Suppose that the price p (in dollars) and the demand x (in thousand of units) of a commodity satisfy the demand equation 6p+x+xp=94
How fast is demand changing when the price is set at $9 and the price is rising at the rate of $2 per week?
dx/dt
=
The demand is decreasing at the rate of _________units per week.

Answers

Answer 1

The demand is decreasing at the rate of 2units per week.

Given the price p (in dollars) and the demand x (in thousands of units) of a commodity satisfy the demand equation 6p+x+xp=94

Differentiating the function with respect to time will result in;

[tex]6\frac{dp}{dt}+\frac{dx}{dt} + x \frac{dp}{dt} + p\frac{dx}{dt} = 0[/tex]

Given the following paramters

p = $6

dp/dt = $2/wk

Substitute the given parameters into the formula to have:

[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0[/tex]

To get the demand x, we will simply substitute  p = 9 into the expression to have:

6(9)+x+9x=94

10x+54 = 94

10x = 94 - 54

10x = 40

x = 4

Substitute x = 4 into the derivative to have:

[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 2(4) + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 8 + 9\frac{dx}{dt} = 0\\20 + 10\frac{dx}{dt} =0\\10\frac{dx}{dt} =-20\\\frac{dx}{dt} =\frac{-20}{10}\\\frac{dx}{dt} =-\$2/wk[/tex]

Hence the demand is decreasing at the rate of 2units per week.

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Related Questions

$1689 invested for 4 years at 3% compounded annually ?

Answers

The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901

The amount of money gained after an investment is compounded is given by:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Where P is principal, A is the final amount, r is the rate, n is the number of times compounded per period and t is the time

Given that P = $1689, t = 4, r = 3% = 0.03, n = 1, hence:

[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=1689(1+\frac{0.03}{1} )^{4*1}\\\\A=\$1901[/tex]

The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901

Find out more at: https://brainly.com/question/14295570

To study the effects of a medication on migraines, every 10th adult from an alphabetized list of patients who suffer from migraines were selected. Then, the sample was surveyed about the number of migraines they have each month. The names of the 50 adults selected were written on equal sized tiles, placed in a bag, and mixed well. The people with names on the first 25 tiles selected were given the migraine medication. The remaining 25 people were given a placebo. After six months, all patients were surveyed again about the number of migraines they had each month. The change in the mean number of migraines between the two groups was compared. Which of the following is the best description of the randomization approach? random selection random assignment both random selection and random assignment neither random selection nor random assignment

Answers

Answer:

Random Assignment

Step-by-step explanation:

For which function is the ordered pair (2, 12) not a solution?
A) y= 6 x
B) y= x - 10
C) y= 14 - x
D)y= x + 10​

Answers

Answer:

option b

Step-by-step explanation:

y=12 x=2

12 is not equal to 2-10.

lemme know if you didn't understand

A metal rod is
7
8
meters long. It will be cut into pieces that are each
1
56
meters long. How many pieces will be made from the rod?

Answers

Answer:

5

Step-by-step explanation:

I'm not so sure with the number's you submited but I assume it's 7,8m and 1,56 m

1. convert them to cm (780 cm and 156 cm )

2. 780/156 = 5

A) 37.68 square inches B) 72.52 square inches C) 108.12 square inches ) D) 113.09 square inches​

Answers

Answer:

The answer is D.

Step-by-step explanation:

Radius is half of diameter. So the radius of the circle is 6 in.

The formula for getting the area of circle is:

A = π[tex]r^{2}[/tex]                                π = 3.1416

A = (3.1416)(6)[tex]^{2}[/tex]

A = (3.1416)(36)

A = 113.09 square inches

5 1/8 - 3 2/3 =? ..............................

Answers

Answer:

1  11/24

Step-by-step explanation:

5 1/8= 41/8  

3 2/3 = 11/3

41/8 -11/3 = (41*3)/(8*3)   -(11*8)/(3*8)

              =123/24 -88/24

               = (123-88)/24

              =35/24

              =1  11/24

Simplify: 8√3 + 12√3

Answers

Answer:

20√3

Step-by-step explanation:

This table shows data collected by a runner.

A three column table with 7 rows. The first column, Time in minutes, has the entries, 1, 2, 3, 4, 5, 6. The second column, Distance in miles, has the entries, 0.19, 0.38, 0.57, 0.76, 0.95, 1.14. The third column, Elevation in meters, has the entries, 12, 28, 67, 98, 124, 145.

Which statement about the scenario represented in the table is true? Assume time is the independent variable.

The distance run is a nonlinear function because it does not have a constant rate of change.
The elevation is a nonlinear function because it does not have a constant rate of change.
Both the distance run and the elevation are nonlinear functions because they do not have constant rates of change.
Both the distance run and the elevation are linear functions because they have a constant rate of change.

Answers

Answer:

a

Step-by-step explanation:

Answer:

The correct answer is B, The elevation is a nonlinear function because it does not have a constant rate of change.

Step-by-step explanation:

Given 4(3x-8)=52 prove x=7

Answers

Answer:

4(3x-8)=52

divide both sides by 4

4/4(3x-8)=52/4

3x-8=13

add both sides by 8

3x-8+8=13+8

3x=21

divide both sides by 3

3x/3=21/3

x=7

Step-by-step explanation:

this question got asked three times =)

Answer:

52 is the answer

Step-by-step explanation:

You always work with your paratheses first. Work with your variable(s) to make things easier. Plug in the number given for your variable.

3(7)=21

Subtract the numbers in the paratheses once you have found the number with the variable.

21 - 8 = 13

Last step is to combine the number in the parentheses with the number(s) out of the parentheses. Depending on the equation, the number outside of the parentheses will have to be added/subtracted/multiplied/divided. In this equation, we have to multiply since there´s no given sign for multiplying. You automatically know you have to multiply because the number is right next to the parentheses.

4 * 13 = 54 or 13 * 4 = 54

I hope this helps u! :D

Calculator
What is the measure of angle X?
Enter your answer as a decimal in the box. Round only your
answer to the nearest hundredth.
mZX

Answers

Answer:

X = 81.20º

Step-by-step explanation:

sinX = opp/hyp

sinX = 84/85

X = arcsin(84/85)

use calculator

X = 81.20º

Please take a look at the picture.

Answers

Answer:

Should be b-1

Step-by-step explanation:

because b is at a positive point and it should become a negative

B-1 is the answer hopefully you got got it submitted and corrected

Plz help me well mark brainliest! Only if u are right!

Answers

Answer:

[tex]x=-6\frac{1}{2}[/tex]

Step-by-step explanation:

I hope this help you

Answer:

B. x = -6 1/2

Step-by-step explanation:

13 3/4 + x = 7 1/4

55/4 + x = 29/4

x = -26/4 ~ -6 1/2

find the quotient please

Answers

the answer is C, hope this helps

The table below shows the number of classes offered at a fine arts school in New York.
Art: 45
Dance: 30
Music: 40
Theater: 35
What part-to-whole ratio represents the number of music classes offered at the school? ​

Answers

Answer:

40:140

Step-by-step explanation:

The explanation.is in the diagram above

Justin has $500 in a savings account at the beginning of the summer. He wants to have at least $300 in the account by the end of the summer. Justin withdraws $20 each week for food, clothes, and movie tickets. How many weeks (w) can Justin withdraw money from his account?

Answers

Answer:

10 weeks

Step-by-step explanation:

1 because 20 times 10 is 200 and if he starts with 500 then he can withdraw 20 dollars a week for 10 weeks to have 300 left by the end of the summer, hope this helps :)

here is the other question

Answers

Answer:

1. -3 × A1 + A2 --> B2

2. [tex]-\frac{1}{7}[/tex] × B2 --> C2

Step-by-step explanation:

1. -3 × A1 + A2 --> B2

(4x × -3) + 12x = -12x + 5x = -7x

(2y × -3) + 6y = -6y + 6y = 0y

(-10 × -3) + -9 = 30 - 9 = 21

2. [tex]-\frac{1}{7}[/tex] × B2 --> C2

-7x × [tex]-\frac{1}{7}[/tex] = 1x

21 × [tex]-\frac{1}{7}[/tex] = -3

Same process as last time

IF YOU HELP ME WITH THIS YOU ARE AUTOMATICALLY MY FAVORITE PERSON
Determine the intercept of the line
Y-intercept ( , )
X- intercept ( , )

Answers

Answer:

Y-intercept: (0, 2.5)

X-intercept: (3.5, 0)

the numbers one through 10 are written on individual cards and place in a bag. If you reach into the bag to pull out card what is the probability that it will be a 7​

Answers

Answer:

1 in 10 chance

Step-by-step explanation:

There are 10 cards, so since you reach into the bag and pull out only 1 card, there is a 1 in 10 chance.

how do you do this?? could you kindly include your work pls..

Answers

Answer:

B.  0.

Step-by-step explanation:

(x + 2y)dy/dx = 2x - y

dy/dx = (2x -y)/(x + 2y)

Using implicit differentiation and the Quotient Rule:

d^2y/dx^2 =  (x + 2y)(2 - y*dy/dx) - ((2x - y)(1 + 2y*dy/dx)) / (x + 2y)^2

At the point (3, 0), dy/dx = (6-0)/(3 + 2(0)) = 2.

So substituting in d^2y/dx^2, we have:

(3 + 0)(2 - 0) - (6-0)(1 + 2(0))/  (3+0)^2

= (6 -  6) / 9

= 0.

write an equation to represent CJ’s total pay

Answers

Answer:

P = 15h

I hope it helps.

If the area of rectangular plot is 200 cm and its length is 10 m. find out its breadth.​

Answers

Answer:

The area of a rectangle is A=l x w.

So, 200=10 x w

Divide both sides by 10.

20 = w

The width of the rectangle is 20 m.

:)

In a raffle 1000 tickets are being sold, at $1 each. The first prize is $100, and there are 3 second prizes of $50 each. How much does the price of the ticket exceed the expected value

Answers

Answer:

The price of of the ticket exceeds its value by $ .75

Which repression is equivalent to:
(Picture)

Answers

Answer:

sry I just wanted the points I'm in middle school so I don't know this stuff either but can you give free brainlyest I'm soo close to my next rank I'd really appreciate it if you would

Kelly sells 62 shares of stock she owns for a total of $433. If the stock was in two different companies, one selling at $6.50 a share and the other at $7.25 a share, how many of each did she sell?

Answers

Answer:

s = 40 shares (# of 7.25 shares)

x = 22 shares (# of 6.50 shares)

Step-by-step explanation:

Quantity Equation:: x + s = 62 shares

Value Equation::: 6.50x+7.25s = 433 dollars

---------------------------

Modify for elimination:

6.5x + 6.5s = 6.5*62

6.5x + 7.25s= 433

-----------------------------

Subtract and solve for "s":

0.75s = 30

-----

s = 40 shares (# of 7.25 shares)

x = 22 shares (# of 6.50 shares)

Hope this helps

Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. According to a 2017 large-scale study of elderly ICU patients, the average length of stay in the ICU is 3.4 days (Critical Care Medicine journal article). Assume that this length of stay in the ICU has an exponential distribution. Do not round intermediate calculations.

a. What is the probability that the length of stay in the ICU is one day or less (to 4 decimals)?

b. What is the probability that the length of stay in the ICU is between two and three days (to 4 decimals)?

c. What is the probability that the length of stay in the ICU is more than five days (to 4 decimals)?

Answers

Using the exponential distribution, it is found that there is a:

a) 0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.

b) 0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.

c) 0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:  

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:  

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = e^{-\mu x}[/tex]

In this problem, the mean is of 3.4 days, hence, the decay parameter is:

[tex]\mu = \frac{1}{3.4}[/tex]

Item a:

[tex]P(X \leq 1) = 1 - e^{-\frac{1}{3.4}} = 0.2548[/tex]

0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.

Item b:

[tex]P(X \leq 2) = 1 - e^{-\frac{2}{3.4}} = 0.4447[/tex]

[tex]P(X \leq 3) = 1 - e^{-\frac{3}{3.4}} = 0.5862[/tex]

[tex]P(2 \leq X \leq 3) = 0.5862 - 0.4447 = 0.1415[/tex]

0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.

Item c:

[tex]P(X > 5) = e^{-\frac{5}{3.4}} = 0.2298[/tex]

0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.

A similar problem is given at https://brainly.com/question/17039711

If 20% of a number is 28 and 25% of the same number is 35, find 45% of that number.

Answers

answer: 63
explanation: 20% + 25% = 45% and 20%= 28
25%= 35
thus, 28 + 35 = 45% = 63

It is 30 miles into the town. Use the formula to work out how many km this is

Answers

Answer:

30*1.609=48.27

Hope This Helps!!!

Rewrite 2/9+5/12 with a common denominator.

Answers

Step-by-step explanation:

direct add the upper both numerator and bottom both denominator ,Then you will get the answer,Then reduce it to lowest form

sorry for bad english

edit:Wrong answer

2/9 + 5/12

LCM = 36

=》2/9 = 2×4/9×4 = 8/36

=》5/12 = 5×3/12×3 = 15/36

2/9 + 5/12

= 8/36 + 15/36 (LCM = 36)

= 23/36 -----> 2/9 + 5/12 with a common denominator.

________

Hope it helps ⚜

32 is 40 percent of what number? A 12.8 B 128 C 114 D 124​

Answers

Answer: C

.Step-by-step explanation:

it was right for me so if its wrong im sorry :)

A nutrition company is marketing a low-calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories. Determine how many calories 14 brownies would have. Round to the nearest calorie

Answers

14 brownies would have about 233.0 calories

The number of calories in 14 brownies is 233 calories.

The first step is to determine the average calorie in 1 brownie.

Average calorie = 50 calories / 3 = 16.667 calories

In order to determine the number of calories in 14 brownies, multiply the average calorie by 14 brownies.

Total calories = 16.67 x 14 = 233 calories

A similar question was answered here: https://brainly.com/question/15420908

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