Answer :
The variation "Z varies directly with the sum of the squares of x and y" can be written into symbols and it looks like this: (with a constant k)
[tex]Z=k(x^2+y^2)[/tex]Applying when x = 4 and y = 3, we have:
[tex]\begin{gathered} Z=k(x^2+y^2) \\ 5=k(4^2+3^2) \\ 5=k(16+9) \\ 5=25k \\ \text{Divide both sides by 25} \\ \frac{5}{25}=\frac{25k}{25} \\ \frac{1}{5}=k \end{gathered}[/tex]The value of the constant k is 1/5.
The general formula is stated above and that is z = 1/5 (x² + y² ).