ank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentrationof 0.5 pounds of salt per gallon of water is pumped into tank A at the rate of 4 gallons per minute.The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute.The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallonsper minute, and the solution from tank B is also pumped out of the system at the rate of 4 gallons perminute. Find the differential equations with initial conditions for the amounts,x(t)andy(t), of saltin tanks A and B, respectively, at time t.

Answers

Answer 1

Answer:

[tex]\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}[/tex]

[tex]\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}[/tex]

x(0)=20,y(0)=5

Step-by-step explanation:

We are given that

Tank A contains water=80 gallons

x(0)=20,y(0)=5

Tank B contains water=30 gallons

Rate=4 gallon/min

Concentration of salt  is pumped into tank=0.5 pound /gallon of water

Solution pumped from tank A to tank B at the rate=6 gallons/min

Solution pumped from tank B to tank A at the rate=2gallon/min

Solution from tank B is pumped out of the system at the rate=4 gallon/min

We have to find the DE at time t

For x

Rate in=[tex]0.5\times 4+y(t)/30\times 2[/tex]

Rate in=[tex]2+y/15[/tex]

Rate out=[tex]x/80\times 6[/tex]

Rate out=3x/40[/tex]

[tex]\frac{dx}{dt}=[/tex]Rate in-Rate out

[tex]\frac{dx}{dt}=2+y/15-3x/40[/tex]

[tex]\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}[/tex]

For y

Rate in=[tex]x/80\times 6[/tex]

Rate in=3/40x

Rate out=[tex]y/30\times (4+2)[/tex]

Rate out=y/5

[tex]\frac{dy}{dt}=[/tex]Rate in-Rate out

[tex]\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}[/tex]


Related Questions

Bebe's Bakery can bake 175 loaves of bread in 5 hours as shown on the double number line diagram below. 5 Number of Hours Loaves of Bread 175 At that rate, how many loaves of bread can Bebe's Bakery bake in 8 hours? A. 35 loaves B. 240 loaves C. 280 loaves D. 350 loaves​

Answers

Answer:

double number line diagram below. 5 Number of Hours Loaves of Bread 175 At Bakery bake in 8 hours? A. 35 loaves B. 240 loaves

Step-by-step explanation:

a. y = 3x + 1 and x + y = 5
How do you solve this?

Answers

The first on is X= -1/3 and the second on is might be 5 but I am not sure also I may not be 100% but I think iits right hope it helped

Answer:

Step-by-step explanation:

x + y = 5

y = 3x + 1

x + 3x + 1 = 5

4x + 1 = 5

4x = 4

x = 1

1 + y = 5

y = 4

(1, 4)

PLZZZZ HELPP ASAP!!! In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at least one of the number cubes. Make a list of all the different possible outcomes when two number cubes are rolled. What fraction of the possible outcomes is favorable? Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain. Answer:

Answers

Hey there!

You should not expect more than 34 times to be favorable, because favorable outcomes are about 28% of outcomes, and 28% of 100 is 28, which is less than 34.

6/21 outcomes will be favorable.

Here is a list of all possible out comes:

1 - 1

1 - 2

1 - 3

1 - 4

1 - 5

1 - 6

2 - 2

2 - 3

2 - 4

2 - 5

2 - 6

3 - 3

3 - 4

3 - 5

3 - 6

4 - 4

4 - 5

4 - 6

5 - 5

5 - 6

6 - 6

The underlined ones have one or two 3's in their outcome. There are 21 outcomes total, and 6 of them have 3's in them. We will find the percentage by doing 6/21 = .286, or 28.6%. This means that for every 100 outcomes, you should expect about 29 of them to be favorable.

I hope it helps and have an amazing day! You've got this!

Which expression is equivalent to -3/4(1/5-1/8

Answers

Answer:

11/40

Step-by-step explanation:

Simplify: 14 + 3k = 6k - 7k


4k = 14


14 = -k


k = 14


4k = -14

Answers

Simplified it is 4k = -14

The table shows the temperature (y) at different altitudes (x), This is a linear relation ship. Use the equation y= -0.004x+69 to determine the temperature at an altitude of 5,000 feet.

Answers

Answer:

49

Step-by-step explanation:

i just did it

Sharon bought 6 new folders for $1.15 each and 15 pens that were priced at 5 for $4.75. What is the total amount she spent?

Answers

Answer:

$21.15

Step-by-step explanation:

6 x 1.15 = 6.9 (because we're working with money, we'll add a zero at the end for the ones place) = 6.90

15/5 = 3 then 3 x 4.75= 14.25

14.25 + 6.90 = 21.15

Hope this helped <3

Answer:

$21.15

Step-by-step explanation:

Total Folder Amount: $1.15 • 6 = $6.90

Total Pen Amount: $4.75 • 3* = $14.25

*She bought 15 pens. The pens were 5 pens for $4.75. 15÷5=3*

$14.25 + $6.90 = $21.15

12x-20=n(3x-5) plzzzz help fast

Answers

Answer:

n=4 x=4

Step-by-step explanation:

3-5 = -2

12-20 = -8

find their what they have in common = 4

12·4= 48

3·4= 12

rearrange = 48-20 = n (12-5)

we should end up with 28 = n · 7

now we just need to figure out what ? · 7 = 28 which is 4

n = 4

I'm not sure if I did this correctly but I hope it helps

pls i need help due tonight

Answers

Answer:

-3/4

Step-by-step explanation:

-1 1/4 = -5/4

1/2 = 2/4

-5 + 2 = -3

-3/4

Answer: The answer is -3/4

Step-by-step explanation: covert the mixed numbers to improper fractions, then find the LCD and combine.

integers between -9 and -2

Answers

Answer:

Step-by-step explanation:

the integers are -8,-7,-6,-5,-4,-3,

Please help me....................

Answers

Answer:

B = 43°

a = 44.7

c = 53.3

Step-by-step explanation:

✔️B = 180° - (90° + 47°) (sum of interior angles of a ∆)

B = 180 - 137

B = 43°

✔️Use trigonometric ratio formula to find a:

reference angle = 47°

Opposite = a

Adjacent = 29

Thus,

tan 47 = a/29

Multiply both sides by 29

29*tan 57 = a

44.7 = a

a = 44.7 (nearest tenth)

✔️Use trigonometric ratio formula to find a:

reference angle = 47°

Opposite = a = 44.7

Hypotenuse = c

Thus,

Sin 47 = 44.7/c

Multiply both sides by c

c*sin 57 = 44.7

Divide both sides by sin 57

c = 44.7/sin 57

c = 53.3 (nearest tenth)

Find the values of x and y.

Answers

Answer:

x = 20 (degrees)

y = 70 (degrees)

Step-by-step explanation:

The angle adjacent to the one labeled 40° is supplementary, so it would measure 140°. And the obtuse triangle is an isosceles, which means that x is half of 180° - 140°, so x = 1/2(40°) = 20°

To find y, subtract 90° and x from 180°

y = 180° - 90° - 20°

y = 70°

Answer:

x = 20 and y = 70

Step-by-step explanation:

x = 20 and y = 70

How are the hypotenuse and legs of a right triangle related?

Answers

Answer:

The sum of the legs is equal to the hypotenuse.

Step-by-step explanation:

I hope that this helps u..

Answer:

The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the hypotenuse (side c in the figure). The sides and the adjacent to the right angle are called legs (or catheti, singular: cathetus).

Solve -2a - 5 > 3
Which graph shows solutions
I-Ready diagnostic

Answers

Answer:

Step-by-step explanation:

Here you go mate

Step 1

-2a-5>3  Equation/Question

Step 2

-2a-5>3  Simplify

-2a-5>3

Step 3

-2a-5>3  Divide

answer

a<-4

Hope this helps

Natalie has 16 close friends. How many ways can she choose 5 to E
bridesmaids in her wedding?

Answers

Answer:

80 ways

Step-by-step explanation:

You just miltiply 16 by 5 and you get your answer. Hope this helps!!!!!

Please help me ASAP........

Answers

Answer:

More on supplies than she earned in sales.

Answer:

She spent 25 dollars from her pocket. No profit

Step-by-step explanation:

EASY WORK!!! Please look at the picture and yes it’s easy for other people but not for me .

Answers

Answer:

#8 --->      1/4  2/5  1/2  3/5  

#9 --->      6 3/8    6 1/2   6 3/4   6 5/6

#10 --->    1.75 feet is the longest

the other lengths are 1.58 ft. and 1.67 ft.

Step-by-step explanation:

good luck!

it's easy if you turn them into decimals.

to do that, you just divide the numerator (top number) by the denominator (bottom number).

e.i.   1/4= .25  (25%)

       1/2= .5   (50%)

       3/5= .6    (60%)

Answer:

8. 1/4, 2/5, 1/2, 3/5

9. 6 3/8, 6 1/2, 6 3/4, 6 5/6

10. the length of the longest bar is 1.75 feet

Step-by-step explanation:

(just convert all the fractions to decimal, it will be easier for you to do!)

8.

3/5 = 0.6

1/4 = 0.25

1/2 = 0.5

2/5 = 0.4

9.

6 3/4 = 6.75

6 1/2 = 6.5

6 5/6 = 6.83

6 3/8 = 6.375

10.

1 7/12 = 1.583

1 2/3 = 1.6 or 1.7

Ryan has two jobs. He earns $9 per hour for x hours babysitting his cousins and he earns $18 per hour for y hours working at the coffee shop. Ryan will work both jobs. He is able to work no more than 10 hours a week, due to school commitments. Ryan wants to earn at least $72 a week, working a combination of both jobs.

Answers

Answer:

Umm I don't think you wrote out the whole question...

Step-by-step explanation:

$18 nine hours, $9 one hour = $177

$18 eight hours, $9 two hours = $162

$18 seven hours, $9 three hours = $153

$18 six hours, $9 four hours = $144

$18 five hours, $9 five hours = $135

$18 four hours, $9 six hours = $126

$18 three hours, $9 seven hours = $117

$18 two hours, $9 eight hours = $108

$18 one hour, $9 nine hours = $99


If s= 6 inches, and the altitude, h, is 21 inches, what is the volume of the pyramid?

Answers

Answer: 42 inches

Step-by-step explanation:

To find the volume you multiply 1/3 of the base which is 6 then with 1/3 is 2 them multiply the altitude which is 21. So 2 times 21 is 42 inches

Answer:

The volume of the pyramid is 42 inches³.

Step-by-step explanation:

The formula is V = ⅓ A H. 6x21=126, 126x1/3=42.

I I’m just going to quit brain lay because everyone here is just autistic
But if u steel wanna help me than it u can do these problems.
:/

Answers

Answer:

Read the part where it says; These raptors eat primarily flying insects, so they do most of their hunting on the wing.

Step-by-step explanation:

                            </3 PureBeauty

Which regression equation best fits these data ?

Answers

Answer:

C. [tex]y = -0.30\cdot x^{2}-0.48\cdot x+15.83[/tex]

Step-by-step explanation:

The best fit curve for the given set of points is the quadratic form, which is defined by:

[tex]y = A\cdot x^{2}+B\cdot x + C[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]A[/tex], [tex]B[/tex], [tex]C[/tex] - Coefficient.

The coefficient associated with the second-power component determines whether vertex is an absolute maximum or not. The vertex is an absolute maximum if and only if [tex]A < 0[/tex], otherwise it is an absolute minimum. From image we notice that resulting fit curve will have an absolute maximum, then [tex]A < 0[/tex]. Hence, the correct answer is C.

Answer: C

Step-by-step explanation:

If a pound of turkey costs ​$0.82, how much will n pounds​ cost?

Answers

$0.82n is the answer

2 people work together take 5 hours to lay floors. How many hours does it take for 6 people to lay floors

Answers

15 i think is correct

Answer:

It takes ( hours for 6 people to lay floors

Step-by-step explanation:

2=5 divide it and for one person it would take 1 1/2 so then times 1 1/2 by 6.

10 is what % of 50?
5 is what % of 50?
1 is what % of 50?
17 is what % of 50?

Answers

Answer:

10/50 X 100 = 20%

5/50 X 100 = 10%

1/50 X 100= 2%

17/50 X 100= 34%

Answer:

To calculate 10 percent of a number, simply divide it by 10 or move the decimal point one place to the left. To calculate 5 percent of a number, simply divide 10 percent of the number by 2. To find 1% of something (1/100 of something), divide by 100. For 17 is what % of 50 is hard. So maybe this is right? We need to multiply the decimal by the number we are finding the percentage of.

Step-by-step explanation:

10% is what % of 50?

Answer: 5%

5 is what % of 50?

Answer: 10

1 is what % of 50?

Answer: 2

17 is what % of 50?

Answer: 34

Hope this helps!

if I was 15 ft tall and I grew 17 yards how much have I grown​

Answers

Answer:

66 ft or 22 yards

Step-by-step explanation:

1 yard = 3 ft.

Convert 15 ft to yards (multiply by 3) and add 17.

A new car is purchased for 20000 dollars.The value of the cat depreciates at 12.5% per year.What will the value of the car be, to the nearest cent, after 11 years?

Answers

Answer:

$460.38

Step-by-step explanation:

Use the exponential decay formula, y = C(1 - r)^t

Plug in the original price, depreciation rate, and amount of time:

y = 20000(0.875)^11

y = 460.38

So, the car's value after 11 years will be $460.38

Pls help lol I’ve been stuck forever

Answers

I hope this helps...
i’m pretty sure x=13 :) have a good day

When plotting points on the coordinate plane
below, which point would lie on the x-axis?

(6,0)
(0, 2)
(3.8)
(5,5)

Answers

Answer:

(6,0)

Step-by-step explanation:

I will give brainiest to whoever answers correctly !!

Answers

The mark up in the price of the fish dinner is around 50.31%.

Arthur has a box which contains 6 black balls and n (n ≥ 2) white balls, then at random, he takes 3 balls from the box. If the probability of taking any ball is the same and Pₙ is the probability of taking 1 black ball and 2 white balls, what is the largest possible value for Pₙ?​

Answers

Answer:

11/68 or 0.1618

Step-by-step explanation:

Balls

Black - 6White - n

Options of getting 3 balls

1. White, black, black2. Black, white, black3. Black, black, white

Probability P(n) in each option

1. WBB

P(w) = 6/(n + 6)P(b1) = n/(n + 6 - 1) = n/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 1)

P(n) =

P(w)P(b1)(P(b2) = 6/(n+6) × n/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

2. BWB

P(b1) = n/(n + 6)P(w) = 6/(n + 6 - 1) = 6/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 4)

P(n) =

P(b1)P(w)(P(b2) = n/(n+6) × 6/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

3. BBW

P(b1) = n/(n + 6)P(b2) = (n - 1)/(n + 6 - 1) = (n - 1)/(n + 5)P(w) = 6/(n + 5 - 1) = 6/(n + 4)

P(n) =

P(b1)P(b2)(P(w) = n/(n+6) × (n - 1)/(n + 5) × 6/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)

Final equation is same for each case:

P(n) = 6n(n - 1) / (n + 6)(n + 5)(n + 4)

The easy way to find the maximum is to try the numbers or graph.

Both of the methods give the maximum integer n = 11 or n = 12

See attached graph

At both values n we get P(n):

P(11) = 6*11*10 / 15*16*17 = 11/68 = 0.1618 (rounded)P(12) = 6*12*11 / 16*17*18 = 11/68 = 0.1618 (rounded)
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