Question

when e = 4, f = 2, and g = 8. if e varies jointly with f and g, what is the constant of variation? mc003-1.jpg mc003-2.jpg 4 64

Answer 1

e varies jointly with f and g.

e α fg

e = cfg where c = constant of proportionality

e = cfg

c = e/fg

c = 4/(2*8)

c = 4/16 = 1/4 = 0.25

Constant of variation = 0.25

Answer 2

Joint variation says that:

If x varies jointly with y and z i.e,

`x \propto yz` then the equation is in the form of

`x = k (yz)`, where, k is the constant of variation.

As per the statement:

if e varies jointly with f and g

then by definition we have;

`e = k \cdot fg` ......[1]

To solve for k:

When e = 4, f = 2 and g = 8

Substitute these in [1] we have;

`4 = k \cdot 2 \cdot 8`

⇒
`4 = 16k`

Divide both sides by 16 we have;

`(1)/(4) = k`

or

`k = (1)/(4)`=0.25

Therefore, the constant of variation is,
`(1)/(4)` or 0.25.