Question

Suppose j varies jointly with g and v, and j=1 when g=6 and v=3.

Find the constant variation and find j when g=8 and v=11

Answer 1

The constant of variation is
`(1)/(18)`

Value of j is
`(44)/(9)`

Explanation:

Given,

j varies jointly with g and v,

That is,

j ∝ gv

⇒ j = k(gv)

Where, k is the constant of variation,

We have, j = 1 when g = 6 and v = 3

⇒ 1 = k(6 × 3) ⇒ 1 = 18k ⇒ k =
`(1)/(18)`

Thus, the equation that shows the given relation in j, g and v is,

`j=(1)/(18)(gv)`

If g = 8, v = 11,

`j=(1)/(18)* 8* 11=(88)/(18)\implies j=(44)/(9)`

Answer 2

"Joint variation" means "directly, but with two or more variables". Thus, we write as follows:

j α gv

We insert proportionality constant k, to change it to equality.

j = kgv

We solve k,

1 = k (4)(3)
k =1/12

j = gv/12
j = 8(11)/12
j = 22/3