1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dusya [7]
2 years ago
8

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.
Mathematics
1 answer:
adell [148]2 years ago
8 0

Answer:

\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}

\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}

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=0.5\times 4+y(t)/30\times 2

Rate in=2+y/15

Rate out=x/80\times 6

Rate out=3x/40[/tex]

\frac{dx}{dt}=Rate in-Rate out

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

\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}

For y

Rate in=x/80\times 6

Rate in=3/40x

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

Rate out=y/5

\frac{dy}{dt}=Rate in-Rate out

\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}

You might be interested in
Helppp meh please please
Hitman42 [59]
Lol your a little kid but hold on
3 0
3 years ago
Read 2 more answers
Which of the following expressions is always equivalent to -2b + 4 + 4b - 7
spayn [35]

Answer:

c. 2b - 3

Step-by-step explanation:

Simplify the following:

-2 b + 4 + 4 b - 7

Grouping like terms, -2 b + 4 + 4 b - 7 = (4 b - 2 b) + (4 - 7):

(4 b - 2 b) + (4 - 7)

4 b - 2 b = 2 b:

2 b + (4 - 7)

4 - 7 = -3:

Answer:  2 b + -3

3 0
3 years ago
Read 2 more answers
I need help ASAP please
77julia77 [94]

Answer:

360

Step-by-step explanation:

Volume of a rectangle is length times width times height

5 0
2 years ago
Please help!! A. 170 B. 205 C. 230 D. 105
Damm [24]

Answer:

D. 105

Step-by-step explanation:

500-270, there's 230 total 2 head.

270-100 of one head, is 170 purple one head. 170+125 purple equals 295.

296 subtract from 500 total is 205 for total green.

205-100, 105 2 head.

8 0
2 years ago
Pls help ASAP ASAP ASAAPAPIAJNJ
s2008m [1.1K]
Gas cause when water evaporates it turned into air :)
8 0
3 years ago
Other questions:
  • PLEASE SOMEONE HELP ME ON THIS ! 30 points
    9·1 answer
  • What is the pattern in these numbers? Please explain
    9·1 answer
  • You owe your sister $5.35, and she lends you another $4.50, how much do you owe her now
    11·1 answer
  • A computer chip has dimensions of 8mm x 8mm. the scale drawing shows 4cm by 4cm. the answer is 1cm represents 2mm but I don't kn
    10·1 answer
  • What is x in the equation 3x=9
    11·2 answers
  • Which equation could be represented by 5 divided by 1/2 = 10
    10·2 answers
  • A recent study reported that the prevalence of hyperlipidemia (defined as total cholesterol over 200) is 30% in children 2-6 yea
    9·1 answer
  • Find the value of x.
    12·2 answers
  • On a bicycle trail, the city is painting arrows like the one shown below: Upper pointing arrow with height of 11 and length of 9
    8·1 answer
  • Which function is shown in the graph?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!