Question

Question 2 of 15, Step 1 of 11/15Correctz varles directly as V and inversely as y'. if2 = 224 when x = 9 and y = 6, find zifx = 64 and y = 9. (Round off your answer to the nearest hundredth)

Answer 1

Given that "z" varies directly as:

`√(x)`

And it varies inversely as:

`y^3`

You can identify that it is a Combined Variation.

Therefore, it has this form:

`z=k((√(x))/(y^3))`

Where "k" is the Constant of variation.

Knowing that:

`z=224`

When:

`\begin{gathered} x=9 \\ y=6 \end{gathered}`

You can substitute values into the equation and solve for "k":

`224=k((√(9))/(6^3))`
`\begin{gathered} (224)((6^3)/(√(9)))=k \\ \\ k=16128 \end{gathered}`

Then, the equation that models this situation is:

`z=16128((√(x))/(y^3))`

Now you can substitute these values and evaluate:

`\begin{gathered} x=64 \\ y=9 \end{gathered}`

In order to find the corresponding value of "z":

`z=16128((√(64))/(9^3))\approx176.99`

Hence, the answer is:

`z\approx176.99`