Given:
The cost function is
[tex]C(x)=7x[/tex]
The revenue function is
[tex]R(x)=9x-0.001x^2[/tex]
To find:
The marginal cost, marginal revenue, and marginal profit functions.
Solution:
We know that,
[tex]Profit=Revenue-Cost[/tex]
[tex]P(x)=R(x)-C(x)[/tex]
[tex]P(x)=9x-0.001x^2-7x[/tex]
[tex]P(x)=2x-0.001x^2[/tex]
The marginal cost, marginal revenue, and marginal profit functions are the derivatives of cost, revenue and profit functions respectively.
Marginal cost function is
[tex]C'(x)=7\dfrac{d}{dx}x[/tex]
[tex]C'(x)=7(1)[/tex]
[tex]C'(x)=7[/tex]
Marginal revenue function is
[tex]R'(x)=9(1)-0.001(2x)[/tex]
[tex]R'(x)=9-0.002x[/tex]
Marginal profit function is
[tex]P'(x)=2(1)-0.001(2x)[/tex]
[tex]P'(x)=2-0.002x[/tex]
Therefore, the marginal cost, marginal revenue, and marginal profit functions are [tex]C'(x)=7[/tex], [tex]R'(x)=9-0.002x[/tex] and [tex]P'(x)=2-0.002x[/tex] respectively.
three couples go to the movies and sit together in a row of six seats. In how many ways can they arrange themselves if each couple sits together?
Answer:
6
Step-by-step explanation:
im just gonna name these couples by numbers 1 , 2 and 3 and each couple will take up 2 seats together.
1 2 3
3 2 1
2 3 1
1 3 2
2 1 3
3 1 2
Answer:
6 ways
Step-by-step explanation:
1= couple 1
2= couple 2
3=couple 3
1 2 3
1 3 2
2 1 3
2 3 1
3 2 1
3 1 2
Some one help please
25 is what percent of 125?
40 is 25% of what number?
What number is 60% of 200?
Find 16% of 25
50 is ______% of 500
30 is 40% of what?
What is 140% of 20?
600 is 300% of what?
45% of the class is girls. There are 90 girls in the class. How many students are in the class?
40% of the voters voted for Jimmy B. 80 million people voted. How many votes did he get?
300 middle schooler’s vote on their favorite sport. 60 of them like hockey. What percentage of the students like hockey?
Answer:
1. 20%
2. 160
3. 120
4. 4
5. 10%
6. 75
7. 28
8. 200
9. 200 students
10. 32,000,000 votes (32 million)
11. 20%
Step-by-step explanation:
No clue if you want actual work shown but you posed so many questions that it would take forever to type out all the work.
- 11x - 19 = - 41
solve for x
Answer:
-11x -19 = -41
We need to add 19 to both sides then divide to find x.
_____________________
1)) so -11x -19 + 19 = -41 + 19
2)) -11x = -22
3)) -11x/-11 = -22/-11
x = 2
GL!
(side note, i dont usually ask, but it would be great if you could mark me brainliest so I can level up <33)
Answer:
x = 2
Step-by-step explanation:
-11x - 19 = -41
Add 19 to both sides of the equation:
-11x - 19 + 19 = -41 + 19
-11x = -22
Divide both sides by -11
-11x/-11 = -22/-11
x = 2
Which equation has the same solution as x2 + 4x – 13 = 5?
Answer:
x=4
Step-by-step explanation:
Given the function h(x)=-x^2+x+4, determine the average rate of change of the function over the interval −1≤x≤5.
Answer:
average rate of change of h(x) on −1 ≤ x ≤ 5 is then 5
Step-by-step explanation:
change in h(x)
average rate of change = ------------------------
change in x
Calculate h(x) at the interval endpoints: -1 ≤ x ≤ 5, and then subtract h(5) from h(-1):
h(5) = (5)² + 5 + 4 = 34
h(-1) = (-1)² -1 + 4 = 4
change in h(x) = 34 - 4 = 30
change in x: 5 - (-1) = 6 30
average rate of change of h(x) on −1≤x≤5 is then ------------- = 5
6
Solve the simultaneous equations
5x + 3y = 41
2x + 3y = 20
Do not use trial and improvement
The solution to the system of equation is (7, 2)
Using the simultaneous equation:
5x + 3y = 41
2x + 3y = 20
using elimination method
Subtract equation 1 from 2 to have:
5x - 2x = 41 - 20
3x = 21
x = 21/3
x = 7
Substitute x = 7 into equation 1 to get y
5x + 3y = 41
5(7) + 3y = 41
35 + 3y = 41
5y = 41 - 35
3y = 6
y = 6/3
y = 2
Hence the solution to the system of equation is (7, 2)
Learn more here: https://brainly.com/question/15165519
Why is math so hard to learn?
Answer:
why does math even exist
Step-by-step explanation:
Find the angle measure that of each missing angle
Step-by-step explanation:
122+v=180
v=180-122
v=58
w+61=180
w=180-61
w=119
61+58+y=180
119+y=180
y=180-119
y=61
61+x=180
x=180-61
x=119
j=180
PLEASE HELP WILL GIVE BRAINLIEST
Answer: The answer is B.
Step-by-step explanation: This is because the x-axis is days, and the y-axis is pounds. The option B states that Winnie eats 5 pounds of dog food in 2 days, while actually the dog eats 2 pounds of dog food in 5 days.
Answer:
Its B!
Step-by-step explanation:
The X axis represents days and the Y axis represents pounds! 5 is the X axis and 2 is the Y axis! So to make the sentence true, it would be (2,5).
Hope this helps, and don't forget to follow!
8TH GRADE MATH HELP PLEASE
Answer:
55 is the answer hope it helps...
How much?Pls help me.
Answer:
19.8
Step-by-step explanation:
Answer:
$19.80
Step-by-step explanation:
56 text messages = 5.60
1 text message = 5.60 ÷ 56 = 0.1
198 text messages = 0.1 x 198 = 19.8
pls help me with this multiple choice ! thank u
Answer:
The answer will be C x=14 and y=7
Step-by-step explanation:
Hope this HElped
Helppppppppp pLeAsEeEe?
Answer:
The perimeter is 16 yards.
_
Step-by-step explanation:
♤You can solve using the pythagorean theorem.
♡We will be using the variable 'x' to represent the variable 'b' in the picture provided.
◇In the pythagorean theorem, a and b represents bases while the c represents the hypotenuse (diagonal).
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {x}^{2} + {12}^{2} = {20}^{2} \\ {x}^{2} + 144 = 400 \\ \frac{ \: \: \: \: \: - 144 = - 144}{ {x}^{2} = \sqrt{256} } \\ x = 16[/tex]
HELP, this is really hard and i’m struggling
Answer:
B or 2
Step-by-step explanation:
Because 2 and 4 are alternative interior angles that means that they are equal, but on the inside of the traversal (Parallels AB and CD)
Hope this helped :)
Answer:
it should be angle 2 and 4
Step-by-step explanation:
since 2 and 4 are interior angles they are the same and congruent so they have to be equal for the line to be parallel
The original rectangle is 120 centimeters. Calculate the length of a rectangle that is 72% shorter.
What is the answer
Answer:
33.6 cm
Step-by-step explanation:
120 x 0.72 = 86.4
120 - 86.4 = 33.6
The new rectangle which is 72% shorter is 21.6 centimeters.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given The original rectangle is 120 centimeters.
And the new rectangle is 72% shorter or (100 - 72)% = 18% of the original rectangle which is,
= (18/100)×120 centimeters.
= 21.6 centimeters.
Learn more about percentages here :
https://brainly.com/question/24159063
#SPJ2
: Scottie is standing next to a lighthouse on the edge of a cliff overlooking the ocean. The cliff is 30 meters above sea level, and the lighthouse has a height of 15 meters. There is a man fishing in a boat directly below Scottie who has hooked a fish that is 10 meters below the surface of the water.
Complete question :
Scottie is standing next to a lighthouse on the edge of a cliff overlooking the ocean. The cliff is 30 meters above sea level, and the lighthouse has a height of 15 meters. There is a man fishing in a boat directly below Scottie who has hooked a fish that is 10 meters below the surface of the water.
a. Use positive and negative numbers to represent the locations in relation to sea level.
Scottie =
Top of the lighthouse =
The boat =
The fish =
b. How far is Scottie from the fish?
meters.
Answer:
Scottie = +30 m
Lighthouse = +45m
Boat = 0
Fish = - 10m
40 m
Step-by-step explanation:
Scottie = 30m ( height of the cliff) since he is standing on it's edge
Top of lighthouse = since, lighthouse is located on top of the cliff ; height of cliff + height of light house = (30 + 15) = 45m
The boat = 0 (on the surface of water) ; this is the sea level surface or point
The fish = - 10 m (10 meters below the water surface).
Distance between scottie and fish :
30 m - ( - 10m)
30m + 10m
= 40 m
[tex] \frac{5}{7} \times 6[/tex]
what is 5/7 x 6
Answer:
[tex]\frac{30}{7}[/tex]
Step-by-step explanation:
to multiply a number by a fraction, just multiply straight across
you just do 5 * 6 to get 30 and since there isn't anything under the 6, you put an imaginary 1 to get you 7 so your answer will be 30/7
Which of the following is true?
A. The mean is the least
B. The median is the least
C. The mode is the least
D. The mean, median, and mode are equal
need help with this please
Answer:
where is your question friend...
Why did the student dislike the average teacher
Answer:
The teacher disliked her average student because he was like all the other students???
Suppose the line of best fit is drawn for some data points. If the mean of the x-coordinates of the points is -8, and the mean of the y-coordinates of the points is 10, the line must pass through which of these points?
Answer: 10
Step-by-step explanation:
Answer:
(-8, 10)
Step-by-step explanation:
A P E X
Which equation can be used to solve for the value
of x?
Answer:
the orange one
Step-by-step explanation:
the bottom angles are gonna be the same and a triangle is 180 degrees total so
can someone help me find the prerimter of this shape
Answer:
114
Step-by-step explanation:
If this answer helped you then please mark it as brainliest so I can get to the next rank
what is the value of x?
Answer:
x = 9
Step-by-step explanation:
12^2+x^2 = 15^2
==> x = 9
Answer:
9
Step-by-step explanation:
x = [tex]\sqrt{c^{2} - a^{2} }[/tex]
x = [tex]\sqrt{15^{2} - 12^{2} }[/tex]
x = [tex]\sqrt{225 - 144}[/tex]
x = [tex]\sqrt{81}[/tex]
x = 9
A pendulum is swinging back and forth. After ttt seconds, the horizontal distance from the bob to the place where it was released is given by \qquad H(t) = 7 - 7 \cos \left(\dfrac{2\pi (t-2)}{20}\right)H(t)=7−7cos( 20 2π(t−2) )H, left parenthesis, t, right parenthesis, equals, 7, minus, 7, cosine, left parenthesis, start fraction, 2, pi, left parenthesis, t, minus, 2, right parenthesis, divided by, 20, end fraction, right parenthesis. How often does the bob cross its midline? Give an exact answer
Answer:
Every 10 seconds
Step-by-step explanation:
The bob crosses its midline whenever cos(2π(t-2)/20)=0.
Since cosθ=0 when θ=±π/2 + 2πn, we can find then the bob crosses its midline by solving:
2π(t-2)/20 = ±π/2 + 2πn
t-2 = ±5+20n
The solutions are when t = -3, 7, 17, 27, 37, ...
Therefore, the bob passes its midline every 10 seconds.
For the line above, what is the slope? *
Answer: The slope is 2.
Step-by-step explanation:
To get the slope, use this tip: Rise over run
Count how much it rises, which is 4, and how much it "runs' which is 2. Now put rise above run which is 4/2. This simplifies to simply 2.
Answer:
The slope is 2.
Step-by-step explanation:
The points on the line are (1, -2) which can be labeled as x1 and y1, and the other is (3,2) which can be labeled as x2 and y2. you set up the equation in the slope formula, so 2 - - 2 / 3 - 1. Since there are two negatives, the subtraction signs turn into addition signs, and you get 4/2, which simplyfied is 2. Hope this helps :)
how to calculate interest on a loan
Answer:
Gather information like your principal loan amount, interest rate and total number of months or years that you’ll be paying the loan.Calculate your total interest by using this formula: Principal Loan Amount x Interest Rate x Time (aka Number of Years in Term) = Interest.If you take out a five-year loan for $20,000 and the interest rate on the loan is 5 percent, the simple interest formula works as follows:
$20,000 x .05 x 5 = $5,000 in interest
You might encounter simple interest on short-term loans. However, the way most banks and lenders charge interest is more complicated.
Step-by-step explanation:
What value do we need to complete the equation?
Answer:
h/2
Step-by-step explanation:
Solve 5r + 7s = 15 for s
Answer:
Here it is:
:P
Answer:
s=15/7 - 5r/7
Step-by-step explanation:
