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if z varies jointly as the square of x and y, z=24 when x=2 and y=3, find the value of z when x=4 and y=8

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Variation

If z varies jointly as the square of x and y, z=24 when x=2 and y=3, find the value of z when x=4 and y=8.

Solution:

[tex]z = k(xy) {}^{2} \\ 24 = k((2)(3)) {}^{2} \\ 24 = 36k \\2 = 3k \\ k = \frac{2}{3} \\ \\ z = k(xy) {}^{2} \\ z = ( \frac{2}{3}) ((4)(8)) {}^{2} \\ z = ( \frac{2}{3} )(1024) \\ z = \frac{2048}{3} [/tex]

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