Question

Yis inversely proportional to the cube of x. If Y = 6 when x = 2, then the constant of variationis 48.

Answer 1

Given that

Y is inversely proportional to the cube of x. If Y = 6 when x = 2, then the constant of variation is 48.

Explanation -

The given condition can be represented as

`\begin{gathered} Y\propto(1)/(x^3) \\ Y=k*(1)/(x^3) \\ where\text{ k = constant variation} \end{gathered}`

By substituting values we get

`\begin{gathered} 6=k*(1)/(2^3) \\ 6=k*(1)/(8) \\ k=6*8=48 \\ k=48 \end{gathered}`

So the final answer is 48.

Final answer -

Hence the final answer is 48. So, it is true.