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y varies directly as x and inversely as the square of z. y = 16 when x = 72 and z = 6. Find ywhen x = 2 and z= 6.y =(Simplify your answer. Type an integer or a simplified fraction.)

Respuesta :

[tex]\begin{gathered} y\text{ }\propto x\text{ } \\ y\text{ }\propto\text{ }\frac{1}{z^2} \end{gathered}[/tex][tex]\begin{gathered} y\propto x\propto\frac{1}{z^2} \\ y\text{ }\propto\frac{x}{z^2} \\ y\text{ = k }\times\text{ }\frac{x}{z^2} \end{gathered}[/tex]

Where k is a constant

when y = 16 , x = 72 , 6

[tex]\begin{gathered} 16\text{ = }\frac{k\times72}{6^2} \\ 16\text{ }\times36\text{ = 72k} \\ k\text{ = }\frac{576}{72} \\ k=\text{ 8} \end{gathered}[/tex][tex]\begin{gathered} y\text{ = }\frac{8x}{z^2} \\ \text{when x =2 , z = 6} \\ y\text{ =}\frac{8\text{ }\times2}{6^2}\text{ =}\frac{16}{36}\text{ = }\frac{4}{9} \\ \end{gathered}[/tex]

The value of y = 4/9 or 0.44

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