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If a ladder which is 10m long rests agai...

If a ladder which is 10m long rests against a vertical wall. If the base of ladder slides away from the wall at 1 m/s then how fast is the top of the ladder sliding down along the wall when the base is 6 m from the wall ?

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To solve the problem step by step, we will use the Pythagorean theorem and implicit differentiation. ### Step 1: Understand the problem and set up the diagram We have a ladder of length 10 m resting against a vertical wall. Let: - \( x \) be the distance from the base of the ladder to the wall (horizontal distance). - \( y \) be the height of the top of the ladder above the ground (vertical distance). From the problem, we know that the length of the ladder is constant: ...
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