Question

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

Answer 1

If `a` varies inversely as the cube of `b`
then
`color(white)("XXXX")` `a*b^3 = c` for some constant `c`

Given `(a,b) = (27, 1/3)` is a solution for this equation
`color(white)("XXXX")` `27*(1/3)^3 = c`

`rArr` `color(white)("XXXX")` `c=1`

The equation is:
`color(white)("XXXX")`a*b^3 = 1#