Question

p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r= 2.

Answer 1

Explanation:

If a variables varies jointly, we can just divide it by the other variables in relation to it.

For example, since p variables jointly as q and square of r, then

`\frac{p}{q {r}^(2) } = k`

where k is a constant

First, let find k. Substitute p= 200

q= 2, and r=3.

`\frac{200}{2(3) {}^(2) } = k`

`(200)/(18) = k`

`(100)/(9) = k`

Now, since we know our constant, let find p.

`\frac{p}{q {r}^(2) } = (100)/(9)`

Q is 5, and r is 2.

`\frac{p}{5( {2}^(2)) } = (100)/(9)`

`(p)/(20) = (100)/(9)`

`p = (2000)/(9)`