the marginal cost of producing the xth box of cds is given by 8 − x/(x2 1)2. the total cost to produce two boxes is $1,100. find the total cost function c(x).
Answers
The marginal cost of producing the xth box of CDs is given by 8 − x/(x2 1)2. The total distribution cost to produce two boxes is $1,100.
To find the total cost function c(x), we can integrate the marginal cost function to obtain the total cost function. Thus, we have: ∫(8 − x/(x² + 1)²) dx = C(x) + kwhere C(x) is the total cost function and k is the constant of integration. To evaluate the integral, we use the substitution u = x² + 1. Then, du/dx = 2x and dx = du/2x. Substituting, we have:∫(8 − x/(x² + 1)²) dx = ∫[8 − 1/(u²)](du/2x)= (1/2) ∫(8u² − 1)/(u²)² duUsing partial fractions, we can write: (8u² − 1)/(u²)² = A/u² + B/(u²)² where A and B are constants. Multiplying both sides by (u²)², we have:8u² − 1 = A(u²) + BThen, letting u = 1, we have:8(1)² − 1 = A(1) + B7 = A + BAlso, letting u = 0, we have:8(0)² − 1 = A(0) + B-1 = BThus, A = 7 + 1 = 8. Therefore, we have:(8u² − 1)/(u²)² = 8/u² − 1/(u²)².
Substituting, we get:C(x) = (1/2) ∫(8/u² − 1/(u²)²) du= (1/2) [-8/u + (1/2)(1/u²)] + k= -4/u + (1/2u²) + k= -4/(x² + 1) + (1/2)(x² + 1) + k= 1/2 x² - 4/(x² + 1) + kTo find k, we use the fact that the total cost to produce two boxes is $1,100. That is, when x = 2, we have:C(2) = (1/2)(2)² - 4/(2² + 1) + k= 2 - 4/5 + k= 6/5 + kThus, when x = 2, C(x) = $1,100. Therefore, we have:6/5 + k = 1,100Solving for k, we get:k = 1,100 - 6/5= 1,099.2Thus, the total cost function c(x) is given by:C(x) = 1/2 x² - 4/(x² + 1) + 1,099.2
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Related Questions
On a number line ,1.42 would be located.choose all answer that make a true statement
A.To the right of 1.41
B .between 0 and 1
C.between 0.42 and 0.44
D. to the left of 1.43
Answers
Explanation:
Instructions: Using the image below, match each
line with its corresponding perpendicular line, by
dragging and dropping.
A
E
Perpendicular Lines
\(\overline{AC}\) and
\(\overline{BD}\) and
\(\overline{EG}\) and
B
CG EF DH AB GH AE BF CD
H
Answers
The corresponding perpendicular lines to the specified lines, obtained using the definition of perpendicular lines are;
Perpendicular lines
\(\overline{AC}\) and \(\overline{CD}\) or \(\overline{CG}\)
\(\overline{BD}\) and \(\overline{DH}\) or \(\overline{CD}\)
\(\overline{EH}\) and \(\overline{CG}\) or \(\overline{GH}\)
What are perpendicular lines?Perpendicular lines are lines that form an angle of 90°
The perpendicular lines in the figure are the lines that are form a right angle, or that form an angle of 90° with each other, therefore, the perpendicular lines are as follows; the lines;
The line segment \(\overline{AC}\) is perpendicular to the line segment \(\overline{CD}\) and \(\overline{CG}\)
The line segment \(\overline{BD}\) is perpendicular to the line segment \(\overline{DH}\)and \(\overline{CD}\)
The line segment \(\overline{EH}\) is perpendicular to the line segment \(\overline{CG}\) and \(\overline{GH}\)
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a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations. True/False ?
Answers
True, a simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.
What does standard deviation mean ?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
What does a simple random sample mean?
A subset of participants is randomly chosen from a population by the researcher using simple random sampling, a sort of probability sampling.
The probability of being chosen is the same for every person in the population. Then, data are gathered from as much of this randomly selected subgroup as possible.
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Please help me with this!!
Answers
Answer:
its B
Step-by-step explanation:
is X -3 + Y3 in the simplest form
Answers
Answer:
I believe it's Y but I'm not 100 percent sure
Write an equation of the graph shown in terms of cosine:
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Answer:
Step-by-step explanation:
A squiggly line can refer to a variety of different shapes or patterns. To create an equation using cosine that resembles a squiggly line, you can use a combination of sine and cosine functions with different frequencies and amplitudes. Here's an example equation that produces a squiggly pattern:
y = A * cos(B * x) + C * sin(D * x)
In this equation, A, B, C, and D are constants that you can adjust to modify the shape and characteristics of the squiggly line. By experimenting with different values for these constants, you can create various squiggly patterns. Keep in mind that the specific equation may vary depending on the exact shape and features you have in mind for the squiggly line.
Solve the system algebraically. -6x+3y=27 -5x-3y=-16
Answers
Answer:
A) -6x+3y = 27
B) -5x-3y = -16 We add the 2 equations
-11x = 11
x = -1
Putting 1 into equation B)
5 -3y = -16
-3y = -21
y = 7
Step-by-step explanation:
eva is short on frosting she works in a bakery and has 12 case to frost but she is short 4 1/8 cups on the amount of Frosty required she decides that she will spread the frosting she has among the 12 case she makes a sign for the cakes and names them by the value that represents the amount of frosting on each cake compared to the amount should have what does the sign say draggy volume to the box to correctly completes the statement Hicks for sale we are calling these cups we should ask why
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............ ..........
i need this answerd ASAP ill give brainliest to whoever solves it first along with 3
40 points
Answers
Answer:
Below.
Step-by-step explanation:
Mean = (61+59+60+50+54+56+61+63)/8
= 464/8
= 58 degrees
Deviations:
61 - 58 = 3
59-58 = 1
60-58 = 2
50-58 = -8 = 8 (absolute value)
54-58= -4 = 4
56-58 = -2 = 2
61-58 = 3
63-58 = 6
MAD = (3+1+2+8+4+2+3+6) / 8
= 3.625
= 3.6 to the nearest tenth.
The coordinates of the end points of TU are T(2,4) and U(11,13)
Answers
Answer:
\(T(2,4) and U(11,13)\)
Step-by-step explanation:
hello please help me i’m stuck on this one
Answers
Answer:
The answer is number 4
Step-by-step explanation:
The mark equal to the subject with larger or smaller means that the figure should also shake either if there is no equal to smaller than or larger than that can not shake this number
If you need any explanation you can communicate with me
x > 2 is represented by the open circle at 2 going right and x is less than or equal to 2 is presented by the closed circle on -2 going left
2x+ 3x−1 2 − 5x−2 3 =2
Answers
Answer:
0
Step-by-step explanation:
Sole for y
k = p/2(y+w)
y =
Answers
Answer:
Answer: y = (2k -pw)/p
Step-by-step explanation:
\(k = \frac{p}{2} (y + w)\)
multiply 2 on both sides:
\(k \times 2 = 2 \times \frac{p}{2} (y + w) \\ \\ 2k = p(y + w)\)
open the bracket:
\(2k = py + pw\)
subtract pw from both sides:
\(2k - pw = (py + pw) - pw \\ 2k - pw = py\)
divide p on both sides:
\( \frac{2k - pw}{p} = \frac{py}{p} \\ \\ y = \frac{2k - pw}{p} \)
Answer:
\(\pi {y}^{ \alpha \: so \: y = k} \)
If Sarah needs 3 cups of flour for 2 batches of cookies, How many cups of flour would she need for 18 batches of cookies?
Answers
Answer:
24 = 18
Step-by-step explanation:
3 cups = 2 cookies
Meaning she needs 24 cups of flower for 18 cookies
Alex bought 3 tacos for $4.00. How much would she have to pay for 10 tacos at this rate?
Answers
Explanation = This would mean each taco would be roughly 1.3$ since 4/3=1.333, so 1.3x10=13$
consider the fate of billy bibbet. what transformations do you see in him after the fishing trip and how does that set up what he does during the party?
Answers
Billy suffers from a stutter, so he expresses himself in a manner in which he can be successful.
Doctor Spivey grants McMurphy's request for a pass to take a fishing trip with nine other patients, accompanied by two of his aunts.
Why is McMurphy tired after the fishing trip?
McMurphy adds Rub-a-Dub George, a neat-freak Swedish fisherman and sailor, to the group. Nurse Ratched says they can't go because there isn't enough capacity in one car for all the patients when Candy Starr arrives without her buddy to pick up the patients for their outing.
McMurphy has his own weakness, his self-centeredness. At first he is willing to sacrifice the patients for his own well-being
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Find the coefficient of x^4 in 3x^3-5x^4 + x-7
Answers
Answer:
-5
Step-by-step explanation:
the coefficient of x^4 is -5
17. Algebraically determine the domain and the y -intercept of the function y=\log _{4}(2 x+1)-3 .
Answers
The domain of the function is `R` and the y-intercept is `(0, -3)`
Given, `y = log4(2x + 1) - 3`.
To determine the domain of the function,
we should look for all values of `x` that would make the given function undefined.
There are no real values of `x` that would make the function undefined.
Therefore, the domain of the function is all real numbers or `R`.
To determine the y-intercept, substitute `x = 0` in the given function.`
y = log4(2(0) + 1) - 3 = log4(1) - 3 = 0 - 3 = -3`
Therefore, the y-intercept of the function is `(0, -3)`.
Hence, the domain of the function is `R` and the y-intercept is `(0, -3)`.
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I AM SO THANKFUL IF YOU HELP MEE!!!
Answers
Answer:
Step-by-step explanation:
i think its D
what is an equation, in standard form, of the line through (1,7) and (-2, -3)?
Answers
Answer: -23
Step-by-step explanation:
Step-by-step explanation:
The equation of a line is 6x-2y=12. find the x-intercept and the y-intercept. a. x = -2 , y= 6 b. x = 2 , y= -6 c. x = -2 , y= -6 a. x = 2 , y= 6 which shows the line 3x -2y = -18 in slope-intercept form? y=3/2x+9 y=2/3x+9 y=-3/2x-9 y=2/3x-9 a line passes through the point (-1,3) and has a slope of -2. what is the equation of the line in slope-intercept form? y=2x+5 y=-2x+5 y=2x+1 y=-2x+1 a line passes through the points (1,7) and (-4,-3). what is the equation of the line in standard form? 4x-2y=10 4x+2y=10 4x-2y=-10 4x+2y=-10 which points are a solution to the inequality < −3+4? (choose all that apply) (select all that apply.) (0,4) (-2,7) (3,-4) (-1,-5)
a couple has 3 children. they sit in 5 adjacent seats in the same row while watching a movie. if the mother must sit in between the two youngest children, how many seating arrangements are possible?
Answers
Answer: well about 3
Step-by-step explanation:
father(youngest)mom(middle child)oldest
oldest(youngest)mom(middle child)father
father(middle child)mom(youngest)oldest
hope this helps:)
Cruz has been saving his earnings from his lemonade stand. Cruz has 100 dollars to spend. If he buys a new hat for 32 dollars, how many scarves can he buy with the remaining money if they cost 6 dollars each?
Answers
Answer:
11.
Step-by-step explanation:
100-32 = money after hat purchase
(100-32) dollars / 6 dollars / scarf = 11.33 or 11 scarves (because you cannot buy a fraction of a scarf)
Danny bought 2 500 units and 3 000 units of shares of a company at the price of RM1.76 per unit and RM1.68 per unit respectively. At the end, he sold all the shares at the price of RM1.75 per unit. Determine whether Danny gained profit. Give your reason.
Answers
Answer:
Danny made a profit. His income was greater than his cost
Step-by-step explanation:
The amount Danny paid for his shares is ...
2500 × ₹1.76 +3000 × ₹1.68 = ₹4400 +5040 = ₹9440
The amount Danny received for his shares is ...
(2500 +3000) × ₹1.75 = ₹9625
The amount of profit Danny made on his transactions was ...
₹9625 -9440 = ₹185
Danny made a profit. His income was greater than his cost.
There are 4 tulips and 9 daffodils in a flower bed. Write the part-to-whole ratio that compares daffodils to total flowers
Answers
Answer: 9:13
Step-by-step explanation:
4+9= 13
so our total is 13, and there are 9 daffodils
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
9514 1404 393
Answer:
(a) x = (3 -ln(3))/5 ≈ 0.819722457734
(b) y = 10
Step-by-step explanation:
(a) Taking the natural log of both sides, we have ...
2x +1 = ln(3) +4 -3x
5x = ln(3) +3 . . . . . . . . add 3x-1
x = (ln(3) +3)/5 ≈ 0.820
__
(b) Assuming "lg" means "log", the logarithm to base 10, we have ...
log(y -6) +log(y +15) = 2
(y -6)(y +15) = 100 . . . . . . . taking antilogs
y^2 -9x -190 = 0 . . . . . . . . eliminate parentheses, subtract 100
(y -19)(y +10) = 0 . . . . . . . . factor
The values of y that make these factors zero are -19 and 10. We know from the first term that (y-6) > 0, so y > 6. That means y = -19 is an extraneous solution.
The solution is ...
y = 10
__
When solving equations using a graphing calculator, it often works well to define a function f(x) such that the solution is f(x) = 0, the x-intercept(s). That form is easily obtained by subtracting the right side of the equation from both sides of the equation. In part (a) here, that is ...
f(x) = e^(2x+1) -3e^(4-3x)
Answer:
Step-by-step explanation:
e^(2x + 1) = 3e^(4 - 3x)
e^(2x + 1) = e^3(4- 3x)
lne^ (2x + 1) =ln e^3(4- 3x)
2x + 1 = 3*(4 - 3x)
2x + 1 = 12 - 9x
11x + 1 = 12
11x = 12 - 1
11x = 11
x = 1
====================
I've never worked with binary logs but I'll give this my best shot. If someone comes along and gives you a different answer, use it.
lg(y-6) + lg(y + 15) = 2
lg (y - 6)(y + 15) = 2
inverse (y - 6)(y + 15) = 2^2
(y - 6)(y + 15) = 4
y^2 + 9y - 90 - 4 = 0
y^2 + 9y - 94 = 0
y = 6.19
y = -15,19
Estimates are that up to _____% of children with disabilities have some type of nutritional problem. 25 45 55 75 90
Answers
Estimates suggest that up to 90% of children with disabilities have some type of nutritional problem.
These children often face unique challenges that can contribute to a higher risk of nutritional deficiencies or imbalances.
Disabilities can affect various aspects of a child's health, including their ability to eat, digest, absorb nutrients, and maintain a healthy weight.
Additionally, certain disabilities may require specific dietary restrictions or specialized nutritional interventions, which can further complicate their nutritional status.
It is crucial to address these nutritional issues and provide appropriate support to ensure the optimal growth and development of children with disabilities.
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How many one-degree angles together form angle R shown in the figure? (1 point)
A circle with two arrows that meet together at its center. The circle is divided into sixty three hundred sixtieths. The divisions are marked as zero three hundred sixtieths, sixty three hundred sixtieths, one hundred twenty three hundred sixtieths, one hundred eighty three hundred sixtieths, two hundred forty three hundred sixtieths and three hundred three hundred sixtieths. One arrow points to three hundred three hundred sixtieths and the other arrow to one hundred eighty three hundred sixtieths.
a
0
b
60
c
90
d
120
Answers
Answer: D:120
Step-by-step explanation: since the angle goes from
180/360 to 300/360 we will have to do 300-180 which gives us 120
What is the reflection?And how would I solve it?
Answers
Answer:
To reflect a point, you need to find the exact point of each corner of the figure. The first point could be say, -5, -1. You know that you go 5 points to the left to get to the line so you go another 5 points to the left from the line. So basically find the opposite of each number, so -5, -1 so it becomes 5, 1.
The next point would be -5, -6 so it becomes 5, 6.
-7, -5 turns into 7, 5.
Plot all of the points and it should look like this graph below.
Step-by-step explanation:
What number must you add to the polynomial below to complete the square?X^2-10x
Answers
To complete the polynomial we have to have something of the form:
\(x^2+2bx+b^2\)Then, to complete the polynomial given we must add
\(\begin{gathered} (-5)^2=25 \\ x^2+2(-5)x+(-5)^2\text{ } \end{gathered}\)Joy completes 1/10 of her painting each day. How much of her painting
does she complete in a 5-day week?
Answers
Answer:
1/2
Step-by-step explanation:
If joy completes 1/10 of the painting every day, for her to complete it in five days, we need to add 1/10 with each other five times.
1/10+1/10+1/10+1/10+1/10
Since the denominators are all the same, they stay constant at 10. The numerator we can add since the denominators are the same.
5/10 simplifies to 1/2
Answer:
\(\frac{1}{2}\)
Step-by-step explanation:
We multiply 1/10 with 5 and then simplify.
\(\frac{1}{10}*5=\frac{5}{10} =\frac{1}{2}\)