Question

What is the value of r?

Answer 1

The value of r is 6.

We can start by cubing both sides of the equation.

This gives us:

`(9r)/(2)` =
`\left((1)/(2)r\right)^3`

Simplifying the right-hand side, we get:

`(9r)/(2)` =
`(1)/(8)r^3`

Multiplying both sides by 8, we get:

36r =
`r^3`

Subtracting 36r from both sides, we get:

`r^3` - 36r=0

Factoring the left-hand side, we get:

(r)(r-6)(r+6)=0

Setting each factor equal to zero, we get the following solutions:

r=0

r=6

r=-6

However, the question specifies that r > 0, so the only valid solution is

r = 6.

Therefore, the value of r is 6.