Question

The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9?

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Answer 1

`\huge \purple{ \boxed{ y = (2)/(3) }}`

Explanation:

Since, the variables x and y are inversely proportional.

`\therefore \: y \: \: \alpha \: \: (1)/(x) \\ \implies \: y = (k)/(x) \\ (k = constant) \\ \implies \: xy = k ...(1)\\ plug \: y = 2, \: \: x = 3 \: in \: equation \: (1) \\ we \: find \\ 2 * 3 = k \\ k = 6 \\ plug \:k = 6 \: in \: equation \: (1) \\ xy = 6 \\ (this \: is \: the \: equation \: of \: variation) \\ when \: x = 9 \: \: y =? \\ \\ 9y = 6 \\ y = (6)/(9) \\ \huge \red{ \boxed{ y = (2)/(3) }}`