Question

If p is inversely proportional to the square of q, and p is 9 when q is 5, determine p

when q is equal to 3.

Answer 1

p = 125

Explanation:

Given p is inversely proportional to q³ then the equation relating them is

p =
`(k)/(q^3)` ← k is the constant of proportion

To find k use the condition p = 9 when q is 5, then

9 =
`(k)/(5^3)` =
`(k)/(125)` ( multiply both sides by 125 )

k = 1125

p =
`(1125)/(q^3)` ← equation of proportion

When q = 3, then

p =
`(1125)/(3^3)` =
`(1125)/(9)` = 125