# How do you write the equation if A varies inversely as the cube of b and b is 1/3 when a is 27?

Jun 7, 2015

If $a$ varies inversely as the cube of $b$
then
$\textcolor{w h i t e}{\text{XXXX}}$$a \cdot {b}^{3} = c$ for some constant $c$

Given $\left(a , b\right) = \left(27 , \frac{1}{3}\right)$ is a solution for this equation
$\textcolor{w h i t e}{\text{XXXX}}$$27 \cdot {\left(\frac{1}{3}\right)}^{3} = c$

$\Rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$c = 1$

The equation is:
$\textcolor{w h i t e}{\text{XXXX}}$a*b^3 = 1#