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