If a variable z is jointly proportional to a set of variable x^2 and y^2, the z = kx^2y^2, where k is the constant of proportionality.

First we will find k.

z = 379 when x = 7 and y = 5

379 = k*7^2*5^2

by solving we find:

k = 379/1225

click here to see the step by step solution of the equation:

for x = 6 and x = 4 we have:

z = (379/1225)*6^2*4^2

z = 218304/1225

z = 178 254/1225

z = 178.21