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
posledela
3 years ago
8

6. A tank contains 100-gallon of pure water. At time t = 0, a solution containing 2 lb of salt per gallon flows into the tank at

a rate of 3 gallons per minute, and the well-stirred mixture flows out at a rate of 4 gallons per minute. Find the amount (in lb) of salt Q in the solution as a function of t in minutes.
Mathematics
1 answer:
SOVA2 [1]3 years ago
7 0

Answer:

The answer is below

Step-by-step explanation:

Let Q represent the amount of salt in the tank at time t.

\frac{dQ}{dt}= flow\ in - flow\ out\\ \\flow\ in=3\ gal/min*2\ lb/gal=6\ lb/min\\\\net\ gain\ in\ tank\ volume=3-4=-1, henceflow\ out= \frac{4Q}{100-t} \\\\\frac{dQ}{dt}= 6-\frac{4Q}{100-t} \\\\\frac{dQ}{dt}+ \frac{4Q}{100-t}=6\\\\The \ integrating\ factor\ is:\\\\IF=e^{\int\limits {\frac{4}{100-t} } \, dt }=e^{-4\int\limits {\frac{-1}{100-t}}=e^{-4ln(100-t)}=(100-t)^{-4}}\\\\Multiplying\ through  \ by\ IF: \\\\(100-t)^{-4}\frac{dQ}{dt}+ (100-t)^{-4}\frac{4Q}{100-t}=6(100-t)^{-4}\\\\

Integrating:\\\\A(100-t)^{-4}=-2(100-t)^{-3}+c\\\\A=-2(100-t)+\frac{c}{(100-t)^{-4}} \\\\at, t=0,A=0\\\\0=-2(100-0)+\frac{c}{(100-0)^{-4}}\\\\c=0.02\\\\A=-2(100-t)+\frac{0.02}{(100-t)^{-4}}

You might be interested in
Unit to measure the length of a boat
Gnoma [55]
Boat are measure by FEET
5 0
3 years ago
Read 2 more answers
The perimeter of a triangle is 27 inches. The second side is 3 inches longer than the first side and the third side is twice as
Angelina_Jolie [31]
Divided 27 inches by the length of each side.
3 0
2 years ago
Rewrite this number sentence 50 1/2 divided by 1/4 using multiplication
Shalnov [3]
This division question is asking how many 1/4 you can fit into 50 1/2.

We can fit 4 of them into 1 whole (4 x 1/4 = 1)
We can fit 8 of them into 2 wholes (8 x 1/4 = 2)

and so on.

But we have 50 1/2 wholes, so we would need 50 1/2 x 4.

The new number sentence is 50 1/2 x 4.
3 0
3 years ago
Read 2 more answers
Find the equation of the linear function represented by the table below in slope--
Vika [28.1K]

Answer:

the answer is 9

Step-by-step explanation: 1+1+1+1+1+1+1+1+1=9

3 0
3 years ago
Michael earns $21 per hour and works 40 hours per week. How many overtime hours would he have to work in a week for his time-and
Nata [24]

Answer:

81 hours

Step-by-step explanation:

He gets 10.5 dollars an hour over time and when he's working regular he earns 840 dollars so 840 divided by 10.5 is 80 so add an extra hour and he then makes more.

7 0
2 years ago
Other questions:
  • What is least 1.11, 0.111,1.01,1.001
    6·1 answer
  • Use the​ power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonome
    11·2 answers
  • The radius of a nitrogen atom is 5.6 × 10-11 meters, and the radius of a beryllium atom is 1.12 × 10-10 meters. Which atom has a
    14·1 answer
  • Isidro wants to purchase a used scooter that costs 79.95 the sales tax is found by multiplying the price of the scooter by 0.065
    8·1 answer
  • The legs of the right triangle are 2 and 4. Find the length of the hypotenuse.
    7·1 answer
  • If K(5,-2) is rotated 90°, what will be the coordinates of its image?
    11·1 answer
  • Which number sentence is not true?
    10·1 answer
  • Mrs. Reyes asked 3 girls and 4 boys to help with a project. She had each student make 8 paper airplanes. Drag steps to show how
    6·1 answer
  • Mason is laying tiles on his entryway. The tiles are each 2/9 feet long, and the entryway is 7 1/2 feet long. How many tiles wil
    10·1 answer
  • Fast and all the answer right I give the person Brainliest
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!