math

p varies directly as the square of q and inversely as r when p=36, q=3 and r=4 calculate q when p=200 and r=2

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  1. p = k (q^2)(1/r)

    when p=36,q=3,r=4
    so:
    36 = k(9)(1/4)
    k = 36(4)/9 = 16

    p = 16q^2/r
    when p=200, r=2
    200 = 16q^2 /2
    q^2 = 400/16
    q = 20/4 = 5

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  2. p = kq^2/r, so pr/q^2 = k, a constant.

    So, you want to find q such that

    200*2/q^2 = 36*4/3^2
    400/q^2 = 16
    q^2 = 25
    q = 5

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  3. p=k(q^2)/r
    36=(k*3^2)/4
    36=(9*k)/4
    9*k=144
    k=16

    p=16(q^2)/r
    200=(16*q^2)/2
    16*q^2=400
    q^2=400/16
    q^2=25
    q=√25
    q=5

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