A tank contains 210 liters of fluid in which 30 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t.

Answers

Answer 1

Answer:

[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min

Step-by-step explanation:

The mass flow rate dA(t)/dt = mass flowing in - mass flowing out

Since water is pumped in at a rate of 3 L/min, and it contains no salt, the concentration in is thus 0 g/L. the mass flow in is thus 0 g/L × 3 L/min = 0 g/min.

Let A(t) be the mass present at any time, t. The concentration at any time ,t is thus A(t)/volume = A(t)/210. Since water flows out at a rate of 3 L/min, the mass flow out is thus, A(t)/210 g/L × 3 L/min = A(t)/70 g/min.

So, dA(t)/dt = mass flowing in - mass flowing out

dA(t)/dt = 0 g/min - A(t)/70 g/min

dA(t)/dt =  - A(t)/70 g/min

 Since the tank initially contains 30 g of salt, the initial mass of salt in the tank is 30 g. So A(0) = 30

So, the initial value problem is thus  

dA(t)/dt =  - A(t)/70 , A(0) = 30

Separating the variables, we have

dA(t)/A(t) = -dt/70

Integrating both sides, we have

∫dA(t)/A(t) = ∫-dt/70

㏑A(t) = -t/70 + C

taking exponents of both sides, we have

A(t) = exp(-t/70 + C)

A(t) = exp(-t/70)expC

[tex]A(t) = e^{-t/70}e^{C}\\A(t) = Ce^{-t/70} whereC = e^{C}[/tex]

A(0) = 30, So

[tex]A(0) = Ce^{-0/70}\\30 = Ce^{0}\\C = 30[/tex]

[tex]A(t) = 30e^{-t/70}[/tex]

The rate at which the number of grams of salt in the tank is changing at time t is

[tex]dA(t)/dt = \frac{d30e^{-t/70} }{dt} \\dA(t)/dt = -\frac{30e^{-t/70} }{70}\\dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex]

So, the rate at which the number of grams of salt in the tank is changing at time t is

[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min


Related Questions


When Joe solved a system using substitution, he got 7 = 9. What can Joe
conclude? *
The solution to the system is (7.9).
The system of equations does not have a solution,
The work must be incorrect because it is not possible to get this equation
The system of equations has infinitely many solutions,

Answers

Answer:

The system of equations does not have a solution

Step-by-step explanation:

Whenever you get a number = a different number, that means there's no solution.

5th grade math. correct answer will be marked brainliest. what are the last 2 boxes?

Answers

Answer:

you forgot (2,28) :)

Step-by-step explanation:

the answer should be (5,37)

Can someone explain the washer method in calculus and help me solve this problem?

Answers

Answer:

Step-by-step explanation:

Is my Answers Correct? Very easy Question!

Answers

Answer:

Step-by-step explanation:

Correct

Step-by-step explanation:

the 5th one on the right is standard form,

the second one is perfect square form.

A single six-sided die is rolled. Find the probability of rolling a seven.

Answers

Answer: there is no probability to roling a 7

Step-by-step explanation: there are  only 6 sides to the die that is rolled

What is the answer to -5+(-5r)+10

Answers

Answer:

=−5r+5

Step-by-step explanation:

Let's simplify step-by-step.

−5−5r+10

=−5+−5r+10

Combine Like Terms:

=−5+−5r+10

=(−5r)+(−5+10)

=−5r+5

Answer: -5r+5

Step-by-step explanation: 1rst: Eliminate redundant parentheses

                                               -5+(-5r)+10

                                               -5-5r+10

                                             2nd: Add the numbers

                                                -5-5r+10

                                                5-5r

                                             3rd: Rearrange terms

                                                5-5r

                                                -5r+5

Please!!!!! help!!!!!

Answers

Answer:

x = 6, x = 8, and x = 10

Step-by-step explanation:

Since 44 > 35, that means that

[tex]2x + 3 > x + 8\\x + 3 > 8\\x > 5[/tex]

so that means the ones that work are x = 6, x = 8, and x = 10

Show how you found the slope and y-intercept

Answers

Answer:

Slope: [tex]\frac{5}{2}[/tex]

y-intercept: 0

Step-by-step explanation:

First, find the slope. Use two points given to you. In this case, I will use the following:

(x₁ , y₁) = (2 , 5)

(x₂ , y₂) = (4 , 10)

Use the following equation:

slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the corresponding numbers to the corresponding variables:

slope (m) = [tex]\frac{10 - 5}{4 - 2}[/tex] = [tex]\frac{5}{2}[/tex]

Note the slope intercept form:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

Plug in the slope into m for the equation:

[tex]y = \frac{5}{2} x + b[/tex]

Choose a point to use to find b. In this case, I will use (2 , 5). Plug in 2 for x, and 5 for y:

[tex]5 = \frac{5}{2}(2) + b[/tex]

Simplify. Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other:

[tex]5 = \frac{5}{2}(2) + b\\5 = 5 + b\\5 (-5) = 5 (-5) + b\\b = 5 - 5\\b = 0[/tex]

Y-intercept: 0

Which phrase best describes the relationship indicates by the scatter plotting?​

Answers

Answer:B

Step-by-step explanation:

When 6 is added to four times a number, the result is 50​

Answers

x=the number
4x+6=-50
4x=-50-6
4x=-56
x=-56/4
x=-14

Answer:

50-6= 54

54÷4= 13.5

editing for clarity.

first you subtract the 6 from the 50 to find out what the "4 times a number" came to.

in this case, 50-6, which equals 54.

then, you divide the 54 by 4 to get 13.5.

so, the whole math problem would be

4 times 13.5 plus 6 equals 50.

A bus can hold a total of 60 students. The bus is 73% full how many students are on the bus?​

Answers

Answer:

44

Step-by-step explanation:

so youre looking for 73% of students rite? of means multiplication , you just times 73% by 60

73%*60=43.8

but there cant be point 8 of a person unless theyre missin a couple limbs, so you round up to 44!

hope it helps :)

44
---------------------

There are 4 oranges, 7 bananas, and 5 apples in a fruit basket.
Ignacio selects a piece of fruit at random and then Terrance
selects a piece of fruit at random.

probability of two bananas
p( two bananas )​

Answers

                                                                                                                                                   

                                                                                                                       .hnsxasy543esx nuyAtre

Please help I'm confused with what to put in those boxes

Answers

It is asking how many layers which is 5 because in order to build it it went up 5
and the numbers in each layer is 3 going across

in a classroom 1/6 of the students are wearing blue shirts and 2/3 of wearing white shirts there are 36 students in the class how many students are wearing blue shirts​

Answers

Answer:

6 students are wearing blue shirts

Step-by-step explanation:

you divide 36 by 6 and that equals 1/6 of the students.

Factorise
7lm - 21lmn​

Answers

Answer:

7lm - 21lmn

taking common 7lm

7lm(1-3n)

u={1,2,3,4,5,6,7,8,9}
a={2,4,6,8}
b={3,6,9}

What is the set AUB?

Answers

Answer:

AUB = {2,3,4,6,8,9}

Step-by-step explanation:

The set u should not be included in set AUB

Laura had a toy robot collection. 4/7 of her 28 robots make noise. How many of Laura’s robots make noise? If you guys answer can you please do show you work.

Answers

Answer:

4/7 of 28 robots is 16.

Step-by-step explanation:

This is because 4/7 is equal to 16/28 when you simplify it. multiply 7 by four and you get 28 as your denominator and 16 as your numerator.

Please Help me, what the answer

Answers

It’s either 1. Or 2. I’m really not sure which one tho so sorry! There’s not enough information given but if I had to guesstimate I would say 1.

Answer and explain ILL MARK BRAINLIEST I DONT UNDERSTAND

Answers

First let's reduce the feet to miles

there are 5280 feet in a mile therefore

26400 feet=5 miles

31680 feet=6 miles

Jet A(the first jet) descends 5 miles in 96 miles

Jet B(the second jet) descends 6 miles in 120 miles

We can compare these as fractions to see which is steeper. This can be viewed as slope and the origin (0,0) is the airport.

slope: 6/120=?=5/96

1/20=?=5/96

Now we know that 5/100 =1/20 so 5/96 must be bigger than 5/100 because you are dividing by a smaller number.

so 1/20<5/96

So Jet B is descending steeper than Jet A.

As for linear model, I don't exactly know what your teacher means but I think I actually used the linear model when I'm thinking of steepness as slope in the coordinate plane, I will include a picture.

In this extremely zoomed out graph, you can see the blue line is just slighly higher than the red line(slope as in explanation is way easier to tell) this could be seen as the linear model) :) Hope it helped!

Please Help. Will give Brainliest.

Answers

Answer:

translation.........

What is the measure of angle A?
Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth.

Answers

Answer: 45 degrees

Step-by-step explanation:

Answer is 45 degrees

Barbara charges $3.50, plus $2.25 for each hour she babysits. If Barbara charges $21.50, how many hours does she babysit?

Answers

Answer:

8 hours

Step-by-step explanation:

The equation is 2.25X + 3.50 = 21.50

X represents the unknown amount of hours she worked. 2.25 is the cost per hour. 3.50 is the fee she charges for every gig. That fee only happens once a gig so naturally it wasn't the number x was placed with.

2.25X + 3.50 = 21.50

2.25X + 3.50 - 3.50 = 21.50 - 3.50

2.25X = 18

2.25X = 18

2.25 2.25

X = 8

NEEd help quickly please!!! The basketball game had 500 people in attendance. If the ratio of Pioneer fans to Lion fans is 15:5, how many MORE Pioneer fans were there? Pls use tape diagram.

Answers

Answer:

Step-by-step explanation:

15(500/20)-5(500/20)

375-125

250

There were 250 more Pioneer fans than Lion fans.

They boost the economy

Answers

Answer:

I think the question is incorrect

Step-by-step explanation:

they boost the economy why is this in mathematics

‍♀️‍♀️

PLS HELP I DONT KNOW THIS ONE ITS URGENT

Answers

Answer:

A. [tex] \frac{UV}{VW} = \frac{ZY}{YX} [/tex]

Step-by-step explanation:

WX, VY, and UZ are parrelel to each other, therefore, base on triangle proportional theorem, the two transversal lines are divided proportionally by the 3 parallel lines.

Thus, we would have the following equation which is true:

[tex] \frac{UV}{VW} = \frac{ZY}{YX} [/tex]

I cut a pizza in half. Then I cut each half into 3 equal pieces and each piece into 2 equal slices. I sold 6 slices. What fraction of the pizza did I sell?​

Answers

Answer:

6/12

Step-by-step explanation:

im pretty sure, i did it on a paper correct me if im wrong sorry if i am

A polynomial function has zeros at 5/2 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function in standard form that could represent this function

Answers

Answer:

-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7

Step-by-step explanation:

[tex](x-5/2)^{2}(x-3)(x-0)^4 =0\\(2x-5)^{2}(x-3)(x)^4 =0[/tex]

Expand and get

-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7

The standard form will be  [tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]

What will be the standard form of the given expression?

The given expression is

[tex](x-\dfrac{5}{2})^2(x-1)^2(x-0)^4=0[/tex]

[tex](x^2-5x+\frac{25}{4} )(x^2-2x+1)(x^4)=0[/tex]

[tex](x^4-2x^3+x^2-5x^3+10x^2-5x+\dfrac{25x^2}{4} -\dfrac{50}{4} x+\dfrac{25}{4} ) x^4=0[/tex]

[tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]

Thus the standard form will be  

[tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]

To know more about Polynomials follow

https://brainly.com/question/15702527

Use the bar graph to find the probability of the event

Not spinning a 1

Answers

10+8 you add all the data to get your answer

Look at the image. Could someone please help me out? Only question B Thank you! WILL GIVE BRAINLYEST​

Answers

Answer:

y = 3

Step-by-step explanation:

2x+6y=5x+4y   if x=2

2(2)+6y=5(2)+4y

4+6y=10+4y

-4     =-4

6y=6+4y

-4y=   -4y

2y=6

/2=/2

y=3

HELPPPPP PLSSSSSS !!!!!!!


Charmaine is having a party. She'll have 4 tables for every 8 guests. Complete the table below showing the number of tables and the number of guests​

Answers

Answer:

Top is 18, Bottom goes 6 for 12, then 7 for 14, then 10 for 20

Step-by-step explanation:

2 guests = 1 table

Divide 8 and 4
Which would be 2 so 2 people for table
Other Questions
Which type of public policy is the following policy? Government issues a tariff on foreign goods. A. Domestic Policy B. Foreign Policy D. Not A Public Policy C. Both Domestic and Foreign Show work please for brainly? HEEEEEEEEEELP! ASAP Find the missing value.Hint: Use the number line to find the missing value.4 =-2 + HELP WITH A THESIS STATEMENTI basically need a thesis statement on how DNA analysis relates to chemistry. The only problem is that I'm having trouble making it 'arguable'. My ideas were:-DNA analysis relates to chemistry because it applies that knowledge when analyzing the DNA samples left at crime scenes in order to identify the suspect.-DNA analysis relates to chemistry because it's a subcategory of chemistry, also known as forensic chemistry, where DNA left at crime scenes is analyzed to potentially link a suspect to a crime.Do either of these sound good and are they arguable? If not can you reword it to be? ...............................................................So help. Below is the number of minutes Leo played during each of his six basketball games,17.50, 23.00, 24.00,9.00, 12.25, 14.75Using the data, create a histogram. What effect do you think possession of the atomic bomb will have on the role ofthe US in the postwar world? plz plz hury plz hury plz plz Joe is 6 feet tall and cast a 3 foot shadow. He is standing next to a building that cast a shadow that is 20 feet long. How tall is the building. how do I say Christmas in German Find the annual interest rate. $I=\$160$ , $P=\$2000$ , $t=8$ months The annual interest rate is %. please help me !!! i'll give brainliest Writeusing eighths.1/2 +1/4 using eights This one is hard. Civil war questions but they need to be made up like what ifs Can someone please help me... por qu se deca que el chiquillo era certero al responderpgina 102 espaol 6to What the purpose of the adjective part of speech in a sentence Find the value of x. how many solutions does the system have ? ( y=3x + 2 ( y=3x + 6 Which of the following statements about research paper theses is FALSE?A. A thesis statements states the issue to be discussed throughout the research paper.B. The thesis appears in the first paragraph of a research paper.C. Once a thesis statements is decided it is final and should not be changed in any way.D A thesis statement is supported by evidence throughout the paper.Please select the best answer from the choices provided