Answer:
![y = 2x^4](https://tex.z-dn.net/?f=y%20%3D%202x%5E4)
Step-by-step explanation:
The given statement can be represented as:
![y\ \alpha\ x^4](https://tex.z-dn.net/?f=y%5C%20%5Calpha%5C%20x%5E4)
![x =3; y = 162](https://tex.z-dn.net/?f=x%20%3D3%3B%20y%20%3D%20162)
Given
Represent this as an equation
![y\ \alpha\ x^4](https://tex.z-dn.net/?f=y%5C%20%5Calpha%5C%20x%5E4)
Convert variation to equation
![y = kx^4](https://tex.z-dn.net/?f=y%20%3D%20kx%5E4)
Where k is a constant of variation.
Substitute ![x =3; y = 162](https://tex.z-dn.net/?f=x%20%3D3%3B%20y%20%3D%20162)
![162 = k * 3^4](https://tex.z-dn.net/?f=162%20%3D%20k%20%2A%203%5E4)
![162 = k * 81](https://tex.z-dn.net/?f=162%20%3D%20k%20%2A%2081)
Solve for k
![k = 162/81](https://tex.z-dn.net/?f=k%20%3D%20162%2F81)
![k =2](https://tex.z-dn.net/?f=k%20%3D2)
To get the equation, we have:
![y = kx^4](https://tex.z-dn.net/?f=y%20%3D%20kx%5E4)
Substitute 2 for k
![y = 2x^4](https://tex.z-dn.net/?f=y%20%3D%202x%5E4)
You forgot to put a picture
Given:
![a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}](https://tex.z-dn.net/?f=a%3D1.6%2Cb%3D%5Cdfrac%7B1%7D%7B-2%7D%2Cc%3D%5Cdfrac%7B-5%7D%7B-7%7D)
To verify:
for the given values.
Solution:
We have,
![a=1.6,b=\dfrac{1}{-2},c=\dfrac{-5}{-7}](https://tex.z-dn.net/?f=a%3D1.6%2Cb%3D%5Cdfrac%7B1%7D%7B-2%7D%2Cc%3D%5Cdfrac%7B-5%7D%7B-7%7D)
We need to verify
.
Taking left hand side, we get
![a(b-c)=1.6\left(\dfrac{1}{-2}-\dfrac{-5}{-7}\right)](https://tex.z-dn.net/?f=a%28b-c%29%3D1.6%5Cleft%28%5Cdfrac%7B1%7D%7B-2%7D-%5Cdfrac%7B-5%7D%7B-7%7D%5Cright%29)
![a(b-c)=1.6\left(-\dfrac{1}{2}-\dfrac{5}{7}\right)](https://tex.z-dn.net/?f=a%28b-c%29%3D1.6%5Cleft%28-%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B5%7D%7B7%7D%5Cright%29)
Taking LCM, we get
![a(b-c)=1.6\left(\dfrac{-7-10}{14}\right)](https://tex.z-dn.net/?f=a%28b-c%29%3D1.6%5Cleft%28%5Cdfrac%7B-7-10%7D%7B14%7D%5Cright%29)
![a(b-c)=\dfrac{16}{10}\left(\dfrac{-17}{14}\right)](https://tex.z-dn.net/?f=a%28b-c%29%3D%5Cdfrac%7B16%7D%7B10%7D%5Cleft%28%5Cdfrac%7B-17%7D%7B14%7D%5Cright%29)
![a(b-c)=\dfrac{8}{5}\left(\dfrac{-17}{14}\right)](https://tex.z-dn.net/?f=a%28b-c%29%3D%5Cdfrac%7B8%7D%7B5%7D%5Cleft%28%5Cdfrac%7B-17%7D%7B14%7D%5Cright%29)
![a(b-c)=-\dfrac{68}{35}\right)](https://tex.z-dn.net/?f=a%28b-c%29%3D-%5Cdfrac%7B68%7D%7B35%7D%5Cright%29)
Taking right hand side, we get
![ab-ac=1.6\times \dfrac{1}{-2}-1.6\times \dfrac{-5}{-7}](https://tex.z-dn.net/?f=ab-ac%3D1.6%5Ctimes%20%5Cdfrac%7B1%7D%7B-2%7D-1.6%5Ctimes%20%5Cdfrac%7B-5%7D%7B-7%7D)
![ab-ac=-\dfrac{16}{20}-\dfrac{8}{7}](https://tex.z-dn.net/?f=ab-ac%3D-%5Cdfrac%7B16%7D%7B20%7D-%5Cdfrac%7B8%7D%7B7%7D)
![ab-ac=-\dfrac{4}{5}-\dfrac{8}{7}](https://tex.z-dn.net/?f=ab-ac%3D-%5Cdfrac%7B4%7D%7B5%7D-%5Cdfrac%7B8%7D%7B7%7D)
Taking LCM, we get
![ab-ac=\dfrac{-28-40}{35}](https://tex.z-dn.net/?f=ab-ac%3D%5Cdfrac%7B-28-40%7D%7B35%7D)
![ab-ac=\dfrac{-68}{35}](https://tex.z-dn.net/?f=ab-ac%3D%5Cdfrac%7B-68%7D%7B35%7D)
Now,
![LHS=RHS](https://tex.z-dn.net/?f=LHS%3DRHS)
Hence proved.