Question

If y is directly proportional to x3 and y=9 when x=5, find y if x=4. (Round off your answer to the nearest hundredth.)

Answer 1

For this problem, we were informed that the variable "y" is directly proportional to the cube of x. We were also informed that y is equal to 9 when x is equal to 5, from this we need to determine the value of y when x is equal to 4.

Since the two variables are directly proportional, we can write them as shown below:

`y=k\cdot x^3`

Where "k" is an unknown constant number that we need to determine. Since we have a point on this function (5, 9), we can determine "k" by replacing these coordinates on the expression.

`\begin{gathered} 9=k\cdot(5)^3 \\ 9=k\cdot125 \\ k=(9)/(125) \end{gathered}`

With the value of k, we can complete the expression:

`y=(9)/(125)x^3`

Now we can replace "x" with 4 to determine the value of y.

`\begin{gathered} y=(9)/(125)\cdot(4)^3 \\ y=(9)/(125)\cdot64 \\ y=(576)/(125) \\ y=4.61 \end{gathered}`

The value of y is approximately 4.61.