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
Triss [41]
3 years ago
6

A tank contains 350 liters of fluid in which 10 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

mped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Physics
1 answer:
aleksandr82 [10.1K]3 years ago
4 0

Answer:

A(t) = -340e^{-t/70} + 350

Explanation:

Since fluid is pumping in and out at the same rate (5L/min), the total fluid volume in the tank stays constant at 350L. Only the amount of salt and its concentration changed overtime.

Let A(t) be the amount of salt (g) at time t and C(t) (g/L) be the concentration at time t

A(0) = 10 g

Brine with concentration of 1g/L is pouring in at the rate of 5L/min so the salt income rate is 5 g/min

The well-mixed solution is pouring out at the rate of 5L/min at concentration C(t) so the salt outcome rate is 5C g/min

But the concentration is total amount of salt over 350L constant volume

C = A / 350

Therefore our rate of change for salt A' is

A' = 5 - 5A/350 = 5 - A/70

This is a first-order linear ordinary differential equation and it has the form of y' = a + by. The solution of this is

y = ce^{bt} + \frac{a}{b}

So A = ce^{\frac{-t}{70}} + \frac{5}{1/70} = ce^{-t/70} + 350

with A(0) = 10

c + 350 = 10

c = 10 - 350 = -340

A(t) = -340e^{-t/70} + 350

You might be interested in
The speed of an object changes only when it is acted on by an unbalanced force.
Nikitich [7]

Answer:

If an object has a net force acting on it, it will accelerate. The object will speed up, slow down or change direction. An unbalanced force (net force) acting on an object changes its speed and/or direction of motion. An unbalanced force is an unopposed force that causes a change in motion.

Explanation:

I hope this helps you out and if your feeling generous plz mark brainliest it helps me a lot thank you:)

6 0
3 years ago
1) Freddy drives 4 miles east to his friend's house. He then travels 9 more miles east to the supermarket. Finally on his way ba
timurjin [86]

Answer:

<h3>B. 19miles</h3>

Explanation:

If Freddy drives 4 miles east to his friend's house. He then travels 9 more miles east to the supermarket. Finally on his way back home he out  of gas 6 miles after leaving the supermarket, the distance travel by fred will be the sup of all the distances he covered throughout the journey.

Distance covered by fred = 4miles + 9miles + 6miles

Distance covered by fred = 13miles + 6miles

Distance covered by fred  = 19miles

8 0
3 years ago
PLZ ANSWER THE QUESTION ​
adelina 88 [10]

Answer:

a

Explanation:

t

7 0
3 years ago
Time Intervals in Ice Ages
stepladder [879]
It started off with 68% less than it did at the peak, and later created a void and melted the remainder of the ice at about 92%
8 0
3 years ago
Can someone answer my last question you could get 25 points total​
enyata [817]

Answer:

Hi where is question. Hope you understand me

5 0
2 years ago
Other questions:
  • A coil consists of 200 turns of wire. Each turn is a square of side d = 18 cm, and a uniform magnetic field directed perpendicul
    12·1 answer
  • Suppose a cart is being moved by a certain net force. If a load is added to the cart so its mass is doubled, what is the ratio o
    8·1 answer
  • A string is wrapped several times around the rim of a small hoop with radius 7cm and mass 2kg. The free end of the string is hel
    8·1 answer
  • A middle-age star that burns hydrogen is a A.neutron star B.white dwarf c.main sequence star D.pusar
    9·1 answer
  • An example of a constant acceleration is
    14·2 answers
  • An object blocks the path of a wave causing the wave to change direction is called what
    11·2 answers
  • During an experiment, you take a measurement of 18.3 inches. What is this measurement in centimeters? 1 in = 2.54 cm
    15·2 answers
  • 10 m/s in 10<br> 3. A car accelerates from 0 m/s to 50 m/s in 10 seconds. What is the acceleration?
    13·1 answer
  • What work is done when we apply a force of 5N and move in the direction of the force 2m?
    6·1 answer
  • Y’all wann trade in rob.lox I have a violet Valkyrie
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!