The variable a is the length of the ladder. The variable h is the height of the ladder’s top at time t, and x is the distance from the wall

Question

The variable a is the length of the ladder. The variable h is the height of the ladder’s top at time t, and x is the distance from the wall to the ladder’s bottom. Suppose that the length of the ladder is 7.0 meters and the top is sliding down the wall at a rate of 0.4 m/s. Calculate dx/dt when h = 5.4. (Round your answer to three decimal places.)

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Rylee 1 month 2021-09-10T21:44:21+00:00 1 Answer 0

Answers ( )

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    2021-09-10T21:46:03+00:00

    Answer:

      0.485 m/s

    Step-by-step explanation:

    The Pythagorean theorem tells you …

      a² = h² +x²

    Differentiating with respect to time, we find …

      0 = 2h·h’ +2x·x’

    Solving for x’, we get …

      x’ = -h'(h/x)

    To evaluate this, we need to find the value of x when h=5.4. We can do this using the original Pythagorean relation.

      7.0² = 5.4² + x²

      x = √(49-29.16) ≈ 4.454

    Then the desired rate of change is …

      x’ = -(-0.4 m/s)(5.4/4.454) ≈ 0.485 m/s

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45:7+7-4:2-5:5*4+35:2 =? ( )