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
The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss a
TiliK225 [7]
The wind chill equations I have found are more complicated than that.

7 0
3 years ago
Read 2 more answers
Factor f(x)=-20x^2 +23x -6
azamat
34 Squared, I think if im wrong im very sorry
8 0
3 years ago
What is m-a = n+p, for a
sergeinik [125]

Answer:

A=m-n-p

Step-by-step explanation:

So solve for a, we have to isolate it on one side, so -a=n+p-m. So a=m-n-p

5 0
3 years ago
Read 2 more answers
PLS HELP ME ASAP FOR 12 AND 14!! (MUST SHOW WORK!!) + LOTS OF POINTS!!
nignag [31]
R for ?
14) 96x1=24r
       96=24r
       r= 4 
5 0
3 years ago
Read 2 more answers
Identify the initial amount a and the decay factor b in the exponential function. y equals 5 times 0.5 superscript x
Ber [7]
\bf \qquad \textit{Amount for Exponential Decay}
\\\\
A=a(b)^x\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
a=\textit{initial amount}\\
b=\textit{decay factor}\\
x=\textit{elapsed time}\\
\end{cases}
\\\\\\
y=\stackrel{a}{5}(\stackrel{b}{0.5})^x
7 0
3 years ago
Other questions:
  • I NEED HELP ASAP PLEASE
    5·2 answers
  • Ben spends 5/8 of his pocket money . He has £1.20 left.<br> How much pocket mone did Ben get?
    12·1 answer
  • Which is one of the transformations applied to the graph of <img src="https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2" id="TexFormula1"
    5·1 answer
  • If 2+3=1 , 4+5=63 , 6+8=48 , then ,3+7=??
    14·1 answer
  • Plzzz help me do this :-)​
    10·1 answer
  • The local newspaper has letters to the editor from 70 people. If this number represents 2​% of all of the​ newspaper's readers,
    12·1 answer
  • Need help ASAP! Thanks :)
    6·1 answer
  • A theme is
    11·2 answers
  • 0+0???????????? ??????
    10·1 answer
  • Mr. Ramirez purchased 20 concert tickets for a total of $225. The concert tickets cost $15 for adults and $10 for children under
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!