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
can you find the error?
Answers
Both step 1 and step 2 were correct with the process of moving the value of x into the place of x and continuing to solve. However, step 3 is incorrect because when it is a negative value being subtracted by another negative value, it remains a negative. So the answer is -14 instead of 14.
Answer:
-32 - 8 = -40
Step-by-step explanation: basicly for 1 instead of putting 3 and 2 together he multiplyed then minus 8
then for 2 he did -6 and -8
then: 14............
A tree that stands 75 feet tall, casts a
shadow of 30 feet at 11:00 am. What is
the ratio of the length of the shadow to the
height of the tree?
Answers
Answer:
30 to 75, 30/75, 30:75
Step-by-step explanation:
What is the value of X
Answers
The answer would be 6 I belive make sure to double check it
Kevin and Randy Muise have a jar containing 34 coins, all of which are either quarters or
nickels. The total value of the coins in the jar is $5.30. How many of each type of coin do
they have?
Answers
Answer:
20 quarters quarters 14 nickles
The blood bank at a hospital has 1,200 units of blood, out of which 37% units are of blood group B+. A clinical researcher randomly selects 300 units of blood and finds that 33% of those are of blood group B+. To test his result, he randomly selects 200 units of blood and finds that 40% of those are of blood group B+. Which of the following is the reason there is a difference between the two percentages selected by the researcher?
Answers
The reason why the two percentages are different is that the sample does not reflect the characteristics of all the units of blood.
What is sampling?Sampling is a statistical technique in which a sample of a statistical population is selected for the study. The objective of sampling is to ensure that its properties can be extrapolated to the total population.
Sampling is a way of saving resources, and at the same time obtaining results similar to those that would be achieved if a study of the entire population were carried out.
According to the above, the clinical researcher who selected a sample of the available blood units obtains different percentages because he selected randomly and this can modify the quantities of samples according to blood type.
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9. If ATLY ~ ACHK, find the value of x.
Answers
Check the picture below.
PLEASEEEE HELP!DUE IN 1 HOUR! A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $3000 when sold. A ranch-style house requires $40,000 of capital and provides an $7000 profit. If the contractor has $3.8 million of capital on hand, how many houses of each type should she build for maximum profit?
Answers
Answer:
Step-by-step explanation:
A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $2000 when sold. A ranch-style house requires $40,000 of capital and provides an $8000 profit. If the contractor has $3.2 million of capital on hand, how many houses of each type should she build for maximum profit?
? colonials
? ranches
For maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses. The maximum profit achievable is $740,000.
Let x be the number of colonial houses built.
Let y be the number of ranch-style houses built.
Now, we can set up the objective function, which represents the total profit:
Total Profit (P) = 3000x + 7000y
The total cost of the houses built cannot exceed the available capital, which is $3.8 million (or $3,800,000):
30,000x + 40,000y ≤ 3,800,000
The number of building lots used cannot exceed the total number of lots available, which is 100:
x + y ≤ 100
Also, we need to consider that the number of houses (x and y) must be non-negative:
x ≥ 0
y ≥ 0
Now, we have the linear programming model with the objective function and constraints.
We need to find the values of x and y that maximize the total profit (P).
Graph the feasible region determined by the constraints (x + y ≤ 100, x ≥ 0, y ≥ 0, 30,000x + 40,000y ≤ 3,800,000), and then evaluate the objective function (P = 3000x + 7000y) at each corner point of the feasible region to find the maximum profit.
The feasible region is a polygon with vertices at the following points:
(0, 0)
(0, 95) (Intersection of x = 0 and y = 95)
(80, 20) (Intersection of x = 80 and y = 20)
(100, 0) (Intersection of x = 100 and y = 0)
Now, evaluate the objective function (P) at each corner point:
(0, 0): P = 0
(0, 95): P = 665,000
(80, 20): P = 740,000
(100, 0): P = 300,000
The maximum profit of $740,000 occurs when the contractor builds 80 colonial houses and 20 ranch-style houses
Hence, for maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses.
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Select the correct answer.
What is the symbolic representation for this argument?
If a polygon has exactly three sides, then it is a triangle
Jeri drew a polygon with exactly three sides.
Therefore, Jeri drew a triangle.
Answers
Answer:
jeri drew a plgon with exatly three sides
Answer:
could you add the choices please
Step-by-step explanation:
it doesnt help without the choices
simplify.
|−6 + (−3)| (−3) + 8 ÷ 2
Answers
6
3
8
6
3
8
to an improper fraction.
Tap for more steps...
51
8
−
2
1
4
51
8
-
2
1
4
Convert
2
1
4
2
1
4
to an improper fraction.
Tap for more steps...
51
8
−
9
4
51
8
-
9
4
To write
−
9
4
-
9
4
as a fraction with a common denominator, multiply by
2
2
2
2
.
51
8
−
9
4
⋅
2
2
51
8
-
9
4
⋅
2
2
Write each expression with a common denominator of
8
8
, by multiplying each by an appropriate factor of
1
1
.
Tap for more steps...
51
8
−
9
⋅
2
8
51
8
-
9
⋅
2
8
Combine the numerators over the common denominator.
51
−
9
⋅
2
8
51
-
9
⋅
2
8
Simplify the numerator.
Tap for more steps...
33
8
33
8
The result can be shown in multiple forms.
Exact Form:
33
8
33
8
Decimal Form:
4.125
4.125
Mixed Number Form:
4
1
8
If the expression inside the absolute value bars which is -6 .Simplifying the expression |−6 + (−3)| (−3) + 8 ÷ 2 is: 9.
What is the expression?Let simplify the given expression step by step:
|-6 + (-3)| = |-9| = 9
First calculate the expression inside the absolute value bars which is -6 + (-3) = -9. Then take the absolute value of -9, which is 9.
(-3) + 8 ÷ 2 = (-3) + 4 = 1
We follow the order of operations (PEMDAS/BODMAS).
First perform the division:
8 ÷ 2 = 4
Add -3 to 4 which gives us 1.
Simplified expression :
9 * 1 = 9
Therefore the expression is 9.
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need help with math probelm
Answers
[tex]28+24=4(7)+4(6)=4(7+6)[=4(13)=52][/tex]
The answer: 4(7+6)
ok done. Thank to me :>
can you help me with this graph question
Answers
explaination: sorry if not correct!
Answer:
D
Step-by-step explanation:
the Max Point is (2,6) so y=b
sorry if u dont get it
Ten men and ten women are to be put in a row. Find the number of possible rows if Beryl, Carol, and Darryl want to stand next to each other in some order (such as Carol, Beryl, and Darryl, or Darryl, Beryl and Carol).
Answers
Answer: 6 possibilities.
Carol, Beryl, and Darryl
Carol, Darryl, and Beryl
Darryl, Carol, and Beryl
Darryl, Beryl, and Carol
Beryl, Darryl, and Carol
Beryl, Carol, and Darryl
Hope this helps :)
An average 1-year-old baby boy weighs around 9.6 kilograms. Convert this
weight into ounces.
Answers
Answer:
338.63 ounces
Step-by-step explanation:
1=35.274
35.274 times 9.6 is 338.6304
I’ll give brainliest to the person who give me the correct answer and pointsss.
Match them
Answers
I think the y=ab^x goes with the first graph and the y=logbc goes with the second
Step-by-step explanation:
pictures
How many roots will the function f(x)= -3x³ - x² + 7x + 6 have?
Answers
Answer:
It will have 3 roots
The number of roots in an equation equals the highest power of that equation.
Step-by-step explanation:
A painter uses 15 gallons of interior paint to cover 300 square yards of wall and ceiling space. On a different job, he uses 8 gallons to cover 160 square yards. No paint is left over on either job. How many gallons of paint are needed to cover 1 square yard?
Answers
Answer:
.05
Step-by-step explanation:
300/15
20 sqr yrds per gal
1/20
1/20 or .05 Gal per sqr yrd
Pls need help
Also making this 10 points so i have 169 points left B)
Answers
Answer:
Second and fourth
Step-by-step explanation:
A line is in point-slope form when you write down as [tex]y-y_0=m(x-x_0)[/tex] - do not be distracted by the signs, +1 and +5 can both be written as -(-1) or -(-5) rispectively.
(15,9) and (x,-3), find all x such that the distance between 2 points is 15
Answers
Answer:
See image
Step-by-step explanation:
I used distance formula to calculate. But if you haven't learned distance formula or solving radical equations, or solving equations by taking sq roots then maybe you were just supposed to graph it and look for the points. The answers came out to be nice neat numbers, so that is possible. x = 6 and x = 24
Monroe uses a microscope observe specimens in science class. The Microscope enlarges objects to 100 times their actual size. Find the size of each specimen as seen in the microscope. Monroe Teacher wants each student to draw a sketch of the longest specimen? Seen through the microscope, a specimen is 0.75 cm long. What is it actual length?
Answers
Answer:
0.0075 centimeters long
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
L x 100 = 0.75 cm
The actual length of the specimen = L
The actual length of the specimen is 0.0075 cm
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Seen through the microscope, a specimen is 0.75 cm long.
The Microscope enlarges objects to 100 times their actual size.
This means,
Let the actual length of the specimen = L
Now,
L x 100 = 0.75 cm
The actual length of the specimen.
L x 100 = 0.75 cm
L = 0.75 / 100
L = 75/10000
L = 0.0075 cm
Thus,
The actual length of the specimen is 0.0075 cm
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7 x [(7 + 7) = 7
Help plz
Answers
Answer:
[tex] \frac{1}{14} [/tex]
Step-by-step explanation:
7 x (7+7)=7
7x [(14)]=7
x=
[tex] x = \frac{1}{14} [/tex]
YOU’RE GETTING a brainlist if you answer these!!!!: If you and I meet halfway between the fountain and the restrooms what are the coordinates of our meeting place?
If my cat and your dog meet halfway between the ball field and the swings what are the coordinates of their meeting place?
Now to the nearest yard how far are you and I to our pets after arriving to our meeting place?
Answers
Answer:
Where's the picture?
Step-by-step explanation:
14. The sun casts a shadow from a flag pole. The height of the flag pole is three times the length of its shadow. The distance between the end of the shadow and the top of the flag pole is 20 feet. Find the height of the flag pole.
Answers
It would be about 6.7 ft
the sum of three consecutive odd integers is 129. find the integers
Answers
Answer:
[tex]\huge\boxed{\sf 41,\ 43, \ 45}[/tex]
Step-by-step explanation:
Let the three consecutive integers be x, x + 2 and x + 4
So, the given condition is:
x + x + 2 + x + 4 = 129
3x + 6 = 129
Subtract 6 to both sides
3x = 129 - 6
3x = 123
Divide 3 to both sides
x = 123/3
x = 41
So, the integers are:
x = 41
x + 2 = 41 + 2 = 43
x + 4 = 41 + 4 = 45
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807-5, 20, -80, 320, ... is a geometric
sequence.
What is the explicit rule
Answers
Answer:
Multiplied by -4
Step-by-step explanation:
-5 (-4) = 20
20 (-4) = -80
-80 (-4) = 320
The length of a rectangle is times the width. If the perimeter is 32 inches, what is the width of the rectangle
Answers
Then l = 3w-4
Perimeter = 2(w+l)
p = 2(w+3w-4) = 2w+6w-8 = 8w-8
Perimeter is 32…
8w-8 = 32
8w = 32+8
8w = 40
w = 5
l = (3×5)-4 = 11
Check… p = 2(5+11) = 2 × 16 = 32
Ans = length is 11
Hope it helps!
Answer:
11
Step-by-step explanation:
r (90 degree) (def) for d (0,5) e (-2,8) f(-3,-5)
Answers
Answer:
d'(5,0) e'(8,2) f(-5,3)
Step-by-step explanation:
When rotating 90 degrees clockwise you only flip the x,y coordinates and changes the x
Example- (4,5) would become (5,-4)
Estimate 196.999 ÷ 1.582?
Answers
Answer:
124.5252844501
Step-by-step explanation:
to estimate we have 125
How much would you have to deposit today to have an accumulated amount 20,000 in 20 years if yearly interest is 4.75% compounded continuously?
Answers
The principal investment required to get a total amount of $20,000.00 from compound interest at a rate of 4.75% per year compounded 12 times per year over 20 years is $7,749.34
Given dataPrincipal =?
Final amount = $20,000
rate = 4.75%
Time = 20 years
First, convert R as a percent to r as a decimal
r = R/100
r = 4.75/100
r = 0.0475 per year,
Then, solve the equation for P
P = A / (1 + r/n)^(nt)
P = 20,000.00 / (1 + 0.0475/12)^(12)(20)
P = 20,000.00 / (1 + 0.003958333)^(240)
P = $7,749.34
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solve the system using substitution x+5y=0 3y+2x=-21
Answers
Answer:
[tex]\left \{ {{x = -15} \atop {y=3}} \right.[/tex]
Step-by-step explanation:
[tex]\left \{ {{x + 5y = 0} (1) \atop {3y + 2x = -21}(2)} \right. <=> \left \{ {{x = -5y} \atop {3y + 2x = -21}} \right. <=> \left \{ {{x = -5y} \atop {3y + 2*(-5y) = -21}} \right. <=> \left \{ {{x = -5y} \atop {3y - 10y = -21}} \right. \\<=> \left \{ {{x = -5y } \atop {-7y = -21}} \right. <=> \left \{ {{x = -5y} \atop {y= 3 }} \right. <=> \left \{ {{x = -5 * 3} \atop {y=3}} \right.=> \left \{ {{x=-15} \atop {y=3}} \right.[/tex]
The sum of two angles is 90°. The difference of twice the larger angle and the smaller angle is 105º. The system of linear equations:
x + y = 90
2x - y = 105
represents this situation where x is the larger angle and y is the smaller angle. Find the measures of the two angles.
SHOW YOUR WORK!!
(this is linear combinations)
Answers
Answer:
x = 65, y = 25Step-by-step explanation:
Given system of linear equations:
x + y = 90 2x - y = 105Add up the equations to eliminate y:
x + 2x = 90 + 1053x = 195x = 65Find y:
y + 65 = 90y = 90 - 65y = 25