Question

When p = 12, t = 2, and s = One-sixth, r = 18. If r varies directly with p and inversely with the product of s and t, what is the constant of variation?

Answer 1

Answer:

$k = \frac{1}{2}$

Step-by-step explanation:

Given

$p = 12$

$t = 2$

$s = \frac{1}{6}$

$r = 18$

$r\ \alpha\ p\ * \frac{1}{s * t}$

Required

Find the constant of variation

From the question, the variation is as follows

$r\ \alpha\ p\ * \frac{1}{s * t}$

$r\ \alpha\ \frac{p * 1}{s * t}$

$r\ \alpha\ \frac{p}{s * t}$

Convert variation to equation

$r\ = k\frac{p}{s * t}$

Where k represents the constant of variation

Make k the subject of formula;

Multiply both sides by s * t

$r * s * t = k\frac{p}{s * t} * s * t$

$r * s * t = kp$

Divide both sides by p

$\frac{r * s * t}{p} = \frac{kp}{p}$

$\frac{r * s * t}{p} = k$

$k = \frac{r * s * t}{p}$

Substitute the values of p, r, s and t in the above equation

$k = \frac{18 * \frac{1}{6} * 2}{12}$

$k = \frac{6}{12}$

Divide numerator and denominator by 6

$k = \frac{1}{2}$

Hence, the constant of variation is; $k = \frac{1}{2}$