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

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.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2