Since r = (5/2) · t2 and R = 8 / (5x)
let's set these two equations equal to each other: (5/2) · t2 = 8 / (5x)
Now, to get rid of denominators, let's multiply both sides by 10x: (10x) · [ (5/2) · t2 = 8 / (5x) ]
---> 25x · t2 = 16
Divide both sides by 25x ---> t2 = 16 / (25 · x2 )
Finding the square root of both sides (and ignoring the negative part because it is outside the domain):
---> t = ( 4/5 ) / sqrt(x)
---> t = 4 / ( 5 · sqrt(x) )
Since the sqrt(x) is in the denominator, it is an inverse proportion.