A company manufactures and sells x VCRs per month. If the cost and revenue equations are C(x) = 200 + 2x, R(x) = 20x − (x^2/50) , use differentials to estimate the change, ∆P, in profit when the production is increased from 100 to 101.

Answers

Answer 1

Answer:

ΔP  = 14

Step-by-step explanation:

Given

[tex]C(x) = 200 + 2x[/tex]

[tex]R(x) = 20x - \frac{x^2}{50}[/tex]

Required

Determine the change in profit

First, we need to determine the profit

[tex]P(x) = R(x) - C(x)[/tex]

[tex]P(x) = 20x - \frac{x^2}{50} - 200 - 2x[/tex]

Collect Like Terms

[tex]P(x) = - \frac{x^2}{50} + 20x - 2x- 200[/tex]

[tex]P(x) = - \frac{x^2}{50} + 18x- 200[/tex]

Differentiate wrt x

[tex]P'(x) = -\frac{x}{25} + 18[/tex]

When Profit increases from 100 to 101, the change becomes

ΔP  [tex]= -\frac{x}{25} + 18[/tex]Δx

Δx[tex]= (x_2 - x_1)[/tex]

Where

[tex]x_2 = 101[/tex]

[tex]x_1 = x = 100[/tex]

So, the expression: ΔP  [tex]= -\frac{x}{25} + 18[/tex]Δx becomes

ΔP  [tex]= (-\frac{x}{25} + 18)(x_2 - x_1)[/tex]

ΔP  [tex]= (-\frac{100}{25} + 18)(101 - 100)[/tex]

ΔP  [tex]= (-4+ 18)(1)[/tex]

ΔP  [tex]= (14)(1)[/tex]

ΔP  = 14


Related Questions

what number is 1/10 of 8000000

Answers

Answer:

800000

Step-by-step explanation:

what is 78756567.998 divided by 76454

Answers

Answer:

1,030.11703766971

Step-by-step explanation:

Just use a calculator (windows + r and then type calc if your on windows or search up calculator)

Find the LCD of the given rational equation:

Answers

Answer:

The correct answer is: D

Step-by-step explanation:

Consider the domain, which in this case x cannot be equal to -4 and -2.

The LCD of the rational equation is (a) (x + 4)(x + 2)(x - 2)

How to determine the LCD?

The rational equation is given as:

[tex]\frac{x}{x + 4} + \frac{x - 1}{x + 2} = \frac{3}{x^2 + 2x - 8}[/tex]

Factorize the denominator of the fraction on the right hand side

[tex]\frac{x}{x + 4} + \frac{x - 1}{x + 2} = \frac{3}{(x - 2)(x + 4)}[/tex]

Write out the common factors in the denominator

LCD = (x + 4)(x + 2)(x - 2)

Hence, the LCD of the rational equation is (a) (x + 4)(x + 2)(x - 2)

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bernie spends three hours a day on homework. if the spends 3/4 of an hour on science, 3/4 of an hour on social studies, and 1/4 of an hour on english, how much time does bernie spend on math

Answers

3/4 of an hour is 45 minutes
1/4 of an hour is 15 minutes
3 hours is 180 minutes

3/4 + 3/4 = 90 minutes ( 45 + 44 )
90 + 15 = 105

180 - 105 = 75 minutes

Bernie will spend 75 minutes on math

Answer:

Step-by-step explanation:

Math = 3 - Science - social studies - english

Math = 3 - 3/4 - 3/4 - 1/4

Math = 3 - 1 3/4

Math = 3 - 1.75

Math = 1.25 or 1 1/4

Alice drops a rubber ball from a height of 4 feet. The equation t2=4/16 represents the amount of time, in seconds, it takes for the ball to reach the ground. How long will it take the ball to reach the ground?

A 1/4 second
B 1/2 second
C 2 seconds
D 4 seconds

Answers

Answer:

Letter B

Step-by-step explanation:

Answer:

I belive the answer is B

Step-by-step explanation:

Walt multiples 25 times 16 using partial products what did walt do wrong

Answers

Answer:

first what the full question and if 25*16/2=200

Step-by-step explanation:

1. Describe how to show that triangle PMO = triangle PMN using the SSS Congruence Postulate. Then, without using a protractor, find a way to show that the triangles are congruent using the SAS Congruence Postulate.

Answers

Answer:

ayudenle porfa :)

Step-by-step explanation:

porfa

what is -1(9)


Ignore theses it said it was too short

Answers

-9, apologies if I got this wrong

|
1.64 divided by what equals 0.04?

Answers

Answer:

41

Step-by-step explanation:

1.64 : x = 0.04 ⇒ x = 1.64 : 0.04

1.64 : 0.04 → 164 : 4 = 41

Check:

1.64 : 41 = 0.04

1.64 divided by the number 41 equals 0.04.

What is the division?

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

The given numbers are 1.64 and 0.04.

Let the unknown number be x.

1.64 divided by x equals 0.04, that is

1.64/x =0.04

0.04x=1.64

x=1.64/0.04

x=41

Therefore, 1.64 divided by 41 equals 0.04.

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Please help!!!- Find the measure of the angle in bold.
Need help to figure out to solve this.

Answers

Answer:

11x-6+(19x+6)=180°

11x+19x-6+6=180°

30x=180

x=180/30

x=6

it means that

19x+6=19*6+6=114+6=120°

is |-4| equal to |4|?

Answers

Answer:

Yes

Step-by-step explanation:

Absolute value measures the distance between the number and 0. The distance between -4 and 0 is 4, and the distance between 0 and 4 is 4. Therefore, they are equal.

Answer:

yes

Step-by-step explanation:

the l l symbol is the absolute value symbol, it counts how far the number is from zero meaning that the outcome is always positive.

Solve for f:
f divided by -2/3 = -1/3

Answers

-f (3/2) = -1/3
-3/2f = -1/3
f= 2/9 or 0.2

Answer:

2/9

Step-by-step explanation:

Write all prime numbers between 10 and 20​

Answers

Answer:

11,13,17,19

Step-by-step explanation:

Answer:

11 , 13 , 17 and 19

Step-by-step explanation:

good luck :)

Question 4
5 pts
4. Cassie has 45 marbles. Abdul has m If Cassie has 9 times as many
marbles as Abdul. Choose the equation that correctly represents the
number of marbles Abdul has.
O 9 x m = 45
O 45 - 9 = m
O C. 9+ m = 45
O D. 9 x 45 = m

Answers

Answer:

8 x m = 45

Step-by-step explanation:

cassie has 9 times which means multiplcation so its the first one

The formula to put in E176 that will give me the sum of all the units sold by the indicated sales rep and product is:

Answers

Question attached

Answer :

There is no such formular

Explanation:

there is no such Formula I'm the options given. However the total product units sold by the sales representative for the period can be calculated in the excel sheet by adding up the cells with the units sold(cells F179,F180... to F186) and inserting the formula in the cell under total units sold by sales representative. So any change of figures in the cells added would reflect in the total units cell E176, if there is an additional figure for units sold in another cell, we could add this cell to formula in E176

−20=−4x−6x Find the value of x

Answers

Answer:

[tex]\huge\boxed{x=2}[/tex]

Step-by-step explanation:

[tex]-20=-4x-6x\qquad|\text{combine like terms}\\\\-20=-10x\qquad|\text{divide both sides by (-10)}\\\\\dfrac{-20}{-10}=\dfrac{-10x}{-10}\\\\2=x\to x=2[/tex]

A river has a current of 2km per hour. Find the rate of Fred’s boat in still water if it travels 30 km downstream and the same time it takes to travel 14 km upstream.

Answers

Answer:

32km

Step-by-step explanation:

PLEASE HELP!!!!


Drag each tile to the correct box.
Match each savings plan to its description.

401(k)
Roth IRA
403(b)
529 plan
health FSA

a tax-deferred retirement savings plan available to employees of some nonprofit
organizations and educational Institutions

a tax-advantaged college savings plan

an employer-offered retirement account that accepts contributions from
employees and employers

a tax-advantaged savings account available through employers to pay for
qualified medical expenses

a retirement Investment account managed by individuals, deposits are taxable,
but funds are tax exempt when withdrawn at retirement

Answers

Answer:

403(b)

529 plan

401(k)

health FSA

Roth IRA

Step-by-step explanation:

I looked it up. Good luck :)

Answer:

401(b)

529 plan

401(k)

health FSA

Roth IRA

Step-by-step explanation:

The following table shows the annual profits for two small florist shops what shop had the greater total profit? How much greater was its profit?


Plz answer ASAP I will mark u brainlyest this is my 5th time asking please answer

Answers

Answer:

Shop A & $400

Step-by-step explanation:

-4.7 + 27.5 + 122.3 = $145.1 (Shop A)

-0. 2 + 14.5 + 130.4 = $144.7 (Shop B)

Difference = 145.1 - 144.7 = $0.4

0.4 × 1000 = $400

Shop A, $400

Have a nice day / night :)

An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a:

Answers

Answer:

the speed value that the radar equipment outputs.

Step-by-step explanation:

A random variable in an experiment is also (and most times the case) called a dependent variable. In this scenario, the random variable would be the speed value that the radar equipment outputs. This is because this value depends on the actual velocity of the cars that pass by the equipment. The faster the car is moving when it passes the radar the higher value will be displayed on the equipment. Therefore, depending completely on the vehicles.

4.8(x-1.75)= -9.6 but without the distributive property​

Answers

4.8(x-1.75)= -9.6
Answer:
x=0.55
X=.55
some teachers require you to put 0.55

What is the ratio of daises to all the flowers in the vase?

Answers

Answer: Do you have the original ration so we can simplify it then??

Step-by-step explanation:

Give a counterexample that disproves each conjecture below.
1) No triangles have two sides of the same length.

2) No women have been elected U.S. senators.

3) All~basketball players are more than 6 feet tall.

4) If you live in Texas, then youlive in Houston.

5} If it is a cell phone, then it has a touch screen.

6) If x is any number, then x2> 2.

8) If x >_ 0, then x + 2 = 7.

9) If x2 =16 , then x = 4.

10) All figures with four sides of equal length are squares.

11) The square of a number rs largex than the number.

12) If a numbex is prime, then it zs an. odd number.

Answers

Answer:

1) No triangles have two sides of the same length.

An isosceles triangle is a triangle that has 2 sides that have a same length.

2) No women have been elected U.S. senators.

Dianne Feinstein, a woman-elected senator of California.

3) All basketball players are more than 6 feet tall.

Isaiah Thomas is a prime example of a basketball player who has the height of 5'9.

4) If you live in Texas, then you live in Houston.

Matthew McConaughey, a born-and-raised Texan star lives in Austin near his mom and other family members.

5) If it is a cell phone, then it has a touch screen.

Before smart phones, there were flip phones where the user would have to dial everything to able to use it.

6) If x is any number, then x2> 2.

Not sure what you meant.

8) If x >_ 0, then x + 2 = 7.

Not sure what you meant.

9) If x2 =16 , then x = 4.

Not sure what you meant.

10) All figures with four sides of equal length are squares.

Rectangles have longer sides equal in length and their shorter sides equal in length with each other, but is not considered a square.

11) The square of a number rs largex than the number.

Not sure what you meant.

12) If a number x is prime, then it zs an. odd number.

Not sure what you meant

Hoped this help!

You should rephrase some of your questions because I have no idea what it's saying.

-Bob Ross

Ik y’all good at math, help me out yall!

Answers

Answer:

i think the answer be 150 feet per minute

hope this is right

Answer:

150

Step-by-step explanation:

use points on the line i'll use (2,300) and (1,150)

m=y2-y1/x2-x1

300-150=150

2-1=1

150/1=150

hope this helps :3

sorry if im wrong

HELP ME PLEASE 9 3/5 + 8 3/5

Answers

Answer:

18 1/5

Step-by-step explanation:

9 3/5 + 8 3/5

We have a common denominator, so add the whole numbers

9+8 = 17

Add the fractions

3/5+ 3/5 = 6/5

17 6/5

We can simplify since we have an improper fraction

17 + 5/5 + 1/5

17+1+1/5

18 1/5

Answer:

18 1/5

Step-by-step explanation:

9 3/5 + 8 3/5=

First we do 9+8 which is 17

3/5+3/5= 6/5

17 6/5

Simplify:

18 1/5

On Joe's bookshelf are: • 8 fiction books 3 non-fiction books • 4 historical drama books Joe will randomly choose 1 book to read from the shelf. What is the probability that he will choose a non-fiction book? A)0.267 B)0.8 C)0.2 D)0.533​

Answers

Answer:

There is a 0.2 chance or 20% change that he will choose a nonfiction book. PLease mark as helpful if it is! thanks

- 8n - 8 = -72
I don’t know how to do this

Answers

Answer:

n=8

Step-by-step explanation:

Add 8 to both sides of the equals sign, then bring down -8n, add -72+8, You'll get -64, lastly you divide -64 and -8, and you'll get your answer

Start by turning everything positive! 8n + 8 = 72.
Then, having the 8 as a positive number, subtract it from the left side. 8n = 64
In our final step, we divide 64 by 8 to find what n is, n= 8
To check your work you can plug it back into the original equation, be sure that both sides equal each other!

What are the scale factor of ABC dilated to XYZ plz help

Answers

Answer:  B) 2/3

====================================

Explanation:

The order is important for ABC and XYZ so we can see what letters pair up.

A pairs with X since they are the first lettersB pairs with Y since they are the second lettersC pairs with Z since they are the third letters

Based on that, we can see that AB pairs with XY as they are the first two letters of ABC and XYZ respectively.

Divide the length XY over AB and reduce

XY/AB = 10/15 = 2/3

We could also divide XZ over AC

XZ/AC = 14/21 = 2/3

and we get the same ratio

What fraction is equivalent to 0.1666666...

Answers

Answer:

1/6

Step-by-step explanation:

The value of the fraction that is equal to the number 0.16666... would be 5/30.

Given that,

Change the number 0.16666... into a fraction.

Used the concept of fraction which stated that,

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction.

Let us assume that the number 0.1666.. equal to x.

Hence,

x = 0.166666 .....  .. (i)

Multiply by 10 on both sides,

10x = 1.66666...  (ii)

Also, multiply by 100 in equation (i),

100x = 16.6666.. (iii)

Subtract equation (ii) from (ii),

100x - 10x = 15

90x = 15

x = 15/90

Simplify for the simplest form,

x = 5/30

Therefore, the value of the fraction is 5/30.

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In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third is 92° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle.

The measure of the first angle is ______
The measure of the second angle is _____
The measure of the third angle is _______

Answers

Answer:

The measure of first angle is 44°.

The measure of second angle is 22°.

The measure of third angle is 114°.

Step-by-step explanation:

First, you have to form expressions for the 3 angles. Let second angle be x :

First angle = (2x)°

Second angle = x°

Third angle = (92 + x)°

Next, you have to add up altogether as the total angles in a triangle is 180° :

2x + x + 92 + x = 180

4x + 92 = 180

4x = 180 - 92

4x = 88

x = 88 ÷ 4

x = 22°

Lastly, you have to substitute the x-value into the expressions :

First angle = 2(22) = 44°

Second angle = 22°

Third angle = 92 + 22 = 114°

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