Answer:
The following two equations model this relationship.
- [tex]\:\sqrt[3]{r}=\:\frac{k}{s^2}[/tex]
- [tex]\:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}[/tex]
Step-by-step explanation:
We know that when 'y' varies inversely with 'x', we get the equation
y ∝ 1/x
y = k / x
k = yx
where 'k' is called the 'constant of proportionality'.
In our case, it is given that the cube root of 'r' varies inversely with the square of 's', then
[tex]\sqrt[3]{r}[/tex] ∝ [tex]\frac{1}{s^2}[/tex]
[tex]\:\sqrt[3]{r}=\:\frac{k}{s^2}[/tex]
or
[tex]\:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}[/tex] ∵ [tex]\sqrt[3]{r}=r^{\frac{1}{3}}[/tex]
Therefore, the following two equations model this relationship.
- [tex]\:\sqrt[3]{r}=\:\frac{k}{s^2}[/tex]
- [tex]\:\:s^2\:r^{\frac{1}{3}}=\:\frac{k}{s^2}[/tex]
