The Lotka-Volterra model predicts cycles in both the rabbit and fox populations, it is not structurally stable and does not accurately represent real predator-prey dynamics. In reality, predator-prey cycles typically have a characteristic amplitude and follow a single closed orbit or a finite number of closed orbits, rather than a continuous family of neutrally stable cycles. More realistic models take into account factors such as competition, spatial heterogeneity, and stochasticity.
a) In the Lotka-Volterra predator-prey model, R(t) represents the population of rabbits at time t, and F(t) represents the population of foxes at time t. The parameter a represents the growth rate of rabbits in the absence of foxes, b represents the rate at which foxes consume rabbits, c represents the death rate of foxes in the absence of rabbits, and d represents the rate at which foxes grow as a result of consuming rabbits.
b) To recast the model in dimensionless form, we can introduce new variables x and y as follows:
x = aR/bF, y = c/F
Using the chain rule, we can then express the derivatives of R and F in terms of the derivatives of x and y:
R' = (bF/a)x' - (bR/a)x'y, F' = (dR/F)x'y - (c/F)y'
Substituting these expressions into the original model, we obtain:
x' = x(1 - y), y' = y(xy - 1)
c) A conserved quantity in terms of the dimensionless variables can be found by taking the derivative of the product xy with respect to time:
d(xy)/dt = x'y + xy' = xy(x - y)
Since the right-hand side is equal to zero when x = y, the quantity xy is conserved along solutions of the differential equations.
d) While the Lotka-Volterra model predicts cycles in both the rabbit and fox populations, it is not structurally stable and does not accurately represent real predator-prey dynamics. In reality, predator-prey cycles typically have a characteristic amplitude and follow a single closed orbit or a finite number of closed orbits, rather than a continuous family of neutrally stable cycles. More realistic models take into account factors such as competition, spatial heterogeneity, and stochasticity.
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#SPJ11:
Write an explicit formula for An, the nth term of the sequence 7, 42, 252, ...
Answer:
Step-by-step explanation:
This is a geometric progression.
Givens
a1 = 7
r = 6
Formula
a_n = a1 * r^(n - 1)
a_n = 7 (6)^(n - 1)
Sample
Try n = 3
a_3 = 7*(6)^(3-1)
a_3 = 7*(6)^2
a_3 = 7 * 36
.a_3 = 252 which is exactly what it should be.
1. "Six less than twice a murider."
A. 6 - 2x
B. 2x - 6
C. 6x-2
D. 2 - 6x
2. "Five times the sum of a number and four."
A. 5y + 4
B. 4(y + 5)
C. 5 + 4y
D. 5(y + 4)
3. Which is the correct translation of the given 2(m - 3)?
A. Twice difference of 3 and miste C. Twice the difference of m and 3.
6. Twice the sum of m and 3.6
D. Twice the sum of m and 3.
4. "Ten less than thrice the a number"
A. 10 - 3b
B. 3b - 10
C. 106 - 3
D. 3 - 10b
5. Given, m - 4, complete this: 4
A. minus
B. diminished by
a number
C. subtracted from
D. decreased by
6." The ratio of 7 and a number decreased by 2."
A. 7/(x-2)
B. (71x) - 2
C. 7X-2
D. 7 - 2/x
7. "The difference of 10 and k divided by 4 yields to 2."
A. (10-k)/4 = 2 B. 10 - (k/4) = 2 C. 10K/4 = 2
D.K-10/4 = 2
8. "Four times the sum of 12 and y is equal to 60.
A. 4y + 12 = 60 B. 4 + 12y
C. 4(12) + y = 60 D. 4(12 + y) = 60
9. All of the following are correct except
2x + 4; Twice a pumber
A. increased by B. added to
C. plus
D. more than
= 60
10. "8 times a number decreased by 13 becomes 3."
A. 8x + 13 = 3 B. 86- 13 = 3
C. 13 - 8x = 3
D. 13 + 8x = 3
branleast kpo ang sasagot neto
Answer:
C. 6x-2D. 5(y + 4)C. Twice the difference of m and 3.B. 3b - 10B. diminished bya numberB. (7/x) - 2A. (10-k)/4 = 2D. 4(12 + y) = 60D. more than= 60B. 8x- 13 = 31. "Six less than twice a murider."
A. 6 - 2x
B. 2x - 6
C. 6x-2
D. 2 - 6x
2. "Five times the sum of a number and four."
A. 5y + 4
B. 4(y + 5)
C. 5 + 4y
D. 5(y + 4)
3. Which is the correct translation of the given 2(m - 3)?
A. Twice difference of 3 and miste C. Twice the difference of m and 3.
6. Twice the sum of m and 3.6
D. Twice the sum of m and 3.
4. "Ten less than thrice the a number"
A. 10 - 3b
B. 3b - 10
C. 106 - 3
D. 3 - 10b
5. Given, m - 4, complete this: 4
A. minus
B. diminished by
a number
C. subtracted from
D. decreased by
6." The ratio of 7 and a number decreased by 2."
A. 7/(x-2)
B. (71x) - 2
C. 7X-2
D. 7 - 2/x
7. "The difference of 10 and k divided by 4 yields to 2."
A. (10-k)/4 = 2 B. 10 - (k/4) = 2 C. 10K/4 = 2
D.K-10/4 = 2
8. "Four times the sum of 12 and y is equal to 60.
A. 4y + 12 = 60 B. 4 + 12y
C. 4(12) + y = 60 D. 4(12 + y) = 60
9. All of the following are correct except
2x + 4; Twice a pumber
A. increased by B. added to
C. plus
D. more than
= 60
10. "8 times a number decreased by 13 becomes 3."
A. 8x + 13 = 3 B. 86- 13 = 3
C. 13 - 8x = 3
D. 13 + 8x = 3
branleast kpo ang sasagot neto
Problem 2. Smasher Van bound for Koronadal City leaves Polomolok every 15 minutes
while Nustafa Van leaves every 20 minutes.
5. How often do the two vans leave Polomolok at the same time
a. every 30 minutes
c. every 1 hour
b. every 40 minutes
d. every 2 hours
6. How many times will the Smasher Van leave Polomolok so that the two von leave
together
a. 2 times b. 3 times c. 4 times d. 5 times
7. How many times will the Nustafa Van leave Polomolok so that the two vons leave
together
a. 2 times b. 3 times c. 4 times d. 5 times
Answer:
5. c. Every 1 hour
6. c. 4 times
7. b. 3 times
Step-by-step explanation:
The given parameters of the rate of departure of the two vans are;
The rate of departure of Smasher Van bound for Koronadal City = Every 15 minutes
The rate of departure of Nustafa Van= Every 20 minutes
5. The time, 'x', when the two vans leave at the same time is given by the Lowest Common Multiple (LCM) of 15 and 20 as follows;
Multiples of 15 = 15, 30, 45, 60
Multiples of 20 = 20, 40, 60
Therefore, the LCM of 15 and 20 = 60
The time, when the two vans leave at the same time = Every 60 minutes = Every 1 hour
The time, when the two vans leave at the same time = Every 1 hour
6. The number of times the Smasher Van leaves Polomolok so that the two vans leave together is given by the number of multiples 15 minutes in 60 minutes = 60 minutes/(15 minutes) = 4 times
7. The number of times the Nustafa Van leaves Polomolok so that the two vans leave together is given by the number of multiples 20 minutes in 60 minutes = 60 minutes/(20 minutes) = 3 times.
5. c. Every 1 hour
6. c. 4 times
7. b. 3 times
Let's solve it one by one:
The given parameters of the rate of departure of the two vans are;
The rate of departure of Smasher Van bound for Koronadal City = Every 15 minutes
The rate of departure of Nustafa Van= Every 20 minutes
5. The time, 'x', when the two vans leave at the same time is given by the Least Common Multiple (LCM) of 15 and 20 as follows;
Multiples of 15 = 15, 30, 45, 60
Multiples of 20 = 20, 40, 60
Therefore, the LCM of 15 and 20 = 60
The time, when the two vans leave at the same time = Every 60 minutes = Every 1 hour
The time, when the two vans leave at the same time = Every 1 hour
6. The number of times the Smasher Van leaves Polomolok so that the two vans leave together is given by the number of multiples 15 minutes in 60 minutes = [tex]\frac{60}{15}=4\text{times}[/tex]
7. The number of times the Nustafa Van leaves Polomolok so that the two vans leave together is given by the number of multiples 20 minutes in 60 minutes = [tex]\frac{60}{30}=3\text{times}[/tex]
Learn more:
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Combine like terms.
38y + 15y =
Answer:
53y
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
38y + 15y
38 and 15 are coefficients
y is a term
Since they are like terms, they can be combined
Step 2: Add
38 + 15 = 53
53y
Enola is a waitress at a restaurant. Each day she works, Enola will make a guaranteed wage of $35, however the additional amount that Enola earns from tips depends on the number of tables she waits on that day. From past experiences, Enola noticed that she will get about $8 in tips for each table she waits on. How much would Enola expect to earn in a day on which she waits on 20 tables? How much expect to make in a day when waiting on t tables?
Answer:
1. 195
2. Y= 8t +35
Step-by-step explanation:
Answer:
$195; y=8t+35
Step-by-step explanation:
You can make an equation to find out how much Enola earns a day:
y=8t+35 ––This shows that "y" is the earnings for the day, "8t" represents $8 per table, and the "+35" represents the guarenteed $35 a day.
To answer the first question, the replace t with 20: y=8(20)+35
y=160+35
y=195
*For the second answer, I would put the equation because you do not know the number of tables because it is unspecified.
***You can change the "y" to whatever if you need to
Plz help I’m timed!!!!
Answer:
(x, y) right-arrow (x minus 5, y minus 3)
Step-by-step explanation:
we know that
The translation of the pre-image STU to the image ST'U' is 3 units down and 5 units to the left
That means
3 units down -----> y-3
5 units to the left -----> x-5
therefore
The rule of the translation is
(x,y) -----> (x-5,y-3)
Write the inequality in words.
5n – 10 > 26
Ten less than five times a number is greater than twenty-six.
Ten less than a number is less than or equal to twenty-six.
Five times n less than ten is twenty-six.
Ten plus five times a number is less than or equal to twenty-six.
Answer:
The mathematical sentence that describes the inequality 5n - 10 > 26 is: Ten subtracted from 5 times n is greater than 26. I hope this mathematical sentence is what you are looking for,
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
n
>
36
/5
Interval Notation:
(
36
/5
,
∞
)
Answer:
The Answer is, (A) Ten less than five times a number is greater than twenty-six.
Step-by-step explanation:
** PLEASE ANSWER I’L GOVE YOU BRAINLYLIST**
Penelope eats 4 chocolates per day, because in one day, 20 chocolates are in the box. Then, after 2 more days, 8 chocolates are eaten. That means, if she eats an even amount of chocolates, she eats 4 chocolates per day. To check this pattern, on the fourth day, there are 8 chocolates left. 12 - 8 = 4, and the pattern would continue. On the fifth day, 4 chocolates would be left, and on the sixth day, 0 chocolates would be left.
Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?
Answer:
£2.4 is the anwser im pretty sure
Step-by-step explanation:
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Please find the value of X and Y will mark brainliest
Answer:
y=34.5 degrees
x=17 degrees
Step-by-step explanation:
2y=69 because it is a corresponding congruent angle
y=34.5 degrees
2y=3x+18
69=3x+18
3x=51
x=17
What is the length of AB? A.2.59 B.9.66 C.10.35 D38.64
Answer:
what
Step-by-step explanation:
is the questionn
Ed spoke to his cousin in Australia, who told him it was 28 degrees Celsius that day. Ed wasn’t sure if that was hot or cold, so he converted the temperature to degrees Fahrenheit. What is the temperature in degrees Fahrenheit?
Use the formula, F = StartFraction 9 Over 5 EndFraction C + 32, where F is the number of degrees in Fahrenheit and C is the number of degrees in Celsius. Round your answer to the nearest whole number.
48Degrees Fahrenheit
50Degrees Fahrenheit
82Degrees Fahrenheit
108Degrees Fahrenheit
Answer:
82
Step-by-step explanation:
Do the equation
Answer:
82.4 degrees Fahrenheit. one degree Celsius is 33.8 degrees Fahrenheit. hope this helps mark me brainliest!!
Step-by-step explanation:
Hello I need someone to help me answer 10 algebra 1 math test questions i will pay money after or give brainiest on each question I need it today!!
uhh so i need help with this , it would be very nice if ya’ll helped a sis out
9514 1404 393
Answer:
(c) (3, 6)
Step-by-step explanation:
The only point that is on the line is (3, 6).
__
I find a graphing calculator to be a useful tool.
__
For solving this "by hand," you put the x- and y-values into the equation and check to see if it is true.
A. 2(0) +3(12) = 36 ≠ 24
B. 2(2) +3(9) = 31 ≠ 24
C. 2(3) +3(6) = 24 . . . . . a solution
D. 2(8) +3(0) = 16 ≠ 24
find the slope of the line
Answer:
A) 2
Step-by-step explanation:
Maybe Answer:
D) -1/2
solve the 6 linear equations
-(x+2)=2(3x-6)
solve CORRECTLY for brainly and 20 points
Answer:
k/4 + 3 = 14
k = 44
Step-by-step explanation:
Step 1: k + 12 = 56
Step 2: k = 56 - 12
Step 3: k = 44
Multiply both sides of the equation by 4Subtract from both sidesSubtract 12 from 56 to get 44Answer:
The answer are
t=4
f=4
e=2
k=44
a=-4
n=11
Please help me I'll give you the crown if its right
In the figure below, mROP = 125°.
Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
Step-by-step explanation:
first we notice that the line RS makes a diagonal in the circle.Since we are given ROP we can find SOP by:
180⁰-125⁰=55⁰
since they are in each others opposite point they are equal so that means that if we try the equation we did before: SOQ =ROP and QOR=SOP
Step-by-step explanation:
step 1. mPOS = 180 - 125 = 55°. (supplementary angles)
step 2. mQOS = 125° (vertical angles)
step 3. mQOR = 180 - 125 = 55° (supplementary angles).
Which is an example of a function?
the distance to school and the time you spend at school
the price of a piece of cloth and the length of the cloth
the price of a movie ticket and the height of the customer
the time it takes to mow a lawn and the age of the person mowing the lawn
Answer:
The price of a piece of cloth and length of cloth.
Step-by-step explanation:
A function must be measurable, attainable, and reasonable and the variables must complement each other
Measuring the distance to and time spend at school doesnt complement each other
The price of a movie ticket doesn't change based on height
Mowing a lawn doesnt matter how old you are
The price of cloth can change based on how long or short the cloth is.Shorter clothes are cheaper, while Longer clothes are more expensive.
Answer:
The example of a function is:
The price of a piece of cloth and the length of the cloth.
Step-by-step explanation:
We know that a function is a relation in which each element of a set is mapped to a single element of the other set.
i.e. an element has just one image.
1)
The time it takes to mow a lawn and the age of the person mowing the lawn.
This is not a example of function since, the time taken by two person's of different age may be same to mow a lawn.
This means that there is more than one image of a single element i.e. time.
2)
The distance to school and the time you spend at school.
The time one spend at school at different days may be different even if the distance to school is same.
3)
The price of a movie ticket and the height of the customer.
Two person's with different height will buy a movie ticket at the same cost.
Hence, this relation won't be a function.
4)
The price of a piece of cloth and the length of the cloth.
As we know that the price of a cloth is fixed according to the length.
Hence, the relation is a function.
( As corresponding to each price we have a unique length if a piece of clothing )
what’s the answer ???
Answer:1/4
Step-by-step explanation:
Answer:
answer is
1
blank will have 1.
plz mark my answer as brainlist plzzzz if you find it useful.
PLS HELP I WILL GIVE BRAINLIEST THANK U PLSSS
Please help and hurry please
Answer:
x=7.48
Step-by-step explanation:
13^2+x^2=15^2
169+x^2=225
x^2=56
x=7.48
Answer:
x = 7.48 (2d.p.) or 7.5 (1 d.p.)
Step-by-step explanation:
Use Pythagoras' Theorem.
15 x 15 (or 15²) = 225
13 x 13 = 169
√H - A = O
225 - 169 = 56
√56 = 7.48 (2d.p.) or 7.5 (1 d.p.)
Convert the following decimal to a fraction.
Answer: 7.15
Step-by-step explanation:
143
20
=7 and 3 over 207
3
20
=7.15
Answer:
7 12/10000
Step-by-step explanation:
FOUR FRIENDS SHARE 3 SHEETS OF PAPER EQUALLY.
WHAT FRACTION OF A SHEET OF PAPER DOES EACH FRIEND GETS?
SOLVE AND EXPLAIN
Answer:
[tex]\frac{3}{4}[/tex] of a sheet of paper
Step-by-step explanation:
Hi!
This isn't the easiest to explain with numbers but I'll do it with an example instead.
If you had 60 cookies and had to split it equally with you and one of your other friends, how would you do it?
You would do [tex]\frac{60}{2}[/tex], right? Because you have 60 cookies and you're dividing it amongst 2 people.
It's the same idea here!
We take the number of sheets of paper, and we divide it by the number of people we have to share it with.
so we do [tex]\frac{3}{4}[/tex]. You don't even have to simplify in this case because this is a fraction and this is the simplest form of this fraction as well
I hope this made sense, let me know if you have any questions
Answer:
A
Step-by-step explanation:
Help please...........
Answer:
18
Step-by-step explanation:
3 x 6=18
how many solutions 9x +2y =9 / -3x + y=2
Answer choices-
1 solution
No solution
Infinite solutions
the solution to the system is (1,3)
the solution to the system is (3,1)
the solution to the system is (1/3,3)
Answer:
Maybe the sum was a simultaneous equation....if so, this is the solution.
and the answer comes (1/3, 3)
Hope it helps! :)
6. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
Write a rule for the linear function in the table.
X F(x)
1 -7
2 -10
3 -13
4 -16
A. f(x) = -3x - 4
B. f(x) = x - 7
C. f(x) = -1/3x - 4
D. f(x) = 3x + 4
Answer:
I think the answer is B. f(x) = -1/3x - 4
Step-by-step explanation:
Use the given functions to set up and simplify
4−16.
XF(x)=X
Fx
1 − 7 = −6
2 − 10 = −8
3 − 13 = −10
4 − 16 = −12
15 points + brnlist , need help asap!!! (with a picture)
Answer:
C
Step-by-step explanation:
According to my calculations Its c
what is the answer to (13x+30)-(20x+6)
- Ashanti earns $50 an hour. How much does she earn in 6 hours?
Solution:-
Given,
Ashanti earns=$50 an hour
Ashanti earns in 6 hours=?
Now,
Ashanti earns in 60 hours=$50×6
=$300
Therefore,Ashanti earns $300 in 6 hours.