Question

If y varies inversely as x2 and y = 3 when x = 2, find the equation that connects x and y.

Answer 1

Answer:  y = 12/(x^2)

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Explanation:

"y varies inversely as x^2" means y = k/(x^2) for some constant k.

Plug in (x,y) = (2,3) and solve for k

y = k/(x^2)

3 = k/(2^2)

3 = k/4

3*4 = k

12 = k

k = 12

The original equation updates to y = 12/(x^2)

As a check, plugging in x = 2 should lead to y = 3

y = 12/(x^2)

y = 12/(2^2)

y = 12/4

y = 3 ... we get the proper y value, so the answer is confirmed.