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The variable x varies directly as the square of y, and y varies directly as the cube of z. If x equals -16 when z equals 2, what is the value of x when z equals 1/2?

 Jan 11, 2019
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x = k y^2     and y = kz^3     where k = some constant

   we can combine the constants and sub z^3 in for y

x = k (z^3)^2 = k z^6        now sub in x = -16   and z = 2

-16 = k (2)^6

k = -1/4 

 

so the equation becomes   x = -1/4 z^6      NOW, sub in z = 1/2

                                           x = -1/4 (1/2)^6 = - 1/256

 Jan 11, 2019

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