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Answer:
[tex]y=\dfrac{6xz^2}{w}[/tex]
Step-by-step explanation:
When y varies jointly as x and z, the equation is written ...
y = k·x·z
Here, the joint variation is not with z, but with z². There is also an inverse variation with w, so the entire relation is ...
y = k·x·z²/w
We want to find the value of k for the given values of the variables. So, we can solve for k to get ...
[tex]k=\dfrac{wy}{xz^2}=\dfrac{8\cdot\dfrac{27}{2}}{2\cdot3^2}=\dfrac{4\cdot27}{2\cdot9}=2\cdot3=6[/tex]
Then the equation of variation is ...
[tex]\boxed{y=\dfrac{6xz^2}{w}}\qquad\textbf{matches B}[/tex]
