the cube root of r varies inversely with the square of s. which two equations model this relationship?
To model the relationship between the cube root of r (let's denote it as c) and the square of s (s^2), we can use the formula for inverse variation, which states that the product of two variables is constant.
The equation for inverse variation is: c * s^2 = k, where k is the constant of variation.
In this case, we are given that the cube root of r varies inversely with the square of s. Therefore, we can rewrite the equation as follows:
c * s^2 = k
Now, to find the two equations that model this relationship, we manipulate the equation to represent r instead of c.
1. Equation 1:
Since c represents the cube root of r, we can rewrite the equation as follows:
r^(1/3) * s^2 = k
2. Equation 2:
Alternatively, we can rewrite the equation in terms of r^3 by cubing both sides:
(r^3) * s^2 = k^3
So, the two equations that model the relationship between the cube root of r and the square of s are:
1. r^(1/3) * s^2 = k
2. (r^3) * s^2 = k^3