Question

If p varies directly as the cube root of Q and P is equal to 3 and Q is equal to 125 find Q when P is equal to 18/5

Answer 1

Q = 216

Explanation:

given P varies directly as
`\sqrt[3]{Q}` , then the equation relating them is

P = k
`\sqrt[3]{Q}` ← k is the constant of variation

to find k substitute P = 3 when Q = 125 into the equation

3 = k ×
`\sqrt[3]{125}` = k × 5 = 5k ( divide both sides by 5 )

`(3)/(5)` = k

P =
`(3)/(5)`
`\sqrt[3]{Q}` ← equation of variation

when P =
`(18)/(5)` , then

`(18)/(5)` =
`(3)/(5)`
`\sqrt[3]{Q}` ( multiply both sides by 5 to clear the fraction )

18 = 3
`\sqrt[3]{Q}` ( divide both sides by 3 )

6 =
`\sqrt[3]{Q}` ( cube both sides )

6³ = (
`\sqrt[3]{Q}` )³ , then

216 = Q