Question

Write an equation describing the relationship of the given variables Y varies inversely as the square of x and when x=3, y=4

Answer 1

`y=(36)/(x^2)`

Step-by-step explanation

We want to find the equation that describes the relationship of the given variables.

y varies inversely as the square of x. This implies that:

`\begin{gathered} y\propto(1)/(x^2) \\ \Rightarrow y=(k)/(x^2) \end{gathered}`

where k = constant of proportionality

When x = 3, y = 4. Substitute that into the equation above and solve for k:

`\begin{gathered} 4=(k)/(3^2) \\ 4=(k)/(9) \\ \Rightarrow k=4\cdot9 \\ k=36 \end{gathered}`

Hence, the equation that represents the relationship of the variables is:

`y=(36)/(x^2)`

That is the answer.