Need help on math problems involving variations!

Question

1.) m varies directly as a and b; m=10 when a=4 and b=7. Find m when a=11 and b=8.

2.) q varies jointly as x and y. Find q when x=2 and y=5, given that q=90 when x=3 and y=5.

3.) F varies jointly as x and y. If F=1 when x=1/2 and y=1/3, find F when x=2 and y=3.

4.) v varies directly as the square of x and inversely as the cube of y. Find v when x=3 and y=2, given that v=2 when x=4 and y=3.

5.) Let x be proportional to p and q^2, and inversely proportional to r^3. If x=9 when p=4, q=9, and r=3, find x if p=6, q=2, and r=5.

Thanks in advance!

Answer 1

4) v=kx^2/y^3

2= k(4^2)/(3^3)

2 =k16/27

k = 2(27/16) = 27/8

v = (27/8)(3^2)/(2^3 = (27/8)(9/8) = 243/64

v = 243/64 when x=3 and y=2