Question

z is jointly proportional to x^2 and y^2. If z=379 when x=7 and y=5, find z when x=6 and y=4

Answer 1

Given:

z is jointly proportional to x² and y². This can be written as,

$z=kx^{2} y^2$

We need to determine the value of z when x = 6 and y = 4

Value of constant k:

If z = 379 when x = 7 and y = 5, then, we get;

$370=k(7)^2(5)^2$

Simplifying the terms, we get;

$370=k(49)(25)$

$370=1225k$

Dividing both sides of the equation by 1225, we get;

$0.309=k$

Thus, the value of k is 0.309

Value of z:

The value of z can be determined by substituting $k=0.309$ , $x=6$ and $y=4$ in $z=kx^{2} y^2$

Thus, we get;

$z=0.309(6)^2(4)^2$

$z=0.309(36)(16)$

$z=177.98$

Thus, the value of z is 177.98