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Calculus

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A 5m long ladder rests on a vertical wall. if the bottom of the ladder slides away from the wall at 1m/s, how fast is the angle between the lader and the ground changing when the bottom of the ladder is 3m from the wall?

  • Calculus - ,

    Let X be the distance of the bottom from the wall. Let A be the angle

    X = 5 cos A
    dX/dt = (dX/dA)*(dA/dt)
    = -5 sin A* dA/dt
    dA/dt = (1 m/s)(-1/5)(1/sinA)
    In this case, sin A = 4/5 when X =3 m.

    dA/dt will be in radians per second.

  • Calculus - ,

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  • Calculus - ,

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