yy varies directly as the square root of xx and inversely as

yy varies directly as the square root of xx and inversely as the cube of zz. If y=y= 6 when x=x= 65 and z=z= 4, find yy when x=x= 169 and z=z= 5. Round the answer to the nearest hundredth.

Solution

y varies directly as the square root of x and inversely as the cube of z:

y = k[sqrt(x)/z^3] where k is a constant

Now y1/y2 = sqrt(x1/x2)(z2^3/z1^3)

6/y2 = sqrt(65/169)(5/4)^3

= sqrt(5/13)(5/4)^3

=1.21

6/y2 = 1.21

y2 =4.96