Given that T varies inversely as the square of x and T = 16 when x = 2 find T when x = 8.

Answer 1

"t varies inversely as the square of x" means t = k/x²

If t = 16 and x = 2 then:

16 = k/2²

16 = k/4

4•16 = k

k = 64

That means t = 64/x²

When x = 8, we can calculate t:

t = 64/8²

t = 64/64

t = 1

Answer 2

Tx² = k

16(2)² = k

64 = k

T(8)² = 64

T = 1