Question

y varies directly as x and inversely as the square of z. y = 16 when x = 32 and z = 4. Find ywhen x=3 and z= 6.y=(Simplify your answer. Type an integer or a simplified fraction.)

Answer 1

y varies directly as x and inversely as the square of z means:

`y=(kx)/(z^2)`

where k is some constant. Substituting with y = 16, x = 32, and z = 4, and solving for k:

`\begin{gathered} 16=(k\cdot32)/(4^2) \\ (16\cdot4^2)/(32)=k \\ 8=k \end{gathered}`

Substituting with k = 8, x = 3, and z = 6, and solving for y:

`\begin{gathered} y=(8\cdot3)/(6^2) \\ y=(2)/(3) \end{gathered}`