We know that z is proportional to x^3 and y^2.
We can express this with a proportionality constant k as:
[tex]z=k\cdot x^3\cdot y^2[/tex]
We know that when x = 5 and y = 4, z = 28.
We can use this to find the value of k as:
[tex]\begin{gathered} z=kx^3y^2 \\ 28=k(5)^3(4)^2 \\ 28=k*125*16 \\ k=\frac{28}{125*16} \\ k=\frac{28}{2000} \\ k=0.014 \end{gathered}[/tex]
We can know calculate z for x = 6 and y =5:
[tex]\begin{gathered} z=0.014x^3y^2 \\ z=0.014*6^3*5^2 \\ z=0.014*216*25 \\ z=75.6 \end{gathered}[/tex]
Answer: 75.6
