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Math Help - Related Rates

  1. #1
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    Related Rates

    A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 2.5 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? (Round your answer to two decimal places.)

    using similar triangles:


    y/12 = 2/12-x

    y = 12 / 12-x

    y = 24 (12-x)^-1

    dy/dt = -24(12-x)^-2 (-dx/dt)

    dy/dt = 24(dx/dt) / (12-x)^2


    Given:

    dy/dt = ?
    dx/dt = -2.5
    x = 4

    Plug in:


    dy/dt = 24(-2.5) / (12-4)^2

    dy/dt = -.9375

    dy/dt = -.94

    Web assigned marked my final answer wrong.
    Why is my answer wrong?

    Thanks.
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  2. #2
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    Re: Related Rates

    Quote Originally Posted by NeoSonata View Post
    A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 2.5 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? (Round your answer to two decimal places.)

    using similar triangles:

    y/12 = 2/12-x

    y = 12 / 12-x

    y = 24 (12-x)^-1

    dy/dt = -24(12-x)^-2 (-dx/dt)

    dy/dt = 24(dx/dt) / (12-x)^2


    Given:

    dy/dt = ?
    dx/dt = -2.5
    x = 4

    Plug in:

    dy/dt = 24(-2.5) / (12-4)^2

    dy/dt = -.9375

    dy/dt = -.94

    Web assigned marked my final answer wrong.
    Why is my answer wrong?

    Thanks.
    There is a difference between "how fast is the length of his shadow on the building decreasing" and "how fast is the length of his shadow on the building changing"

    You have answered the latter, not the former ....
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