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diamong [38]
3 years ago
12

PLEASE ANSWER NUMBER 15 ‼️‼️‼️‼️

Mathematics
1 answer:
elena-s [515]3 years ago
8 0

Answer:

C

Step-by-step explanation:

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Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow
Gala2k [10]

Answer:

a) dx / dt = - x / 800

b) x = 500*e^(-0.00125*t)

c) dy/dt = x / 800 - y / 200

d) y(t) = 0.625*e^(-0.00125*t)*( 1  - e^(-4*t) )

Step-by-step explanation:

Given:

- Out-flow water after crash from Lake Alpha = 500 liters/h

- Inflow water after crash into lake beta = 500 liters/h

- Initial amount of Kool-Aid in lake Alpha is = 500 kg

- Initial amount of water in Lake Alpha is = 400,000 L

- Initial amount of water in Lake Beta is = 100,000 L

Find:

a) let x be the amount of Kool-Aid, in kilograms, in Lake Alpha t hours after the crash. find a formula for the rate of change in the amount of Kool-Aid, dx/dt, in terms of the amount of Kool-Aid in the lake x:

b) find a formula for the amount of Kook-Aid in kilograms, in Lake Alpha t hours after the crash

c) Let y be the amount of Kool-Aid, in kilograms, in Lake Beta t hours after the crash. Find a formula for the rate of change in the amount of Kool-Aid, dy/dt, in terms of the amounts x,y.

d) Find a formula for the amount of Kool-Aid in Lake Beta t hours after the crash.

Solution:

- We will investigate Lake Alpha first. The rate of flow in after crash in lake alpha is zero. The flow out can be determined:

                              dx / dt = concentration*flow

                              dx / dt = - ( x / 400,000)*( 500 L / hr )

                              dx / dt = - x / 800

- Now we will solve the differential Eq formed:

Separate variables:

                              dx / x = -dt / 800

Integrate:

                             Ln | x | = - t / 800 + C

- We know that at t = 0, truck crashed hence, x(0) = 500.

                             Ln | 500 | = - 0 / 800 + C

                                  C = Ln | 500 |

- The solution to the differential equation is:

                             Ln | x | = -t/800 + Ln | 500 |

                                x = 500*e^(-0.00125*t)

- Now for Lake Beta. We will consider the rate of flow in which is equivalent to rate of flow out of Lake Alpha. We can set up the ODE as:

                  conc. Flow in = x / 800

                  conc. Flow out = (y / 100,000)*( 500 L / hr ) = y / 200

                  dy/dt = con.Flow_in - conc.Flow_out

                  dy/dt = x / 800 - y / 200

- Now replace x with the solution of ODE for Lake Alpha:

                  dy/dt = 500*e^(-0.00125*t)/ 800 - y / 200

                  dy/dt = 0.625*e^(-0.00125*t)- y / 200

- Express the form:

                               y' + P(t)*y = Q(t)

                      y' + 0.005*y = 0.625*e^(-0.00125*t)

- Find the integrating factor:

                     u(t) = e^(P(t)) = e^(0.005*t)

- Use the form:

                    ( u(t) . y(t) )' = u(t) . Q(t)

- Plug in the terms:

                     e^(0.005*t) * y(t) = 0.625*e^(0.00375*t) + C

                               y(t) = 0.625*e^(-0.00125*t) + C*e^(-0.005*t)

- Initial conditions are: t = 0, y = 0:

                              0 = 0.625 + C

                              C = - 0.625

Hence,

                              y(t) = 0.625*( e^(-0.00125*t)  - e^(-0.005*t) )

                             y(t) = 0.625*e^(-0.00125*t)*( 1  - e^(-4*t) )

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The pattern 7, 8, 10, ________, ________ follows the rule multiply by 2, then subtract 6. What are the next two terms?
Y_Kistochka [10]

Answer:

14 22

Step-by-step explanation:

i think it is

4 0
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Number 16: complete the table
soldier1979 [14.2K]

Answer:

7.5

Step-by-step explanation:

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The Answer is C.Radius
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Table show step by step how do you simplify the algebraic expression 3(x-5)+4x. <br>Justify step 4​
ale4655 [162]
<h3>Answer: Commutative Property (choice C)</h3>

===================================================

Explanation:

Here are all of the justifications for each step

  • Step 1. None needed. This is the original expression
  • Step 2. Distributive property
  • Step 3. Multiply  (the 3 and 5 multiply to 15)
  • Step 4. Commutative property. Specifically, this is the commutative property of addition which allows us to add any two numbers in any order we want. In this case, the  -15 and 4x terms swap places.
  • Step 5. Associative property. The parenthesis group the first two terms away from the third term.
  • Step 6. Combine like terms. Both 3x and 4x have an x only so they are like terms that combine to 7x. You can think of it as 3+4 = 7, then you just tack an x onto everything to get 3x+4x = 7x.
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3 years ago
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