(1 point) Consider the system of equations =»(1- * -x), taking (x, y) > 0. (a) Write an equation for the (non-zero) vertical (x-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (-)nullcline: (Enter your equation, e.g., y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria = (Enter the points as comma-separated (x,y) pairs, e.g., (1,2), (3,4).) (c) Use a phase plane plotter (such as pplane) to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position (2,), trajectories ? the point (Enter the point as an (x,y) pair, e.g., (1,2).)

Answers

Answer 1

(a) An equation for the (non-zero) vertical (x -)nullcline of this system is  and for the (non-zero) horizontal (y-)nullcline is y = 1 - x/3 and x = 1 - y/4

(b) The equilibrium points for the system are (0,0) and (1,1).

c) If we start at the initial position (2,2), trajectories approach the point (1,1).

The system of equations we will consider is:

dx/dt = x(1 - x/3 - y)

dy/dt = y(1 - y/4 - x)

To find the vertical (x-)nullcline, we set dx/dt to 0 and solve for y. This gives us:

1 - x/3 - y = 0

y = 1 - x/3

Similarly, to find the horizontal (y-)nullcline, we set dy/dt to 0 and solve for x. This gives us:

1 - y/4 - x = 0

x = 1 - y/4

The nullclines represent the points in the phase plane where either dx/dt or dy/dt is zero.

Therefore, any trajectory that passes through a nullcline will be tangent to that nullcline.

To find the (non-zero) vertical (x-)nullcline, we set x = 0 and solve for y. This gives us y = 1/x.

Therefore, the equation of the vertical nullcline is y = 1/x.

Similarly, to find the (non-zero) horizontal (-)nullcline, we set y = 0 and solve for x. This gives us x = y.

Therefore, the equation of the horizontal nullcline is x = y.

Next, we want to find the equilibrium points of the system, which are the points in the phase plane where both x and y are zero.

To find the equilibrium points, we set x = 0 and y = 0 and solve for x and y. This gives us two equilibrium points: (0,0) and (1,1).

To confirm that these are indeed equilibrium points, we can substitute them into the original equations and verify that x and y are both zero at these points.

Finally, we want to estimate trajectories in the phase plane using a phase plane plotter.

Suppose we start at the initial position (2,2). We can use the phase plane plotter to draw the trajectory that passes through this point. We observe that the trajectory approaches the equilibrium point (1,1) as t goes to infinity.

Therefore, we can complete the sentence as follows: If we start at the initial position (2,2), trajectories approach the point (1,1).

To know more about equilibrium points here

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Complete Question:

Consider the system of equations

d x / d t = x ( 1 − x / 3 − y )

d y / d t = y ( 1 − y / 4 − x ) . taking (x, y) > 0.

(a) Write an equation for the (non-zero) vertical (x -)nullcline of this system; And for the (non-zero) horizontal (y-)nullcline:

(b) What are the equilibrium points for the system? (Enfer the points as comma-separated (x.y) pairs, e.g., (1, 2), (3,4).) (

c) Use your nullclines to estimate trajectories in the phase plane, completing the following sentence: If we start at the initial position ( 2 , 1 2 ) . trajectories the point (Enter the point as an (x.y) pair. o.g.. (1, 2).) Analysing s


Related Questions

Tito builds a model of the solar system. In his model, the diameter of the sphere representing Jupiter is 7
inches. What is the circumference of a cross section through the center of the model of Jupiter? Use 3.14
for π


Answers

Answer:

21.99

Step-by-step explanation:

C = 2 * Pi * (r)

Diameter = 7

Radius = 3.5

Pi

21.99

A store wants to mark up
their prices by 12%.
What would the markup
be on a $40 lamp?
What is the final price?
And how did you solve it

Answers

Answer:Plus, calculate your profit margins, total revenue and more with FreshBooks ... Whether you sell online or in a retail store, you can set the perfect price for each ... service sold, you want to charge a price that's a percentage above how much it costs ... If Product A costs $10, the marked-up selling price would be $15 ( $10 x .50 ...

Step-by-step explanation:

Plus, calculate your profit margins, total revenue and more with FreshBooks ... Whether you sell online or in a retail store, you can set the perfect price for each ... service sold, you want to charge a price that's a percentage above how much it costs ... If Product A costs $10, the marked-up selling price would be $15 ( $10 x .50 ...

Answer:

$44.80

Step-by-step explanation:

Here' s  an equation to help you with percent problems:    part            %

                                                                                               -------    =    -----

                                                                                              whole         100

Because you want to find 12%, the % in the equation would be replaced with 12. The part would be x because that's what u need to find. The whole would be 40. Cross multiply to get 100x = 480. Divide 480 by 100 to get x = 4.80. Add 4.80 to 40.00 to get the final price. The final price is $44.80.

Write and equality for an each situation .

Gary has at least 25 blue t shirts
The room can hold no more than 50 people .

Answers

Answer:

50-25? so the answer is twenty five?

Step-by-step explanation:

25 hope this helps!!!

jane spend $42 for her for shoes this was $14 less than twice what she spent for a blouse how much was the blouse​

Answers


42=2b-14 where b=price of the blouse
42+14=2b
56=2b
b=56/2
b=$28 is the price of the blouse



HELP ANSWER FAST!!!!

Answers

D = -2, -1, 3, 5
R = -7, 0, 4
Function? Yes

Jimmy invests $2500 in an account with a 5% interest rate, making no other deposits or withdrawals. What will Jimmy’s account balance be after 8 years if the interest is compounded 6 times each year?
URGENT PLEASE

Answers

Answer:

We conclude that the total amount accrued, principal plus interest,  from compound interest on an original principal of  $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

Step-by-step explanation:

Given

Principle P = $2500

Interest rate r = 5% = 0.05

Time period t = 8 years

To determine

Accrue Amount A = ?

Using the compound interest equation

[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]

where:

A represents the Accrue Amount

P represents the Principal Amount

r represents the interest rate

t represents the time period in years

n represents the number of compounding periods per unit t

Important tip:

Given that the interest is compounded 6 times each year, therefore, the value of n = 6.

now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation

[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]

[tex]A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}[/tex]

[tex]\:A=2500\left(1+\frac{0.05}{6}\right)^{48}[/tex]

[tex]A=2500\times 1.48935[/tex]      ∵  [tex]\left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935[/tex]

[tex]A=\:3723.38[/tex] $

Therefore, we conclude that the total amount accrued, principal plus interest,  from compound interest on an original principal of  $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

The length of what line segment would be multiplied by pi to find the circumference of Circle P?

Answers

9514 1404 393

Answer:

  QS

Step-by-step explanation:

The circumference is pi times the diameter. The only segment shown that is a diameter is QS.

pls help soon reward brainiest

Answers

Answer:

x=-6

Step-by-step explanation:

answer choices:90ft square inches, 45ft square inches, 80ft square inches ​

Answers

Answer:

CAUSE I FEEL THE BREK FEEL THE BREK FELLLLLLL THE BREKK

Step-by-step explanation:

please help picture attached ​

Answers

Answer:

triangle B and D

1)y=4
2)y=4x
3)y=4x+4
4)x=4

Answers

Answer:

I think number letter shape 14

Answer:

I am pretty sure that the answer is y=4x

Which triangle makes this statement true?

Answers

Answer:

Step-by-step explanation:

The question is kind of confusing but I think the answer is A.

Answer:

C is the correct answer

Step-by-step explanation:

I did this exact one and it was right I hope this helps! Have a good day! :)

Proof:

Which is closest to the quotient 4,367 divided bye 0.004?


A. 1,000
B. 10,000
C. 100,000
D. 1,000,000

Answers

Answer:

6.) 1,000,000

Step-by-step explanation:

Answer:

ye

Step-by-step explanation:

McKenzie earns $15 per lawn mowed she also earned $10 for babysitting she earned 100 total, what does that look like in algebra form? Please help.

Answers

Answer:

15a + 10b = 100

Step-by-step explanation:

Given:

Cost of each lawn mowed = $15

Cost of each babysitting = $10

Total money earned = 100

Find:

Algebra form

Computation:

Assume;

Number of lawn mowed = a

Number of babysitting = b

So,

15a + 10b = 100

2
1
X 46
7. Find the m 2 JKL
in rhombus JKLM

Answers

Step-by-step explanation:

since KLJ is a parallelogram, it can be split into 2 congruent triangles, as seen above. The angles remain the same, so we know angle KJL is also 25 degrees. Using the triangle angle sum theorem (all sides of a triangle add up to 180 degrees), we can determine the missing angle measure is 25 degrees. It would have been nice if the question told us JKLM was also a rhombus.

Evaluate the formula for distance to solve the problem. Then use the drop-down menus to complete the statements.

Distance = rate times time

During a big race, Jeff races his car at a rate of 125 miles per hour for 3.2 hours. What is the distance of the race?

First, write the
.

Next, use parentheses when you substitute
in for r and
in for t.

Now, simplify by
125 and 3.2.

Jeff raced for a distance of
miles.

Answers

Answer:

First, write the  

✔ formula: d = rt

.

Next, use parentheses when you substitute  

✔ 125

in for r and  

✔ 3.2

in for t.

Now, simplify by  

✔ multiplying

125 and 3.2.

Jeff raced for a distance of  

✔ 400

miles.

Step-by-step explanation:

Enter a digit in each box to complete the division problem.

Please answer i’ll give brainliest

Answers

Step-by-step explanation:

2527 is the first line so 5 in the box

then 47 so a 4 in that box

top answer row

315 E7 so a 5 in that box.

Please help answer all please thank you

Answers

Answer:

The answers are, in order:

1. Isolate

2. substitute

3. variable

Step-by-step explanation:

You're welcome :)

find an equation of line containing (3, -4) and having slope -2. if this line contains the points (a, 8) and (5, b) find a and b

Answers

Answer:

a = -3

b = -8

Step-by-step explanation:

Equation for a line is:

y-coordinate = (slope * x-coordinate) + y-intercept

For (3, -4): -4 = (-2 * 3) + y-intercept

y-intercept = 2

Equation for all points on this line is:

y = -2*x + 2

For (a, 8): 8 = (-2 * a) + 2

For (5, b): b = (-2 * 5) + 2

Omg pls help in my math. It is 6th grade

Answers

Answer:

1. You have to shade 38/100 squares

2. You have to shade 65/100 squares

3. 3/5=15/25, 6/10, 9/15

Yes he’s right or she ?

What does y = 1/3x + 5 look like on a graph?

Answers

It’s gonna cross the 5 on the y axis, and it’ll be decreasing because the rise/run is 1/3

Please help, I beg of y'all

FIND BD -

Answers

9514 1404 393

Answer:

  14 units

Step-by-step explanation:

The angle bisector divides the sides proportionally.

  BD/BA = CD/CA

  (x+4)/8 = (2x+1)/12

  3(x +4) = 2(2x +1) . . . . . multiply by 24 (the least common denominator)

  3x +12 = 4x +2 . . . . . . . eliminate parentheses using the distributive property

  12 = x +2 . . . . . . . subtract 3x

  10 = x . . . . . . . . . subtract 2

Then the length of BD is ...

  BD = x +4

  BD = 10 +4 . . . . substitute the value of x

  BD = 14

Jasmine had some candy to give to her three children. She first took four pieces for herself and then evenly divided the rest among her children. Each child received two pieces. With how many pieces did she start?

Answers

Answer:

10 pieces

Step-by-step explanation:

She gave herself 4 pieces, and each child 2 pieces. If she has 3 children, she gave them 6 pieces.

(3*2=6) and then you add with the amount she gave herself, (6+4) that would be 10.  She started with 10 pieces.

An equation would be:

x= 4+(2*3)

I hope this helps!

(Also this equation seems a bit easy, am I reading it wrong? If I am be sure to correct me :) )

y=-3x-5
y=4x+30
PLS HELP ASAP

Answers

{y,x} = {10,-5}

Step-by-step explanation:

sorry if this dont make sense

solve equation [2] for the variable y

y = 4x +30

plug this in for variable y in equation [1 ]

(4x+30) +3x= -5

solve [1] for the variable x

7x= - 35

x= - 5

by now we know this much

y= 4x+30

x= - 5

use the x value to solve for y

y=4 (-5) + 30 = 10

solution

{y,x} = {10,-5}

I need help with this assignment please help me ​

Answers

Answer:

Step-by-step explanation:

a. 7*7*7= 7 cubed(when we divide powers we subtract them)

what equation represents the table ?

Answers

Answer:

y=x-2

Step-by-step explanation:

we know that y-intercept is -2

y=?x-2

So now we would have to find slope

the slope would be 1

soo that makes the equation would be

y=x-2

I hopes this helps.

Have a good day!!

A man with a height of 5ft casts a shadow of 2ft. What will be the height of a tree that casts a shadow of 40ft at the same time?

Answers

Answer:

19

Step-by-step explanation:

Answer:

100 ft.

Step-by-step explanation:

Let x = height of tree

height/height = shadow length/shadow length

5/x = 2/40

2x = 200

x = 100 ft.

Enola surveyed 300 of the students in her school about their favorite color. 78 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was purple?

Answers

Answer:

26%

Step-by-step explanation:

I did some simple math here: a percentage represents a number over 100.

To find the percentage, I just divided 78 by 300 and got 0.26

I then multiplied by 100 to get 26%

Hope this helps! Have a great day!

Write your own Algebraic expression with four terms that can simplify to 12x+4​

Answers

Answer:

11x+1x + 2+ 2

Step-by-step explanation:

Find the equation of the line with slope −15 and y-intercept (0,−2).

Answers

Answer:

y = -15x - 2

Step-by-step explanation:

Please let me know if you want me to write an explanation for my answer :)

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Then a new firebrandwould have to be secured, and this often meant a long journey and a deal of trouble.In 1827, John Walker, a druggist in a small English town, tipped a splint with sulphur, chlorate ofpotash, and sulphid of antimony, and rubbed it on sandpaper, and it burst into flame. The druggisthad discovered the first friction-chemical match, the kind we use to-day. It is called friction-chemicalbecause it is made by mixing certain chemicals together and rubbing them. Although Walker's matchidid not require the bottle of acid, nevertheless it was not a good one. It could be lighted only by hardrubbing, and it sputtered and threw fire in all directions. In a few years, however, phosphorus wassubstituted on the tip for antimony, and the change worked wonders. The match could now belighted with very little rubbing, and it was no longer necessary to have sandpaper upon which to rubit. It would ignite when rubbed on any dry surface, and there was no longer any sputtering. This wasthe phosphorus match, the match with which we are so familiar,How does the author develop the idea that relying on nature was problematic? Please respond inthree to five complete sentences, using evidence from the text to support your answer. (5 points) find two numbers whose sum is 15 and whose product is 44. write the answers as integers or simplified fractions. D(x+2)(x+6)=0In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:O zero product propertyO division propertyO transitive propertyO multiplication propertyHOI All the following were original members of the European Community, the predecessor to the European Union,EXCEPT(A) France (D) Italy(B) Belgium (E) The Netherlands(C) United Kingdom Please answer and explain so I can understand Following circuits are two implementations of 2-input AND gate. Which one is faster, and explain why? Is it consistent with your intuition? Assume = k = 2, Cgate = C X 2-NAND 2-NOR 6C A B When it comes to mate selection, too much choice is not always the best thing. in the book, paradox of choice, schwartz described two types of people. those who spend a lot of time and energy researching options often ended up less satisfied when they finally make a decision. schwartz labeled those people:___________. i. satisficers ii. sufficers iii. maximizers iv. decisionizers