Answer:
[tex]k = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]p = 12[/tex]
[tex]t = 2[/tex]
[tex]s = \frac{1}{6}[/tex]
[tex]r = 18[/tex]
[tex]r\ \alpha\ p\ * \frac{1}{s * t}[/tex]
Required
Find the constant of variation
From the question, the variation is as follows
[tex]r\ \alpha\ p\ * \frac{1}{s * t}[/tex]
[tex]r\ \alpha\ \frac{p * 1}{s * t}[/tex]
[tex]r\ \alpha\ \frac{p}{s * t}[/tex]
Convert variation to equation
[tex]r\ = k\frac{p}{s * t}[/tex]
Where k represents the constant of variation
Make k the subject of formula;
Multiply both sides by s * t
[tex]r * s * t = k\frac{p}{s * t} * s * t[/tex]
[tex]r * s * t = kp[/tex]
Divide both sides by p
[tex]\frac{r * s * t}{p} = \frac{kp}{p}[/tex]
[tex]\frac{r * s * t}{p} = k[/tex]
[tex]k = \frac{r * s * t}{p}[/tex]
Substitute the values of p, r, s and t in the above equation
[tex]k = \frac{18 * \frac{1}{6} * 2}{12}[/tex]
[tex]k = \frac{6}{12}[/tex]
Divide numerator and denominator by 6
[tex]k = \frac{1}{2}[/tex]
Hence, the constant of variation is; [tex]k = \frac{1}{2}[/tex]
