MATH

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IN A PHYSICS EXPERIMENT,THE DISTANCE OF X AND Y CM HAS A CONNECTION TO EACH OTHER BY 1/X + 1/Y = 1/5.IF THE DISTANCE OF Y IS INCREASING AT THE RATE 16 CMS^(-1),FIND THE RATE OF CHANGE OF THE DISTANCE OF X WHEN Y=9 CM.

  • MATH -

    So we have
    1/x + 1/y = 1/5
    differentiate with respect to t
    (-1/x^2)dx/dt + (-1/y^2)dy/dt = 0
    (-1/x2)dx/dt = (1/y^2)dy/dt

    dx/dt = (-x^2/y^2)(dy/dt)

    given:
    when y = 9
    1/x + 1/9 = 1/5
    1/x = 4/45
    x = 45/4
    and dy/dt = ???? , not clear what you mean by
    16 CM^(-1)

    what ever it is, sub into
    dx/dt = (-(45/4)^2 /81) (????)
    = (-25/16)(????)

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