z varies directly as x⎯⎯√ and inversely as y2. If z=176 when x=49 and y=8, find z if x=81 and y=6. (Round off your answer to the nearest hundredth.)

Question

I can't seem to figure these ones out! any extra help would be great

Answer 1

I'm not sure if you mean sqrt of x (typing is not clear in the question).

Assume z varies with sqrt(x), => z = c sqrt(x), same with y^2, z=k/y^2

z=176, when x=49 and y=8 => 176 = c sqrt(49), c = 176/7, 176 = k/8^2 = k/64, k = 176*64 = 11264

x = 81, z = 176/7 x sqrt (81) = 176 x 9/7 = 226.28

y=6, z = 11264/36 = 312.89