Question

If A varies inversely as the square of B, what is the effect on B if A is multiplied by 3? Please explain.

Answer 1

If A is multiplied by 3, B will be reduced by a factor
`(1)/(√(3))`

Explanation:

Writing the inverse proportionality relationship and expressing the dependence of B on A leads to the following:

`A = (1)/(B^2)\implies |B| = (1)/(√(A))\\B'=(1)/(√(3A))= (1)/(√(3))(1)/(√(A))=(1)/(√(3))|B|`

In words, if A triples, B will decrease by a factor
`(1)/(√(3))`, or, in other words, the square of B will decrease to one third of its previous value.