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

Answer:

If A is multiplied by 3, B will be reduced by a factor $\frac{1}{\sqrt{3}}$

Step-by-step explanation:

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

$A = \frac{1}{B^2}\implies |B| = \frac{1}{\sqrt{A}}\\B'=\frac{1}{\sqrt{3A}}= \frac{1}{\sqrt{3}}\frac{1}{\sqrt{A}}=\frac{1}{\sqrt{3}}|B|$

In words, if A triples, B will decrease by a factor $\frac{1}{\sqrt{3}}$, or, in other words, the square of B will decrease to one third of its previous value.