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Math

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A ladder 20 ft long rests against a vertical wall. Let \theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to \theta when \theta = pi / 3

  • Math -

    x -- as defined
    y = 20cosØ

    x^2 + y^2 = 400
    x^2 + 400cos^2 Ø = 400
    2x dx/dØ - 2sinØcosØ = 0
    dx/dØ = sinØcosØ/x

    when x = π/3 , sinπ/3 =√3/2, cosπ/3 = 1/2
    x^2 + 400(3/4) = 400
    x = 10
    dx/dØ = (√3/2)(1/2)/10 = √3/40

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