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
Sholpan [36]
3 years ago
8

A 250-gal tank is initially filled with brine (salt-water mixture) containing 100 lb of salt. Brine containing 3 lb of salt per

gallon enters the tank at the rate of 7 gal/s, and the well-mixed brine in the tank flows out at the rate of 9 gal/s. Find the amount x(t) of salt in the tank after 1 minute.
Mathematics
1 answer:
gulaghasi [49]3 years ago
5 0

Answer:

x(t) = 581.66 lb

Step-by-step explanation:

From the given information:

Consider the salt quantity in the tank at time t be x(t) lb.

∴ the rate of change of salt content in the tank is \dfrac{dx}{dt}= Rate \ of \  \ inflow - rate \ of \  \ outflow

where:

the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons

=21 lb/s

rate of outflow = salt conc. in the tank  × flow rate

= x/250 ×  9

= 9x/250  lb/s

∴

\dfrac{dx}{dt} = 21 - \dfrac{9x}{250}

\dfrac{dx}{dt} + \dfrac{9x}{250}= 21

This is a 1st order linear differentiation,

The integrating factor if e^{^{ \int \dfrac{9}{250}\ dt}} = e^{^{ \dfrac{9t}{250} }}

∴

e^{^{ \dfrac{9t }{250}}} \ \ x(t) = \int 21 e^{\dfrac{9t}{250}} \ dt + C

e^{^{ \dfrac{9t }{250}}} \ \ x(t) =  21 \times \dfrac{250}{9}e^{\dfrac{9t}{250}} + C

x(t) = \dfrac{1750}{3}+Ce^{^{\dfrac{-9t}{250}}}     at  t = (0) and x(0) = 100 lb

Hence;

100 = \dfrac{1750}{3}+C

C = \dfrac{1750}{3} -100

C = - \dfrac{1450}{3}

∴x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9t}{250}}}

after time t = 1 minute i.e 60 s

x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9 \times 60}{250}}}

x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-540}{250}}}

x(t) = 581.66 lb

You might be interested in
Joe is riding his bicycle. He rides for 3 hours at a speed of 4.8 kilometers per hour. For how many kilometers does he ride?
eduard

Answer:

14.4km

Step-by-step explanation:

<h2>Speed = distance / time </h2>
  • speed = 4.8 km/h
  • time = 3 hrs
  • distance = ?

Distance = speed  * time

Distance = 4.8 * 3 = 14.4km

5 0
2 years ago
50 w +100 is greater than or equal to 18000
Marrrta [24]
What you would do to “simplify” the equation is 18000-100 then divide by 50. The answer would be 358. Hoped this helped!
8 0
3 years ago
PLEASE HELP! ( no random links ) correct answers please. Find median
BARSIC [14]

Answer:

2

:) hope it helped!

3 0
3 years ago
A pyramid and a cone are both 8 centimeters tall and have the same volume.
Brrunno [24]

Answer:

Step-by-step explanation:

D

6 0
3 years ago
Read 2 more answers
K(t) = 10t - 19<br> k(-5) =
DanielleElmas [232]

Answer:

-69

Step-by-step explanation:

k(-5) = 10*-5 -19

= -50-19

=-69

6 0
3 years ago
Read 2 more answers
Other questions:
  • Look at the images please help
    14·1 answer
  • Using the greatest common factor for the terms, how can you write 56 + 32 as a product?
    7·1 answer
  • Simplify and show your work<br> -8 + 4i / 4 - 4i
    14·1 answer
  • Solve 3x-7=4+6+4x and show your work.<br> Is there one solution, infinite solutions, or no solution?
    14·2 answers
  • The height of a triangle is 2 less than 5 times its base. If the base of the triangle is xfeet, and the area is 12 square feet,
    14·1 answer
  • A band must pay a $2500 entrance fee, It will split the cost between its 25 members. How much will each member pay?
    14·2 answers
  • Susannah made the line plot below to show the distances she hiked each day in the past two weeks.
    9·2 answers
  • Last year, 210 middle school students
    13·1 answer
  • The standard unit for measuring mass is the
    14·1 answer
  • Please solve the first three question with explanation ​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!