Answer:
hence the required minimum production level is 12units
Step-by-step explanation:
Given the cost function expressed as c(x) = x^3 - 24x^2 + 30,000x
The average cost function will be c(x)/x
Dividing the cost function through by x
Average cost function = c(x)/x = x³/x - 24x²/x + 30,000x/x
Average cost function = x²-24x + 30,000
A(x) = x²-24x + 30,000
If the average cost is minimized, hence dA/dx = 0
dA/dx = 2x - 24
0 = 2x - 24
-2x = -24
Divide both sides by -2
-2x/-2 = -24/-2
x = 12
For the second deriviative
d²A/dx² = 2 which is greater than zero
Hence a production level that will minimize the average cost per item of making x items is 12
The production level that will minimize the average cost per item of making x items is x = 12
How to obtain the minimum value of a function?To find the minimum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.
For this case, the function in consideration is: [tex]c(x) = x^3 - 24x^2 + 30000x[/tex]
This is cost function for x items' manufacturing.
The average cost per item would be c(x) / x
This gives us a function a(x) as:
[tex]a(x) = c(x)/x = x^2 -24x + 30000[/tex]
For finding the minimum of a(x), getting its first two derivatives as:
[tex]a'(x) = 2x - 24\\a''(x) = 2 > 0[/tex]
Equating first rate to 0,
[tex]a'(x) = 2x - 24 = 0[/tex] critical point.
Since second rate is positive, the point x = 12 is point of minima, and since only one critical point is there, it is the point on which a(x) is minimum.
Thus, the production level that will minimize the average cost per item of making x items is x = 12
Learn more about minima and maxima of a function here:
https://brainly.com/question/13333267
Carlos cut StartFraction 5 Over 12 EndFraction of a yard of cloth into 5 pieces of equal length. What was the length of each piece of cloth?
Answer:
Each piece of cloth is (1/12) of a yard long.
Step-by-step explanation:
Carlus cut 5/12 of a yard of cloth into 5 pieces of equal length.
To find the length of each piece of cloth, we need to find the quotient between the length of the piece of cloth, and the number of pieces in which we divide it.
This is:
length = [tex]\frac{(5/12)yd}{5} = \frac{5yd}{12*5} = \frac{1yd}{12} \frac{5}{5} = \frac{1 }{12} yd[/tex]
This means that the length of each piece of cloth is (1/12) of a yard long.
Answer:
1/12 trust,
because yes. >3
2022 / 2023
For all values of x, f(x) = 2x-3 and g(x) = x^2 + 1 a) Find fg(x) Simplify and give your answer in the form ax^2 + b b) Find gf(x).
Answer:
fg(x) = 2x² - 1
gf(x) = 4x²-12x +10
Step-by-step explanation:
Given the functions f(x) = 2x-3 and g(x) = x^2 + 1
a) f(g(x)) = f(x²+1)
f(x²+1) = 2(x²+1) -3
f(x²+1)= 2x²+2 -3
f(x²+1) = 2x² - 1
fg(x) = 2x² - 1
Hence function fg(x) is 2x² - 1
b) gf(x) = g(2x-3)
g(2x-3) = (2x-3)² + 1
g(2x-3) = (2x-3)(2x-3) + 1
g(2x-3) = 4x²-6x-6x+9 + 1
g(2x-3) = 4x²-12x +10
gf(x) = 4x²-12x +10
Please help I have been stuck for a while now
Answer:
B. Between x 2 and x 3
Step-by-step explanation:
please help
dgfhkcgfkgnglhgdh
find the value of X
Answer:
x = [tex]\frac{91}{6}[/tex]
Step-by-step explanation:
Given 2 intersecting chords in a circle, then
The product of the parts of 1 chord is equal to the product of the parts of the other chord, that is
6x = 7 × 13 = 91 ( divide both sides by 6 )
x = [tex]\frac{91}{6}[/tex]
does anyone know the surface area of this pyramid?
Answer:
217
Step-by-step explanation:
1/2 * 12 * 7 = 42 this is one side of the pyramid
4x for all sides = 168
add the bottom which is just a square 7*7 = 49
168 + 49 = 217
The function m is given in three equivalent forms. Which form most quickly reveals the vertex
Answer:
m (x) = -2(x-6)^2 +18
Step-by-step explanation:
A landing pad for a helicopter is in the shape of a circle with a radius of
7 meters. Which of the following is
closest to the area of the landing pad?
A. 44 square meters
B. 154 square meters
C. 205 square meters
D. 308 square meters
PLEASE NO LINKS!
Answer:
154 m^2
Step-by-step explanation:
Area of a circle: A = (pi)(radius)^2
Here, r = 7 m, so A = (3.14)(7 m)^2 = 154 m^2
Which speeds are equal to 1/2 mile per hour? Mark all that apply.
5/6 mile/5/12 hour
1/4 mile / 1/2 hour
1/10 hour / 1/5 mile
3/8 mile / 3/4 hour
2/3 hour / 1/3 mile
4/5 mile / 4/10 hour
/
answer :
3/8 mile / 3/4 hour
How long is a string reaching from the top of a 13-ft pole to a point on the 3 points ground that is 7 ft from the base of the pole?
Answer:
14.76 ft
Step-by-step explanation:
L²= 13² + 7²
L² = 169 + 49 = 218
L = √218 = 14.76 ft
Answer:
14.8
Step-by-step explanation:
We use the Pythagoras theorem because the string and the pole are making a right angle triangle
7^2+13^2=c^2
49+169=c^2
218=c^2
14.8=c
Plz help me!!! Giving brainliest if someone else answers it. I put 2 questions
Answer:
1) C
2) A
Hope it Helps!
:)
Flora drew the following graph to answer the question. What was her mistake when she drew her graph? (NO LINKS)
Answer:
Her elevation went down too quickly, if she is going down 300 ft per hour at a constant rate, at 1 hour, she should be at 2700 feet. It should take her about 10 hours to get down the mountain.
2 cups of coffee and 3 cops of tea cost £10.10
Three cups of coffee and 3 cups of tea cost £15.10 work out how much one cup of coffee is and one cup of tea is
Answer:
Fard
Step-by-step explanation:
Hehe funi
two cords.
AD=92 and BC=140
What does m
David and his dad are building a room in the basement. They want the
room to have an area of 150 ft?. If one wall is 11.25 ft. long, how long must the other
wall be? Show your work.
Solve this equation
√x - 7= √x - 7
Answer:
Search on mathaway
Step-by-step explanation:
Help on these please
All the triangles have 180° total angle measurement.
First question:
114 + 37 + x = 180°
151 + x = 180
x = 180 - 151
x = 29°
Second question:
93 + 46 + x = 180
139 + x = 180
x = 180 - 139
x = 41°
Answer:
In the first question x=29 Because the interior of a triangle adds up to 180.So you will add 114+37=151 , 180-151=29
The second question 93+46=139
180-139=41
x=41
Identify fractions greater than 3/5
Please Help Me!
The table lists the steps to construct a tangent to circle P through point T. Drag the steps so they are in order.
Answer:
The answer is already in the correct formation, there is nothing to change.
Answer:
the person above is right.
You have read 25 pages of a book. You plan to read an additional 10 pages each night. Write the explicit formula to represent the number of pages you will read after n nights.
Answer:
p=10n+25
Step-by-step explanation:
Let's have p represent the number of pages you will read. If you read 10 pages per night, then you are multiplying 10 by the number of nights, which gives you 10n. Because you have already read 25 pages, you want to add to the 10n to give you the equation of p=10n+25
Answer:
Pages= 25 + 10n
Step-by-step explanation:
Since the starting point is 25, that remains constant. 10n represents 10 pages per night.
On your last credit card statement, you had a previous balance of $567.18, payments of $120, a periodic rate of 1.56 percent, and new charges totaling $45.17. What is your new balance?
$288.29
$447.18
$499.33
$567.18
Answer:
$499.33
Step-by-step explanation:
Verified correct with test results.
10) What is the value of x in the figure below?
Answer:
x=68
Step-by-step explanation:
let y equal the vertical angles
49+55+ y= 180
y=76
vertical angles are equal
35+76+x=180
x=68
PLEASE HELP I don't understand this stuff yet. Brainliest give away!
Answer: I think the answer is B
Step-by-step explanation: My reasoning is that since some houses are expensive, and some houses are very cheap, the average house is in the middle, and that is the median.
Answer:
c bc he should use the median cause it is in the affect the mean
Step-by-step explanation:
The relationship between the number of pounds (lb) of trail mix and the price
in dollars is shown in the graph. What is the unit price of trail mix?
A. 1 lb/$8
B. $8/1 lb
C. $1/8 lb
D. $16/2 lb
pls answer quickly since this is a quiz :)) picture included above
It is customary to leave a 15% tip for a waiter/waitress. Suppose your meal costs $22.50, What would you tip the wait person? How much totalwould you pay for the meal?
Answer:
$25.88
Step-by-step explanation:
Given data
Cost of meal= $22.50
Tip= 15%
Let us find 15% of $22.50
=15/100*22.50
=0.15*22.50
=3.375
Hence the amount you would pay in total is
=3.375+22.5
=$25.88
Find a third-degree polynomial equation with rational coefficients that has roots 4 and 6 + i.
a. x^3 - 8x^2 - 11x + 148 = 0
b. x^3 - 8x^2 - 12x + 37 = 0
c. x^3 - 12x^2 + 37x = 0
d. x^3 - 8x^2 - 11x = 0
Answer:
I would say A.
Step-by-step explanation:
 What is the volume of this cone?
Answer:
C) volume = 84.8 m³
Step-by-step explanation:
volume = 1/3πr²h = 1/3(3.14)(3²)(3) = 84.8 m³
Answer:
[tex]volume = 28.3m^3[/tex]
Step-by-step explanation:
[tex]volume \: of \: cone = \frac{1}{3} \times 3 \times 3.14 \times { 3}^{2} = 28.3{m}^{3} [/tex]
Pls help. Due in 5 mintues pls.
no files plssssssss!
Answer:
Your answer is the first option, (2,-1).
Step-by-step explanation:
All you have to do is plug the (x,y) values into both equations, then solve and see if they're true.
For the first equation, plug x (aka 2) and y (aka -1) into the places they belong.
2x + y = 3 would become 2(2) + (-1) = 3 after putting the values in the right spots.
Solve.
2(2) = 4.
4 + (-1) = 3
3 = 3.
That means that (2,-1) is the solution for the first equation, however it also needs to be true for the second. Do the same thing and plug the values in their designated spots.
y = x - 3 will become -1 = 2 - 3.
2 - 3 = -1.
So you're left with:
-1 = -1, which means again that (2,-1) is also the solution for that equation.
__________________________________________________________
If you have any questions about any of the process here, ask in the comments of this response and I'll help you out.
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
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Step-by-step explanation: