observe the figure $\"\"$ .

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The rate of change in rope is $\"\"$ .

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(a).

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$\"\"$

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

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$\"\"$

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From the power rule of derivative: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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(b).

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The boat is moving at constant rate $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore the boat gets closer to the dock,hence the speed increases.

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$\"\"$

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(a). $\"\"$ .

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(b). $\"\"$ .

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Therefore the boat gets closer to the dock,hence the speed increases.