Answers
=========================================================
Explanation:
If you know the cost function C(x), to find the marginal cost, we apply the derivative.
Marginal cost = derivative of cost function
Marginal cost = C ' (x)
Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.
[tex]\text{Cost} = \text{antiderivative of marginal cost}\\\\\displaystyle C(x) = \int \left(35x^{4/3} - 14x^{3/4} + 1\right)dx\\\\[/tex]
[tex]C(x) = \frac{1}{1+4/3}*35x^{4/3+1} - \frac{1}{1+3/4}*14x^{3/4+1} + x + D\\\\C(x) = \frac{1}{7/3}*35x^{7/3} - \frac{1}{7/4}*14x^{7/4} + x + D\\\\C(x) = \frac{3}{7}*35x^{7/3} - \frac{4}{7}*14x^{7/4} + x + D\\\\C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\[/tex]
D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).
To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.
Therefore, we go from this
[tex]C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\[/tex]
to this
[tex]C(x) = 15x^{7/3} - 8x^{7/4} + x + 9000\\\\[/tex]
which is the final answer.
Related Questions
35 devide 28 with decimals pls help
Answers
Answer:
1.25
Step-by-step explanation:
The answer in decimal is 1.25
35/28= 1.25
= 35 ÷ 28
by 1
=35 - 28 = 7
Introducing decimals
= 70 to 28
by 2
= 70 - 56 = 14
adding zero to 14
= 140 to 28
by 5
= 140 - 140 =0
the answer is 1.25
I did it this way through division hope you'll understand. All the best.
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 59 kilograms. A
delivery of large boxes and 4 small boxes has a total weight of 149 kilograms. How much does each type of box weigh?
a
Answers
957.75 + 83.86 the sum is
Answers
Answer:
1,041.61
Simply stack the numbers (lining up the decimals) and add right to left.
elliot's jogging rate is 9 km/h. how many kilometers can he travel in
a) 2 hours?
b) t hours.
50 POINTS AND BRAINILEST!
Answers
Answer:
A=18km B=equation is 9t
Step-by-step explanation:
Here's how I found the answer!
A: Here is our current proportion:
9km
--------
1 hr
Here is what we want:
9km xkm
------- = --------
1h 2h
Now, what did I do to 1 to get to 2? I multiplied by 2.
Since this is a ratio, it needs to be proportional.
So, we need to do the same thing for the numerator, 9.
9*2=18.
A=18km
B: This question is asking for an expression, which would be 9t. 9 is the amount he jogs per hour, and t is the hour that is unknown.
The distance travelled by Elliot's is 18 hours.
Given that, Elliot's jogging rate is 9 km/h.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
a) The formula to find the distance is Distance = Speed × Time
= 9 × 2
= 18 hours
b) Distance = 9 × t
=9t hours
Therefore, the distance travelled by Elliot's is 18 hours.
To learn more about the speed, distance, and time visit:
brainly.com/question/4978052.
#SPJ2
Find the value of x.
x=__ (simplify your answer. Type an exact answer isn’t radicals as needed.)
Answers
[tex] {5}^{2} + {x}^{2} = {8}^{2} [/tex]
[tex]25 + {x}^{2} = 64[/tex]
Subtract both sides 25
[tex]25 - 25 + {x}^{2} = 64 - 25[/tex]
[tex] {x}^{2} = 39[/tex]
Thus :
[tex]x = \sqrt{39} [/tex]
[tex]x = 6.245[/tex]
Solve for X 3x - 5X + 8x + x = 42
7
8
6
Answers
Answer:
x = 6
Step-by-step explanation:
3x-5x+8x+x = 42
7x = 42
x = 6
Write the ratio 4 1/5 to 5 2/5 as a simplified fraction
Answers
Answer:
[tex]\huge\boxed{4\dfrac{1}{2}:5\dfrac{2}{5}=5:6}[/tex]
Step-by-step explanation:
[tex]4\dfrac{1}{2}:5\dfrac{2}{5}[/tex]
we convert a mixed number to an improper fraction
[tex]4\dfrac{1}{2}=\dfrac{4\cdot2+1}{2}=\dfrac{9}{2}\\\\5\dfrac{2}{5}=\dfrac{5\cdot5+2}{5}=\dfrac{27}{5}[/tex]
Therefore
[tex]4\dfrac{1}{2}:5\dfrac{2}{5}=\dfrac{9}{2}:\dfrac{27}{5}=\dfrac{9\!\!\!\!\diagup^1}{2}\cdot\dfrac{5}{27\!\!\!\!\!\diagup_3}=\dfrac{1}{2}\cdot\dfrac{5}{3}=\dfrac{1\cdot5}{2\cdot3}=\dfrac{5}{6}=5:6[/tex]
The ratio 4 1/5 to 5 2/5 is equivalent to the simplified fraction 7/9.
How to write the simplified factionTo write the ratio 4 1/5 to 5 2/5 as a simplified fraction, we need to convert both mixed numbers to improper fractions and then find their ratio.
Step 1: Convert the mixed numbers to improper fractions:
4 1/5 = (4 * 5 + 1) / 5 = 21 / 5
5 2/5 = (5 * 5 + 2) / 5 = 27 / 5
Step 2: Find the ratio by dividing the first fraction by the second fraction:
Ratio = (21 / 5) / (27 / 5)
Step 3: To divide by a fraction, multiply by its reciprocal:
Ratio = (21 / 5) * (5 / 27)
Step 4: Simplify the fraction:
Ratio = (21 * 5) / (5 * 27)
Ratio = 105 / 135
Step 5: Simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 15:
Ratio = (105 / 15) / (135 / 15)
Ratio = 7 / 9
Learn more about simplified fraction
https://brainly.com/question/78672
#SPJ3
Can someone please help me with both questions I will mark u brilliant
Answers
1. We can simply multiply 6.50 by 2!
6.50 x 2 = 13
The book cost $13
2. The easiest way to do this is to convert the fractions into decimals.
1/4 = 0.25
1/5 = 0.2
1/8 = 0.125
Add them together: 0.575!
Subtract this from 1: .425
Multiply by 100: 42.5
42.5% is your answer!
Hope this helps!
Answer: B
Step-by-step explanation:
Tracey paid $150 for an item that was originally priced at $510. What percent of the original price did Tracey pay?
Answers
Answer:
29.4118%
Step-by-step explanation
510 * x = 150
x = .2941176
multiply by 100 to get percent
29.4118
HELP
HOW AM I MEANT TO ANSWER THIS QUESTION I WOULD ASO LIKE ANSWER.
THX
Answers
Answer:
= 108
Step-by-step explanation:
the rectangle = 12 * 5 = 60
plan A:
the triangle A with H = (13 - 5)/2 = 8/2 = 4
then triangle A = [tex]\frac{1}{2}[/tex] * 6 * 4 = 24/2 = 12
total triangles = 12 * 4 = 48
hexagon area = 60 + 48 = 108
plan B:
there 13 - 5 = 8
because there are identical triangles, so we can shape both of it being a rectangle with short line is 8/2 =4, and long line is 12
then we calculate that rectangle area = 12 * 4 = 48, then total of the hexagon = 60 + 48 = 108
A six-sided, fair number cube is rolled 100 times as part of an experiment. The frequency of the roll of the number 3 is 20. Which statement about rolling a 3 is correct?
The theoretical probability is 1/6. The experimental probability is 1/6.
The theoretical probability is 1/5. The experimental probability is 1/6.
The theoretical probability is 1/6. The experimental probability is 1/5.
The theoretical probability is 1/5. The experimental probability is 1/5.
Answers
Answer:
The theoretical probability is 1/6. The experimental probability is 1/5.
Step-by-step explanation:
Answer:
c for lazy goofy peoplee
Step-by-step explanation:
Which is the equation of a parabola with Vertex (0,0) and directrix x=-2?
Answers
Answer:
y^2 = 8x
or
x = 1/8 y^2.
Step-by-step explanation:
The general form for this type of parabola is
y^2 = 4ax where the focus is at (a, 0) and the directrix is x = -a
So the equation is y^2 = 4*2x
that is y^2 = 8x.
According to a Gallup poll, 60% of American adults prefer saving over spending. You randomly select 4 adults and ask if they prefer spending over saving. Construct a probability distribution for the random variable x. Then graph the distribution. (Histogram)
Expected Value ______________________________
Standard Deviation _____________________________
B –
I-
N-
S-
Interpretation
Answers
Using the binomial distribution, it is found that:
The expected value is of 2.4.The standard deviation is of 0.76.The distribution is given by the histogram.For each person, there are only two possible outcomes, either they prefer saving, or they prefer spending. The preferences of each person are independent of any other person, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.The expected value is:
[tex]E(X) = np[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]
In this problem:
60% prefer saving over spending, hence [tex]p = 0.6[/tex]4 adults are selected, hence [tex]n = 4[/tex].Then:
[tex]E(X) = np = 4(0.6) = 2.4[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{2.4(0.6)(0.4)} = 0.76[/tex]
The histogram is sketched at the end of the answer.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental
fee to use a kayak for 4 days. She also paid $18 for a guided waterfall tour. Tara
paid $94 in all. What was the rental cost of each day Tara used the kayak?
Answers
Answer:
she will pay $19 for each day
Step-by-step explanation:
94-18=76
76÷4=19
The rental cost of each day Tara used the kayak is $19 if Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
Let x be the rental cost of each day Tara used the kayak.
4x + 18 = 94
4x = 94 - 18
4x = 76
x = 76/4
x = $19
Thus, the rental cost of each day Tara used the kayak is $19 if Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
Multiply
(5x+y)(6x-7y)
Answers
Answer:
30x2−29xy−7y2
Step-by-step explanation:
=(5x+y)(6x+−7y)
=(5x)(6x)+(5x)(−7y)+(y)(6x)+(y)(−7y)
=30x2−35xy+6xy−7y2
=30x2−29xy−7y2
Logan has an automatic hummingbird feeder in his backyard. He fills it to its capacity, 10 fluid ounces. Each day, it releases 1 fluid ounce of nectar.
Write an equation that shows how the number of fluid ounces of nectar remaining, y, depends on the number of days since Logan filled it, x.
Answers
Answer:
-1x+10
Step-by-step explanation:
The equation that shows how the number of fluid ounces of nectar remaining (y) depends on the number of days since Logan filled it (x) is:
y = 10 - x.
The relationship between the number of fluid ounces of nectar remaining (y) and the number of days since Logan filled the hummingbird feeder (x) can be represented using a linear equation.
Initially, when Logan fills the hummingbird feeder to its capacity of 10 fluid ounces, the nectar remaining is 10 fluid ounces.
As each day passes, 1 fluid ounce of nectar is released.
Therefore, the equation that shows how the number of fluid ounces of nectar remaining (y) depends on the number of days since Logan filled it (x) is: y = 10 - x.
Here's an explanation of each component of the equation:
y: This represents the number of fluid ounces of nectar remaining.
As the days pass, this value will decrease as nectar is released.
10: This is the initial amount of nectar in the feeder when Logan fills it to its capacity of 10 fluid ounces.
x: This represents the number of days that have passed since Logan filled the feeder.
Each day, the amount of nectar decreases by 1 fluid ounce, hence the subtraction of "x."
This equation forms a linear relationship where the nectar remaining decreases by 1 fluid ounce for each day that passes.
To learn more on equation click:
https://brainly.com/question/14468218
#SPJ3
I WILL GIVE YOU 200 pts please
1. √−36
2. √−8 ⋅ √−32
3. √− 15 ⋅ √− 25
4. (–3i) (4i)(–5i)
5. (7i)2(6i)
6. 42
7. 55
8. 89
9. (5 – 2i) + (–13 – 8i)
10. (7 – 6i) + (9 + 11i)
11. (–12 + 48i) + (15 + 21i)
12. (10 + 15i) – (48 – 30i)
13. (28 – 4i) – (10 – 30i)
14. (6 – 4i) (6 + 4i)
15. (8 – 11i) (8 – 11i)
16. (4 + 3i) (2 – 5i)
17. (7 + 2i) (9 – 6i)
18.
19.
2
7 − 8
20.
3–
21.
2–
6 + 5
−2
2 − 4
1 + 3
Solve each equation.
22. 52 + 35 = 0
23. 2 2 + 10 = 0
24. 4 2 + 76 = 0
25. −2 2 − 6 = 0
26. −5 2 − 65 = 0
27. 4 2 + 12 = 0
3
Find the values of ℓ and m that make each equation true.
28. 15 – 28i = 3ℓ + (4m)I
29. (6 – ℓ) + (3m)i = –12 + 27i
30. (3ℓ + 4) + (3 – m)i = 16 – 3i
31. (7 + m) + (4ℓ – 10)i = 3 – 6i
32. ELECTRICITY The impedance in one part of a series circuit is 1 + 3j ohms and the impedance in another part of the
circuit is 7 – 5j ohms. Add these complex numbers to find the total impedance in the circuit.
33. ELECTRICITY Using the formula E = IZ, find the voltage E in a circuit when the current I is 3 – j amps and the
impedance Z is 3 + 2j ohms.
Answers
1 = 6i
Add me Ill solve all Cloewyy#8905
What is the correct factorization of x^2 - 2x - 15?
HURRRYYYY PLS
A. 4
B. 5
C.8
D.12
Answers
Answer:
option b
Step-by-step explanation:
[tex] {x}^{2} - 2x - 15[/tex]
[tex] {x}^{2} - 5x + 3x - 15 = 0[/tex]
[tex] x(x - 5) + 3(x - 5) = 0[/tex]
[tex](x - 5)(x + 3) = 0[/tex]
x = -3 (Not possible)
x = 5
So, x = 5
The answer is 10^-2/3+5
Answers
Answer:
k
Step-by-step explanation:
What is an equation of the line that passes through the points (-7, 7) and (3, 7)(
Answers
Answer:
y=7
Step-by-step explanation:
The slope is (7-7)/(3+7) = 0. So, the line is a horizontal line.
The y value of both points is 7.
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 37 fts. The ball's height h (in feet) after 1 seconds is given by the following.
h= 3+37t-16t^2
Find all values of t for which the ball's height is 23 feet.
Answers
Answer:
t=(37+root89)/32,(37-root89)/32
Step-by-step explanation:
Solve the equation:
23=3+37t-16t^2
On Monday there are 25 pencils in a basket, If 3 pencils are taken out of the basket each day, how many pencils are left in the basket on Friday?
Answers
13 cuz add 4 days then friday so 4×3 which is 12 and 12-25 so ye its 13
Find the x-intercepts.
y =
2x2 + 5x + 2/
x2 - 4x + 3
Answers
Answer:
[tex]x=-\frac{1}{2}[/tex] and [tex]x=-2[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{2x^2+5x+2}{x^2-4x+3}[/tex]
[tex]0=\frac{2x^2+5x+2}{x^2-4x+3}[/tex]
[tex]0=\frac{(2x+1)(x+2)}{(x-1)(x-3)}[/tex]
[tex]0=(2x+1)(x+2)[/tex]
[tex]2x+1=0[/tex] and [tex]x+2=0[/tex]
[tex]x=-\frac{1}{2}[/tex] and [tex]x=-2[/tex]
What is 13x4=nx26 and tell me the answer
Answers
Answer:
There are a couple different solutions to your equation:
[tex]x=0[/tex]
[tex]x=\sqrt[22]{\frac{13}{n}}[/tex]
[tex]x=-\sqrt[22]{\frac{13}{n}}[/tex]
[tex]\:n\ne \:0[/tex]
A nut mixture of peanuts and macadamia nuts at a small fair is $1.00 per pound of peanuts and $3.26 per pound of macadamia nuts. Over the
entire day, 131 pounds of the nut mixture were sold for $248.52. If p is the number peanuts and n is the number of macadamia nuts, then the
system of equations that models this scenario is:
p+n=131
P+3.26n = 248.52
ANSWER CHOICES:
(Please help it would mean everything to me. I’d give brainliest <3)
Answers
Answer:
D
Step-by-step explanation:
You can infer to the solution of this problem by looking at the choices. Hope this helped :)
Which is a composite number? A.97 B.89 C.95 D.13
PLEASE I REALLY NEED THE CORRECT ANSWER RIGHT NOW!!!!
Answers
Answer: C. 95 is a composite number.
Step-by-step explanation:
You can look at the ones place of each number to see if any end in 0, 2, 5, or any other digit that indicates that the number is not prime. Since 95 ends in a 5, it can be divided by 5, making it have more factors than 1 and itself. Therefore, 95 is the composite number of the list of numbers.
Answer:95
Step-by-step explanation:composite numbers are numbers that have more factors than 1 and itself, factors are numbers you can multiply to get a number. 95 is a composite number since 1,95, AND 5 are all factors of 95 making it a composite number
Please help me... I really need it.
Answers
Answer:
If you are writing a seesya let me help you
Step-by-step explanation:
Make sure to hilight key info
Also use grammarly to correct past tense and sentences
Make sure to make sense
A farm lets you pick 3 pints of raspberries for $12.00
Answers
do you want me to find the answer or something because ur just doing something and not saying what to do with it
What is the slope of the line (-5,-7) and (4,-1)
Answers
Answer:
2/3
Step-by-step explanation:
slope = change in y / change in x = (-7-(-1))/(-5-4) = (-6)/(-9) = 2/3
Write an equation and solve the sum of twenty one and five
times a number f is 61
Answers
5f = 40
f = 8