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

9514 1404 393

Answer:

  $y=\dfrac{6xz^2}{w}$

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 ...

  $k=\dfrac{wy}{xz^2}=\dfrac{8\cdot\dfrac{27}{2}}{2\cdot3^2}=\dfrac{4\cdot27}{2\cdot9}=2\cdot3=6$

Then the equation of variation is ...

  $\boxed{y=\dfrac{6xz^2}{w}}\qquad\textbf{matches B}$