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
Alina [70]
3 years ago
15

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

W the number of wolves. For example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you would enter (100,10),(200,20),(300,30). Do not round fractional answers to the nearest integer.
Mathematics
1 answer:
zloy xaker [14]3 years ago
4 0

Answer:

(0,0)   (4000,0) and (500,79)

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW

\frac{dW}{dt} = -0.02W + 0.00004RW

To solve this, we first equate \frac{dR}{dt} and \frac{dW}{dt} to 0.

So, we have:

0.09R(1 - 0.00025R) - 0.001RW = 0

-0.02W + 0.00004RW = 0

Factor out R in 0.09R(1 - 0.00025R) - 0.001RW = 0

R(0.09(1 - 0.00025R) - 0.001W) = 0

Split

R = 0   or 0.09(1 - 0.00025R) - 0.001W = 0

R = 0   or  0.09 - 2.25 * 10^{-5}R - 0.001W = 0

Factor out W in -0.02W + 0.00004RW = 0

W(-0.02 + 0.00004R) = 0

Split

W = 0 or -0.02 + 0.00004R = 0

Solve for R

-0.02 + 0.00004R = 0

0.00004R = 0.02

Make R the subject

R = \frac{0.02}{0.00004}

R = 500

When R = 500, we have:

0.09 - 2.25 * 10^{-5}R - 0.001W = 0

0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0

0.09 -0.01125 - 0.001W = 0

0.07875 - 0.001W = 0

Collect like terms

- 0.001W = -0.07875

Solve for W

W = \frac{-0.07875}{ - 0.001}

W = 78.75

W \approx 79

(R,W) \to (500,79)

When W = 0, we have:

0.09 - 2.25 * 10^{-5}R - 0.001W = 0

0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0

0.09 - 2.25 * 10^{-5}R = 0

Collect like terms

- 2.25 * 10^{-5}R = -0.09

Solve for R

R = \frac{-0.09}{- 2.25 * 10^{-5}}

R = 4000

So, we have:

(R,W) \to (4000,0)

When R =0, we have:

-0.02W + 0.00004RW = 0

-0.02W + 0.00004W*0 = 0

-0.02W + 0 = 0

-0.02W = 0

W=0

So, we have:

(R,W) \to (0,0)

Hence, the points of equilibrium are:

(0,0)   (4000,0) and (500,79)

You might be interested in
If you are paid every 3 months, or 4 times a year, what is that called?
ollegr [7]
Thank you! This helped a lot!!! :)
5 0
2 years ago
Express the following as an equation where k represents the contestant of the variation​
mojhsa [17]

Answer:

<h2>add me on sñap my ID is: arshad2623f</h2>

<h2>please i just wanted to make friends cuz I'm alone BTW I'm 15yo</h2>
4 0
3 years ago
100 POINTS AND BRAINLIEST. I need help ASAP.
Svetach [21]

Answer:

Step-by-step explanation:

First what we must do is rewrite the table to find a solution:

0.25^x −0.75x+1

   64     3.25

   16     2.5

    4      1.75

    1      1

 0.25     0.25

 0.0625 −0.5  

 0.015625  −1.25

We see where the values of the function are the same:

x = 0 (1)

x = 1 (0.25)

answer:

x = 0

x = 1

4 0
2 years ago
What is the value of k in the equation k\3 -5=34
Alex
If wrong i apologize but for that equation i got the answer K=117
4 0
3 years ago
Read 2 more answers
Whoever answers will get 60 points. Pls answer based off of the answer choices.
AnnyKZ [126]

Hello from MrBillDoesMath!

Answer:

21

Discussion:

$350  at 6% =                              => as "percent" means per 100

350 * (6/100) =                            => as 350 * 6 = 2100

2100/100 =

21

Thank you,

MrB

7 0
3 years ago
Other questions:
  • Hat is the greatest common factor of 20 and 36? 2 4 5 6
    7·1 answer
  • Willie and Emily each purchase one raffle ticket. If a total of seven raffle tickets are sold, what is the probability that Will
    13·2 answers
  • A car manufacturer claims that the company's newest model has a peak power of exactly 329 horsepower. Katherine is a reporter fo
    13·1 answer
  • The adult skeleton consists of 206 bones. There are 28 bones in the skull and 30 bones in the arms and legs. Out of the 28 skull
    14·2 answers
  • Miguel drove for 8 hours at a constant rate he drove a total of 424 miles.
    14·1 answer
  • Sarah's class went to the science lab for their weekly lab activity. Sarah's group decided that they could complete the lab fast
    7·2 answers
  • I Need Help Finding The Answer To m
    5·1 answer
  • On a standardized aptitude test, scores are normally distributed with a mean of 100 and a standard deviation of 10. Find the per
    8·1 answer
  • Find the missing side of the triangle.
    15·1 answer
  • Please help me on this problem !
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!