Step 1
Write the joint relationship between z,x and y
[tex]z\text{ }\alpha\text{ }\frac{x^2}{y^2}[/tex]
If we add the constant of proportionality k, we will have;
[tex]z\text{ = }\frac{kx^2}{y^2}[/tex]
Step 2
Find the exact relationship between z,x and y by finding the value of k
[tex]\begin{gathered} z=106 \\ x=4 \\ y=4 \\ 106=\frac{4^2(k)}{4^2} \\ k=\frac{106(4^2)}{4^2} \\ k=106 \end{gathered}[/tex]
Hence the relationship is;
[tex]z=\frac{106x^2}{y^2}[/tex]
Step 3
Find z, if x=9 and y=8
[tex]z=\frac{106(9)^2}{8^2}[/tex][tex]\begin{gathered} z=\frac{8586}{64}=134.15625 \\ z\approx134.16\text{ to the nearest hundredths} \end{gathered}[/tex]
Answer; z = 134.16
