$\"\"$

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

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Bottom of the ladder slides away at a rate of $\"\"$ ft/s.

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$\"\"$ is the distance between the bottom of the ladder and wall.

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$\"\"$ .

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$\"\"$ is the shortest distance from the top of the ladder to ground.

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$\"\"$

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From Pythagoras theorem,

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$\"\"$

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$\"\"$

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From the figure, $\"\"$ .

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$\"\"$

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

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$\"\"$

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Substitute $\"\"$ in above expression.

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$\"\"$

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From the figure $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Find the rate at which angle between the ladder and the ground is changing when bottom of the ladder is $\"\"$ ft from the wall.

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Thus, $\"\"$ .

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Find $\"\"$ value when $\"\"$ .

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$\"\"$

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

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$\"\"$

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Rate at which angle between the ladder and the ground is decreasing is $\"\"$ rad/s.

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$\"\"$

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Rate at which angle between the ladder and the ground is decreasing is $\"\"$ rad/s.