Question

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.

Answer 1

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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}`