We are looking at the equation where y varies jointly as x and the square root of z. The initial equation that represents this relationship is written as
[tex]y=kx\sqrt[]{z}[/tex]
where k is the proportionality constant. We need to solve for the value of k given that at x = 1 and z = 16, the value of y is equal to 16. This is done as follows:
[tex]\begin{gathered} 16=k(1)(\sqrt[]{16}) \\ 16=4k \\ \frac{4k}{4}=\frac{16}{4} \\ k=4 \end{gathered}[/tex]
Therefore, the equation that shows the relationship of y to x and z is written as
[tex]y=4x\sqrt[]{z}[/tex]
