Answer:
a_n=a_1+(n-1)d
Step-by-step explanation:
sorry for late anwser
Answer:
(2,2)
Step-by-step explanation:
Keep the denominators the same and subtract the numerators. So for example in your example:
7/8 - 3/8
Leave the 8 alone. Subtract 3 from 7.
7 - 3 = 4
So answer is:
4/8
Sometimes they may have to simplify the answer, and in this case, 4/8 could be simplified to 1/2
Anything times 1 is equal to itself. Anything times less than one is less than itself. Anything times greater than one is greater than itself. Therefore, 125 times .9, which is less than one, is less than 125
Answer:
a) ![\frac{74}{10025}](https://tex.z-dn.net/?f=%5Cfrac%7B74%7D%7B10025%7D)
b) ![\frac{3x-2}{x(8x+1)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x-2%7D%7Bx%288x%2B1%29%7D)
c) ![\frac{-24x^2+32x-2}{(8x^2+x)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-24x%5E2%2B32x-2%7D%7B%288x%5E2%2Bx%29%5E2%7D)
Step-by-step explanation:
For total cost function
, average cost is given by
i.e., total cost divided by number of units produced.
Marginal average cost function refers to derivative of the average cost function i.e., ![\left ( \frac{c(x)}{x} \right )'](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cfrac%7Bc%28x%29%7D%7Bx%7D%20%5Cright%20%29%27)
Given:![c(x)=\frac{3x-2}{8x+1}](https://tex.z-dn.net/?f=c%28x%29%3D%5Cfrac%7B3x-2%7D%7B8x%2B1%7D)
Average cost = ![\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%28x%29%7D%7Bx%7D%3D%5Cfrac%7B3x-2%7D%7Bx%288x%2B1%29%7D)
a)
At x = 50 units,
![\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%2850%29%7D%7B50%7D%3D%5Cfrac%7B150-2%7D%7B50%28400%2B1%29%7D%3D%5Cfrac%7B148%7D%7B50%28401%29%7D%3D%5Cfrac%7B74%7D%7B10025%7D)
b)
Average cost = ![\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%28x%29%7D%7Bx%7D%3D%5Cfrac%7B3x-2%7D%7Bx%288x%2B1%29%7D)
c)
Marginal average cost:
Differentiate average cost with respect to ![x](https://tex.z-dn.net/?f=x)
Take ![f=3x-2\,,\,g=8x^2+x](https://tex.z-dn.net/?f=f%3D3x-2%5C%2C%2C%5C%2Cg%3D8x%5E2%2Bx)
using quotient rule, ![\left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cfrac%7Bf%7D%7Bg%7D%20%5Cright%20%29%27%3D%5Cfrac%7Bf%27g-fg%27%7D%7Bg%5E2%7D)
Therefore,
![\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cfrac%7Bc%28x%29%7D%7Bx%7D%20%5Cright%20%29%27%3D%5Cleft%20%28%20%5Cfrac%7B3x-2%7D%7B8x%5E2%2Bx%7D%20%5Cright%20%29%27%5C%5C%3D%5Cleft%20%28%20%5Cfrac%7B3%288x%5E2%2Bx%29-%2816x%2B1%29%283x-2%29%7D%7B%288x%5E2%2Bx%29%5E2%7D%20%5Cright%20%29%5C%5C%3D%5Cfrac%7B24x%5E2%2B3x-48x%5E2-3x%2B32x%2B2%7D%7B%288x%5E2%2Bx%29%5E2%7D%5C%5C%3D%5Cfrac%7B-24x%5E2%2B32x-2%7D%7B%288x%5E2%2Bx%29%5E2%7D)