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# The variable varies directly as the square of , and varies directly as the cube of . If equals

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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 $$\frac{1}{2}$$?

Mar 23, 2020

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x = ky^2         y = k/z^3      combined      x = k /z^6

-16 = k/ 2^3

k = -128

x = -128 / z^6

x = -128 / (1/2)^3   = -1024

Mar 24, 2020