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college math

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A quantity, W, is directly proportional to x and the square of y and inversely proportional to the cube of z. W-3 when x=4,y=2 and z=4. What is the value of w, when x=5, y=5 and z=4. Give answer to three decimal places. Thanks so much!

  • college math -

    W = k x√y/z^3

    so W=3, x=4,y=2, z=4
    3 = k(4√2/64
    k = 192/(4√2) = 48/√2

    so if x = 5,y=5,z=4
    W = (48/√2)(5)(√5)/64
    = 15√5/(3√2) or after rationalizing the denominator
    = 15√10/8 = appr 5.929

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