Question

Suppose that y is inversely proportional to x. Find the constant of proportionality k if y = 18 when x = 9. k= Using the k from above write the variation equation in terms of x. y = Using the k from above find y given that x = 40. y = If needed, round answer to 3 decimal places. Enter DNE for Does Not Exist, oo for Infinity

Answer 1

Given that y is inversely proportional to x, then they satisfy the following equation:

`y=(k)/(x)`

where k is the constant of proportionality.

Substituting with y = 18 and x = 9, we get:

`\begin{gathered} 18=(k)/(9) \\ 18\cdot9=k \\ 162=k \end{gathered}`

Therefore, the variation equation in terms of x is:

`y=(162)/(x)`

Substituting with x = 40, the value of y is:

`\begin{gathered} y=(162)/(40) \\ y=4.05 \end{gathered}`