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
Salsk061 [2.6K]
3 years ago
14

. A marine biologist needs to add a new chemical to one of her fish tanks (300 L in volume). She adds a chemical solution with c

oncentration 5 mg L at a rate of 3 L min , and the well-mixed fluid drains out of the tank at the same rate. a. Write a differential equation to model the rate of change of the amount of new chemical y in the tank at time t.
Mathematics
1 answer:
posledela3 years ago
4 0

Answer:

A differential equation to model the rate of change of the amount of new chemical y in the tank at time t is given as

(dy/dt) = 15 - 0.01y

Step-by-step explanation:

First of, we take the overall balance for the system,

Let V = volume of solution in the tank at any time

The rate of change of the volume of solution in the tank = (Rate of flow into the tank) - (Rate of flow out of the tank)

The rate of change of the volume of solution = (dV/dt)

- Rate of flow into the tank = Fᵢ = 3 L/min

- Rate of flow out of the tank = F = 3 L/min

(dV/dt) = Fᵢ - F

(dV/dt) = (Fᵢ - F) = 3 - 3 = 0

dV = 0 dt

∫ dV = 0 ∫ dt

V = 0 + c = c

where c = constant of integration.

At t = 0, V = 300 L

With the flow rate in and out of the tank the same, then it means the volume of the tank is unchanged.

Component balance for the amount of chemical in the tank.

- Let the initial amount of chemical in the tank be y₀ = 0 mg

- Let the rate of flow of the amount of chemical coming into the tank = yᵢ = 5 mg/L × 3 L/min = 15 mg/min

- If the amount of chemical in the tank, at any time = y mg

- Concentration of chemical in the tank at any time = (y/V) mg/L = (y/300) mg/L

- Rate at which that amount of chemical is leaving the tank = 3 L/min × (y/300) mg/L = (y/100) mg/L = (0.01y) mg/L

Rate of Change in the amount of chemical in the tank = (Rate of flow of chemical into the tank) - (Rate of flow of chemical out of the tank)

(dy/dt) = 15 - 0.01y

Hope this Helps!!!

You might be interested in
PLEASE HELP ASAP IT IS VERY MUCH APPRECIATED
irakobra [83]
YOUR CORRECT good luckkk
5 0
2 years ago
Read 2 more answers
Ella has 10 more CDs than her friend Krystal has. Iris has 3 times as many CDs as Ella has. Which of the following can be used t
pav-90 [236]

Answer:

3(10+k)=total

Step-by-step explanation:

5 0
2 years ago
Joanne's bus was 27 minutes late tonight. She called to say she would be about a half hour late for dinner. Explain why this was
klemol [59]
This is correct, because it takes 27 minutes to get home so it will probably be about 30 minutes.
4 0
3 years ago
Read 2 more answers
What is 1 2/5 as a whole number need fast
elixir [45]
Do u mean a mixed number?

2 2/5
4 0
3 years ago
HELP ME PLEASEEEE. The volume of a cylinder is 20 ft. Which expression represents the volume of a cone with the same base and he
xz_007 [3.2K]

Answer:

ano tanong Jan paki full Ng tanong

3 0
2 years ago
Other questions:
  • How many bricks are in each of three rows?
    9·1 answer
  • Use picture and numbers to show how to add 3+1 in any order
    9·1 answer
  • Add.<br> (5n^2+4n)+(3n^2+6n)
    7·1 answer
  • What is 132.6 in expanded form
    5·2 answers
  • Without dividing or listing multiples how can you tell if 61 is a multiple of 6
    13·2 answers
  • Y = 7/2x + 10 y = -7/2x - 1/10 these lines have perpendicular slopes. True or false?
    5·2 answers
  • The graph of g(x) = (x + 2)2 is a translation of the
    10·1 answer
  • Select the expression equivalent to (-2x+8.1y)-(-9x+5.3y)​
    10·1 answer
  • 8x - 5 = 28x + 10, what does x equal?
    6·1 answer
  • Could someone please solve this compound inequality?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!