Question

z varies directly as x? and inversely as y? If z = 106 when x = 4 and y = 4, find z if x = 9 and y = 8. (Round off your answer to the nearest hundredth.

Answer 1

Step 1

Write the joint relationship between z,x and y

`z\text{ }\alpha\text{ }(x^2)/(y^2)`

If we add the constant of proportionality k, we will have;

`z\text{ = }(kx^2)/(y^2)`

Step 2

Find the exact relationship between z,x and y by finding the value of k

`\begin{gathered} z=106 \\ x=4 \\ y=4 \\ 106=(4^2(k))/(4^2) \\ k=(106(4^2))/(4^2) \\ k=106 \end{gathered}`

Hence the relationship is;

`z=(106x^2)/(y^2)`

Step 3

Find z, if x=9 and y=8

`z=(106(9)^2)/(8^2)`
`\begin{gathered} z=(8586)/(64)=134.15625 \\ z\approx134.16\text{ to the nearest hundredths} \end{gathered}`

Answer; z = 134.16