Question

Write an equation that describes the following relationship: y varies jointly as I and the square root of z, and whenx = 1 and z = 16, then y = 16.=y =help (formulas)

Answer 1

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

`y=kx\sqrt[]{z}`

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:

`\begin{gathered} 16=k(1)(\sqrt[]{16}) \\ 16=4k \\ (4k)/(4)=(16)/(4) \\ k=4 \end{gathered}`

Therefore, the equation that shows the relationship of y to x and z is written as

`y=4x\sqrt[]{z}`