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Question

A ladder $$10  \ metres$$ long rests with one end against a vertical wall, the other on the floor. The lower end moves away from the wall at the rate of $$2  \  metres/minute$$. The rate at which the upper end falls when its base is $$6  \ metres$$ away from the wall


A
3 metres/min
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B
2/3 metres/min
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C
3/2 metres/min
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D
none of these
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Solution

The correct option is C $$3/2  \ metres/min$$
Given $$\displaystyle\dfrac{dx}{dt}=2 m/min$$
We have, $$x^{2}+y^{2}=100$$
Also, when $$x=6 m \Rightarrow y=8m$$
$$\displaystyle 2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}=0$$
$$\Rightarrow\displaystyle \dfrac{dy}{dt}=-\dfrac{3}{2} m/minute$$

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Mathematics

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