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Length of the rope is $\"\"$ ft.

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Observe the figure $\"\"$ .

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$\"\"$

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Consider $\"\"$ and $\"\"$ .

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Assume $\"\"$ and $\"\"$ .

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Cart A is being pulled away from $\"\"$ at a speed of $\"\"$ ft/s.

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$\"\"$ ft/s.

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From the figure , $\"\"$ .

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$\"\"$ .

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Apply Pythagorean theorem to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Apply Pythagorean theorem to $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ in $\"\"$ .

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$\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Cart A is $\"\"$ ft from point $\"\"$ .

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That is $\"\"$ .

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

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$\"\"$

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

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$\"\"$

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Here, the negative sign indicates distance is decreasing.

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Cart B moving towards $\"\"$ at $\"\"$ ft/s.

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Cart B moving towards $\"\"$ at $\"\"$ ft/s.