Question

If y varies jointly with the square of x and inversely as the cubed root of z and y= 84 when x=6 and z= 27, what is y when x=3 and z=64

Answer 1

Answer:
`y=15.75`

Explanation:

If y varies is jointly with
`x^(2)` and inversely as
`\sqrt[3]{z}`, then you can write the following expression, where k is the constant of proportionality:

`y=k*\frac{x^(2)}{\sqrt[3]{z}}`

If y=84, x=6 and z=27, you can find the constant of proportionality:

`k=y\frac{\sqrt[3]{z}}{x^(2)}`

`k=84\frac{\sqrt[3]{27}}{6^(2)}`

`k=7`

Then, when x=3 and z=64 y is:

`y=7(\frac{3^(2)}{\sqrt[3]{64}})`

`y=(63)/(4)`

`y=15.75`