Answer:
a,b
Step-by-step explanation:
Question 14 is (1,4)
15 rectangle
hope I helped
Answer:
![k = \frac{1}{2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
Given
![p = 12](https://tex.z-dn.net/?f=p%20%3D%2012)
![t = 2](https://tex.z-dn.net/?f=t%20%3D%202)
![s = \frac{1}{6}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B1%7D%7B6%7D)
![r = 18](https://tex.z-dn.net/?f=r%20%3D%2018)
![r\ \alpha\ p\ * \frac{1}{s * t}](https://tex.z-dn.net/?f=r%5C%20%5Calpha%5C%20p%5C%20%2A%20%5Cfrac%7B1%7D%7Bs%20%2A%20t%7D)
Required
Find the constant of variation
From the question, the variation is as follows
![r\ \alpha\ p\ * \frac{1}{s * t}](https://tex.z-dn.net/?f=r%5C%20%5Calpha%5C%20p%5C%20%2A%20%5Cfrac%7B1%7D%7Bs%20%2A%20t%7D)
![r\ \alpha\ \frac{p * 1}{s * t}](https://tex.z-dn.net/?f=r%5C%20%5Calpha%5C%20%5Cfrac%7Bp%20%2A%201%7D%7Bs%20%2A%20t%7D)
![r\ \alpha\ \frac{p}{s * t}](https://tex.z-dn.net/?f=r%5C%20%5Calpha%5C%20%5Cfrac%7Bp%7D%7Bs%20%2A%20t%7D)
Convert variation to equation
![r\ = k\frac{p}{s * t}](https://tex.z-dn.net/?f=r%5C%20%3D%20k%5Cfrac%7Bp%7D%7Bs%20%2A%20t%7D)
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](https://tex.z-dn.net/?f=r%20%2A%20s%20%2A%20t%20%3D%20k%5Cfrac%7Bp%7D%7Bs%20%2A%20t%7D%20%2A%20s%20%2A%20t)
![r * s * t = kp](https://tex.z-dn.net/?f=r%20%2A%20s%20%2A%20t%20%3D%20kp)
Divide both sides by p
![\frac{r * s * t}{p} = \frac{kp}{p}](https://tex.z-dn.net/?f=%5Cfrac%7Br%20%2A%20s%20%2A%20t%7D%7Bp%7D%20%3D%20%5Cfrac%7Bkp%7D%7Bp%7D)
![\frac{r * s * t}{p} = k](https://tex.z-dn.net/?f=%5Cfrac%7Br%20%2A%20s%20%2A%20t%7D%7Bp%7D%20%3D%20k)
![k = \frac{r * s * t}{p}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7Br%20%2A%20s%20%2A%20t%7D%7Bp%7D)
Substitute the values of p, r, s and t in the above equation
![k = \frac{18 * \frac{1}{6} * 2}{12}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B18%20%2A%20%5Cfrac%7B1%7D%7B6%7D%20%2A%202%7D%7B12%7D)
![k = \frac{6}{12}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B6%7D%7B12%7D)
Divide numerator and denominator by 6
![k = \frac{1}{2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Hence, the constant of variation is; ![k = \frac{1}{2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B1%7D%7B2%7D)