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Find an equation of variation for the given situation: y varies jointly as x and the square of z and inversely as w, and y= 27/ 2 when x =2, z=3, and w=8.

Find an equation of variation for the given situation: y varies jointly as x and the-example-1
User Thakur
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Answer:


y=(6xz^2)/(w)

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 ...


k=(wy)/(xz^2)=(8\cdot(27)/(2))/(2\cdot3^2)=(4\cdot27)/(2\cdot9)=2\cdot3=6

Then the equation of variation is ...


\boxed{y=(6xz^2)/(w)}\qquad\textbf{matches B}

User Ziri
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