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2 years ago

For the given cost function C(x), find the oblique asymptote of the average cost function C(X), C(x)=14,000+94x+0.03x^2

1 answer:

5 0

Answer: y = 0.03x + 94

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Explanation:

Lets define A(x) to be the average cost function where
A(x) = C(x)/x
basically you divide the given cost function C(x) by the number of units produced (x)

Dividing C(x) over x leads to:
A(x) = C(x)/x
A(x) = (14000+94x+0.03x^2)/x ... substitution
A(x) = (0.03x^2+94x+14000)/x ... rearrange terms
A(x) = (0.03x^2)/x+(94x)/x+(14000)/x ... break up the fraction
A(x) = 0.03x + 94 + (14000/x) ... simplify

If x were to head off to infinity, then the portion 14000/x approaches 0.

So this is why the oblique asymptote is y = 0.03x + 94

Basically, in the long run, the average cost will approach y = 0.03x + 94

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One state leads the country in tart cherry production, producing 74 out of every 100 tart cherries each year.

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1 year ago

Every day a student randomly chooses a sandwich for lunch from a pile of wrapped sandwiches. If there are six kinds of sandwiche

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Answer:

279,936 ways

Step-by-step explanation:

Every day the student has to chose a sandwich from the pile of 6 sandwiches. So this means the student has to make a choice from the 6 sandwiches for the 7 days. Since the order matters, this is a problem of permutations.

Daily the student has the option to chose from 6 sandwiches. So this means, for 7 days, he has to make a choice out of 6 options. Or in other words we can say, the student has to make selection from 6 objects 7 times.

So, the total number of ways to chose the sandwiches will be 6 x 6 x 6 x 6 x 6 x 6 x 6 = $6^{7}$

Alternate Method:

Since the repetition can occur in this case, i.e. a sandwich chosen on one day can also be chosen on other day, the following formula of permutations ca be used:

Number of ways = $n^{r}$

where n is the total number of choices available which is 6 in this case and r is the number of times the selection is to be made which 7 in this case. So,

The number of ways to chose a sandwich will be = $6^{7} = 279936$ ways

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1 year ago

A study was conducted to determine the mean birth weight of a certain breed of kittens. Consider the birth weights of kittens to

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3.56 +/- 0.011 = ( 3.549, 3.571). This is the answer.

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1 year ago

The grocery store sells kumquats for $5.00 a pound and Asian pears for $3.25 a pound. Write an equation in standard form for the

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2 years ago

Read 2 more answers

Part of a book fell out. The first page of this part has number 143. The last page has a number written with the same digits. Ho

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Answer:

142 pages

Step-by-step explanation:

The parameters given are

First page of part of the book available = 143

The last is numbered with the digits 143

Since the book is said to have been split into two parts with, we have that one part of the book starts from the beginning, while the other part continue from the first part stops

Number on the pages on the first part = from 1 to number on the first page on the second part - 1

Hence, the part of the book available is the second part and the number of pages in the first part = 1 to 142 or 142 pages.

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1 year ago