1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vlada-n [284]
3 years ago
9

The total cost (in hundreds of dollars) to produce x units of a product is c(x) = (3x-2) / (8x+1), find the average cost for eac

h of the following production.a) 50 unitsb) x unitsc) find the marginal average cost function.
Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
3 0

Answer:

a) \frac{74}{10025}

b) \frac{3x-2}{x(8x+1)}

c) \frac{-24x^2+32x-2}{(8x^2+x)^2}

Step-by-step explanation:

For total cost function c(x), average cost is given by \frac{c(x)}{x} 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 )'

Given:c(x)=\frac{3x-2}{8x+1}

Average cost = \frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}

a)

At x = 50 units,

\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}

b)

Average cost = \frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}

c)

Marginal average cost:

Differentiate average cost with respect to x

Take f=3x-2\,,\,g=8x^2+x

using quotient rule, \left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}

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}

You might be interested in
Multiply or divide as indicated 10x^5/2x^2
shepuryov [24]
To perform the following operation, make sure to do the division parts separately and place them back together in the final answer.

10/2 and x^5/x^2

5 and using the exponential laws of division X ^m/X^n = X ^ m-n

The second part evaluates to X^3.

Putting the terms together we get the final answer, which is 5x^3.
3 0
3 years ago
to rent a moving truck for the day it cost $33 +1 dollar for each mile driven write an expression that represents the cost in do
yKpoI14uk [10]

Answer:

33 + 1M

Step-by-step explanation:

5 0
3 years ago
Which fractions are equivalent to 9 6​
Archy [21]

Answer:

2/3

Step-by-step explanation:

3 0
3 years ago
A kitten’s mass at birth was 0.09 kilogram. The kitten gained approximately 0.084 kilogram each week. After how many weeks is th
Naddika [18.5K]
A kitten’s mass at birth was 0.09 kilogram. The kitten gained approximately 0.084 kilogram each week. After how many weeks is the kitten’s mass 1.098 kilograms?
5 0
2 years ago
What is the solution to 4m-4+4m
Sholpan [36]

Answer:

- 4 + 8m

Step-by-step explanation:

4m - 4 + 4m = ?

4m + 4m = 8m

- 4 + 8m is the answer because you can not simplify it anymore.

7 0
3 years ago
Other questions:
  • Leon read 5/7 of the pages in his book.He has 28 pages left to read.How many pages has he read already?
    9·1 answer
  • A successful basketball player has a height of 6 feet 88 ​inches, or 203203 cm. based on statistics from a data​ set, his height
    5·1 answer
  • can someone show me step by step this one too? it says I have to solve for the indicated variable plz help
    15·1 answer
  • Fórmula para sacar el área de un circulo
    7·1 answer
  • At practice, Tom does three times as many push-ups as Justin, and also 50 jumping jacks. He does 72 exercises in
    15·1 answer
  • At 2 pm the level of the water in the pool was 10 ft . at 6 pm the level of water was 2 feet. find the rate of change of the wat
    14·1 answer
  • The amplitude of y = -2 sin 3x is
    10·1 answer
  • 1. Which of the following conversions is possible?
    6·2 answers
  • Simplify the expression<br> 1/2x+3-1/4x-3
    5·1 answer
  • If you can help me with this I would be thankful
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!