calculus

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A ladder 14 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?

  • calculus -

    X = 14 sin theta
    dX/d(theta) = 14 cos theta
    when theta = pi/3, cos theta = 1/2
    Therefore the answer is 7 feet per radian

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