Question

A and b are positive numbers.

a is inversely proportional to b.
when a=4,b=36
find value of a when b=a

Answer 1

a = 12

Explanation:

Given that a is inversely proportional to b then the equation relating them is

a =
`(k)/(b)` ← k is the comstant of proportion

To find k use the condition when a = 4, b = 36, then

4 =
`(k)/(36)` ( multiply both sides by 36 )

144 = k

a =
`(144)/(b)` ← equation of proportion

When b = a , then

a =
`(144)/(a)` ( multiply both sides by a )

a² = 144 ( take square root of both sides )

a = ±
`√(144)` = ± 12

However a is a positive number, thus a = 12