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
Elena-2011 [213]
3 years ago
9

Write a differential equation to represent each situation below. Do NOT solve them. a. A new technology is introduced into a com

munity of 5000 people. If the rate at which the technology is adopted in the community is jointly proportional to the number of people who have adopted the technology and the number of people who have not adopted it, write a differential equation to represent the number of people, x(t), who have adopted the technology by time t. b. A tank with a capacity of 1000 gal originally contains 800 gal of water with 200 lbs of salt in the solution. Water containing 3.5 lbs of salt per gal is entering at a rate of 2 gal/min, and the mixture is allowed to flow out of the tank at a rate of 5 gal/min. Write a differential equation reflecting the information above, clearly stating the requested intermediate results below. Let A(t) represent the amount of salt (in pounds) in the tank after t minutes. Do NOT solve the DE! Show units with each factor in the three setup steps below, and simplify each expression, showing the resulting units as well. *Be sure to include the initial conditions for this DE in your final equation. R_in = Concentration of salt in the tank: c(t) = R_out = Differential equation: A(0) =
Mathematics
1 answer:
Vladimir [108]3 years ago
8 0

Answer:

  a.  x'(t) = kx(5000-x)

  b.  R_in = 7 lbs/min

     R_out = 5c(t) lbs/min

     c(t) = A(t)/(800 -3t) lbs/gal

     A'(t) = R_in - R_out; A(0) = 200 lbs

Step-by-step explanation:

A. When proportionality is joint between x and y, the expression describing that is kxy, where k is the constant of proportionality. Here, the rate of change is jointly proportional to number who have adopted (x) and number of the community of 5000 who have not (5000-x). The corresponding equation is ...

  x'(t) = kx·(5000-x)

We know the initial number of adopters must be greater than 0, or the equation's only solution would be x=0.

__

B. The rate of influx of salt is ...

  R_in = (3.5 lbs/gal)×(2 gal/min) = 7 lbs/min

  The number of gallons in the tank at time t is ...

  v = 800 gal + (2 gal/min - 5 gal/min)(t min) = (800 -3t) gal

For amount of salt A(t) pounds, the concentration c(t) will be ...

  c(t) = A(t)/v = A(t)/(800 -3t) . . . . lbs/gal

The outflow rate will be the product of outflow volume and concentration:

  R_out = (c(t) lbs/gal)(5 gal/min) = 5c(t) lbs/min

And the differential equation for A(t) is ...

  A'(t) = R_in -R_out . . . with initial condition A(0) = 200 lbs.

__

When you go to solve the equation for A'(t), it will need to be cast in terms of A(t):

  A'(t) = 7 -5A(t)/(800 -3t)

You might be interested in
At a concession stand, a pickle and two bags of chips costs a total of $3.25. Three pickles and four bags of chips costs a total
Vladimir [108]
Agggggggg step by step!
6 0
3 years ago
Help ❤️ idc if my name shows
Elan Coil [88]

Answer:

1

Step-by-step explanation:

7 0
2 years ago
Find the first five terms of the recursive sequence <br> an=-6an-1 where a1=4.5
grandymaker [24]

Answer:

4.5, -27, 162,-972, 5832

Step-by-step explanation:

The given recursive definition is,

a_n=-6a_{n-1}, a_1=4.5

This will form a geometric sequence with first term 4.5 and common ratio r=-6.

When n=2, we have:

a_2=-6a_1 \\  \implies \: a_2=-6 \times 4.5 =  - 27

When n=3, we get:

a_3=-6a_2 \\  \implies \: a_3=-6 \times  - 27 =  162

When n=4, we get:

a_4=-6a_3 \\  \implies \: a_4=-6 \times 162 =  - 972

When n=5, we get:

a_5=-6a_4 \\  \implies \: a_5=-6 \times  - 972 = 5832

Therefore the first five terms are:

4.5, -27, 162,-972, 5832

3 0
3 years ago
Can anyone answer this
erik [133]

Answer:

Step-by-step explanation:

1. 10² + 7² = x²

 149 = x²

 x = √149

2. x² + 19² = 21²

 x² = 21² -  19² = 80

 x = √80 = 4√5

3. x² + 16² = 27²

 x² = 27² - 16² = 473

 x = √473

4. 5.3² + 12.8² = x²

 191.93 = x²

 x = √191.93

5. 9² + 20² = x²

 481 = x²

 x = √481

6. 31 = x + 2√(19²-17²) = x + 2·6√2 = x + 12√2

 x = 31 - 12√2

 

5 0
3 years ago
Solve the equation:<br><br> 13x³-159x²-412x-94=0
myrzilka [38]

Answer:

First derivative the equation

39x²-318x-412=0

then use the quadratic formula

then x = 9.29 or x = -1.14

5 0
2 years ago
Other questions:
  • Mike's sister is away at college, and he wants to mail her a 34 in. Softball bat. The packing service sells only one kind of box
    15·1 answer
  • If a = 2.3 units, b = 4 units, c = 6 units, and d = 8 units, what is the volume of the two prisms?
    12·1 answer
  • Which is the approximate solution to the system y = 0.5x + 3.5 and y = −A system of equations. y equals 0.5 x plus 3.5. y equals
    5·2 answers
  • Functions in Math, Please Help​
    6·2 answers
  • HELP ME PLS IVE BEEN WAITING FOR 20 MIN HELP LOVE U GUYS &lt;3
    6·2 answers
  • Tommy and his wife went to the store and bought groceries. Their subtotal was $143.50. If the sales tax was 8%, what was the tot
    10·1 answer
  • Mario’s Restaurant is planning to tile the floor of their outdoor dining area, represented by the composite figure below. The ti
    12·1 answer
  • Is 7/45 a repeating or terminating
    12·1 answer
  • Hi I need help with this problem. can anyone you tell me what 5+(-3)​
    15·2 answers
  • What is the value of 6x+5y​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!