$\"\"$

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A lighthouse is located on a small island $\"\"$ km away from the nearest point $\"\"$ .

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Light makes four revolutions per minute.

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$\"\"$

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Assume A is light house .

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Consider $\"\"$ is the angle between light house and shore line.

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$\"\"$ revolution gives $\"\"$ radians.

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$\"\"$ revolutions gives $\"\"$ radians.

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$\"\"$ rad/min.

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$\"\"$

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From the triangle $\"\"$ ,

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$\"\"$

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

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$\"\"$ .

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Find the rate at which beam of light moving when it is $\"\"$ km from $\"\"$ .

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Therefore, $\"\"$ .

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if $\"\"$ , then $\"\"$ .

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$\"\"$

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Substitute values of $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Therefore, rate at which beam of light moving when it is $\"\"$ km from $\"\"$ is $\"\"$ .

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$\"\"$

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Rate at which beam of light moving along the shoreline when it is $\"\"$ km from $\"\"$ is $\"\"$ .