the system x′ = 2(x −y)y, y′ = x y −2, has an equilbrium point at (1,1). this equilibrium point is a(n)

Answers

Answer 1

The equilibrium point (1,1) in the system x′ = 2(x − y)y, y′ = xy - 2 is a(n) stable spiral.

To determine the type of equilibrium point, we first linearize the system around the point (1,1) by finding the Jacobian matrix:

J(x,y) = | ∂x′/∂x  ∂x′/∂y | = |  2y     -2y  |
        | ∂y′/∂x  ∂y′/∂y |    |  y      x   |

Evaluate the Jacobian at the equilibrium point (1,1):

J(1,1) = |  2  -2 |
        |  1   1  |

Next, find the eigenvalues of the Jacobian matrix. The characteristic equation is:

(2 - λ)(1 - λ) - (-2)(1) = λ² - 3λ + 4 = 0

Solve for the eigenvalues:

λ₁ = (3 + √7i)/2, λ₂ = (3 - √7i)/2

Since the eigenvalues have positive real parts and nonzero imaginary parts, the equilibrium point at (1,1) is a stable spiral. This means that trajectories near the point spiral towards it over time.

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Related Questions

is a(t) = 1200(1 + .03)t a decay function?

Answers

Answer:

Step-by-step explanation:

No, it is an exponential growth function because 1.03>1. An exponential decay function would have a rate less than 1.

Problem situation:
Janelle is at the movie theater and has $20
to spend.
She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99.
How many snacks, x, can Janelle buy?
Inequality that represents this situation:
20 > 8 + 4.99x
Drag each number to show if it is a solution to both the inequality and the problem
situation, to the inequality only, or if it is not a solution.

Answers

Answer:

Rewrite so x is on the left side of the inequality.

8 + 4.99x < 20

Move all terms not containing x to the right side of the inequality.

4.99x < 12

Divide each term by 4.99 and simplify.

x < 2.405

The result can be shown in multiple forms.

Inequality Form:

x < 2.405

Interval Notation:

( −∞ , 2.405 )

Step-by-step explanation:

Answer:

Both:

1

2

Inequality Only:

-4

3/4

2.3

Neither:

2.5

Given that ƒ(x) = x2 + 1 and g(x) = –3, multiply the functions (g · ƒ)(x).

Answers

Answer:

(2+1×-3)(x) = 3×(-3)(x) =-9x

Answer:

(g · ƒ)(x) = –3x2 – 3

Step-by-step explanation:I took the test

hey hons, i'd love some help here if you could take a look and see if you could help i'd be grateful! <33333

Answers

Step-by-step explanation:

A function is a rule that relates how one quantity depends on other quantities

Please help I'm giving 50 points I don't have time to do assignment as of now so can someone do me the favor of doing it?

Answers

Answer:

Step-by-step explanation:

1. Not a function

2. Function

3. Function

4. Not a function

5. Not a function

6. Function

7. Function

8. Not a Function

9. Function

10. Not a Function

Answer:

1. Not a function

2. A function

3. A function

4. Not a function

5. Not a function

6. A function

7. A function

8. Not a function

9. A function

10. Not a function

Step-by-step explanation:

The only rule for a relationship to be a function is...

Only ONE output for ONE input

1. There is more than one output for one input

2. Each input has only one output

3. Each input has only one output

4. There is more than one output for one input

5. There is more than one output for one input

6. Each input has only one output

7. Each input has only one output

8. There is more than one output for one input

9. Each input has only one output

10. There is more than one output for one input

Hope this helps :)

Let me know if there are any mistakes!!

What is 38 times 4 plus the square root of 30

Answers

Answer:157.47722557

Step-by-step explanation:

2x+3y=1470 changed to slope intercept form, write a description which is clear precise and correct of how to graph the line using the slope intercept method,changes equation to to function notation and explains clearly what the graph of the equation represents. graph the equation and labels the intercept correctly. Write at least 3 sentences explaining how the graphs of the two equations are the same and how they are different.

Answers

Answer:

y= 490 - 2x

Step-by-step explanation:

Answer: Do I get brainliest if I try? 7 = 490 - 2x

Step-by-step explanation:

Select all of the following that are true. *
sinA=18/30
sinA=3/5
cosA=10/6
cosA=8/10
cosA=5/3
tanF=24/18
tanF=3/4
tanD=3/4
sinD=18/30

Answers

Answer:

Step-by-step explanation:

sin A = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{6}{10}[/tex] = [tex]\frac{3}{5}[/tex]

cos A = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex]

tan F = [tex]\frac{DE}{FE}[/tex] = [tex]\frac{24}{18}[/tex] = [tex]\frac{4}{3}[/tex]

tan D = [tex]\frac{FE}{DE}[/tex] = [tex]\frac{18}{24}[/tex] = [tex]\frac{3}{4}[/tex]

sin D = [tex]\frac{FE}{FD}[/tex] = [tex]\frac{18}{30}[/tex] = [tex]\frac{3}{5}[/tex]

it says priya's family exchanged 250 dollars for 4,250 pesos. Riya bought a sweater for 510 pesos. how many did the sweater cost?

Answers

$1 = $20.19 pesos, try dividing 510 pesos by 20.19. That should give you the dollar amount.

write : what’s the algebraic expression for the difference of 9 and x

Answers

Answer:

9-x

Step-by-step explanation:

ez dub

Answer:

9-x

Step-by-step explanation:

the difference of (tells you to subtract) 9 and x (9-x)

hope this helps have a blessed

Solve for p.
16p = 160

Answers

Answer

160 divided by 16 = 10

Answer: 16p=160:

P = 10

Step-by-step explanation:

If you times by ten at any time then just add a zero to the end. So just add a zero to 16 to make it 160

In this case your going to solve it like this:

160 / 16 = 10

4. Simplify the expression
2(10) + 2(x-4).
(A) 2x + 16
(B) x+12
© 2x + 12
(D) x + 16

Answers

Answer:

C. 2x + 12

Step-by-step explanation:

2(10) + 2(x-4)

= 20 + 2x - 8

= 2x + 20 - 8

= 2x + 12

find the distance of each the following lines from the origin.
(a),4x_3y=10
b,x_5y+2=0
c,3x+y_7=0​

Answers

Answer:

Step-by-step explanation:

3x+y−7=0 and x+2y+9=0

write in the form y=mx+c

i.e.y=−3x+7,y=  

2

−x

​  

−  

2

9

​  

 

∴m  

1

​  

=−3 and m  

2

​  

∓−  

2

1

​  

 

tan(A−B)=  

​  

 

1+tanAtanB

tanA−tanB

​  

 

​  

 

​  

 

1+(−3)(−y  

2

​  

)

−3−(−y  

2

​  

)

​  

 

​  

 

=  

​  

 

5/2

−5/2

​  

 

​  

=1

∴ Angle b/w then is tan  

−1

(1)=45  

 

=  

4

π

2(6x + 1) - 4(x - 5) = -2

Answers

Answer:

x=−3

Step-by-step explanation:

2(6x+1)−4(x−5)=−2

Step 1: Simplify both sides of the equation.

2(6x+1)−4(x−5)=−2

(2)(6x)+(2)(1)+(−4)(x)+(−4)(−5)=−2(Distribute)

12x+2+−4x+20=−2

(12x+−4x)+(2+20)=−2(Combine Like Terms)

8x+22=−2

8x+22=−2

Step 2: Subtract 22 from both sides.

8x+22−22=−2−22

8x=−24

Step 3: Divide both sides by 8.

8x/8=−24/8

The answer is X=-3b

4(5.8 - 9x) + 8.2 + 22x

Answers

Answer:

157 - 70x

 —————————

     5    

Step-by-step explanation:

Answer:

31.4 - 14x

Step-by-step explanation:

4(5.8 - 9x) = 23.2 - 36x

23.2 - 36x + 8.2 + 22x

23.2 + 8.2 - 36x + 22x

only add/subtract LIKE terms

31.4 - 14x

Simplify (2/3 + 1/6).
Write the sum in the simplest form.

Answers

Lcm of denominators = 3,6= 6

2x2/3x2 + 1/6

(4/6+1/6=5/6

Sum is 5/6
The answer would be 5/6
Because you find the common denominator so it would be 4/6 +1/6= 5/6

Hope this helps

Have a great day/night

Feel free to ask any questions

Mariana gets $15 per hour working at McDonald's and Jayvon gets $15 per hour as well. Jayvon had $50 in the
bank to start. After how many weeks will Jayvon and Mariana have the same amount of money in their bank
accounts?

Answers

Answer:

What r the options?

Step-by-step explanation:

Can someone help me with this problem! I WILL GIVE A BRAINIEST!!! I need it asap PLEASE.

Answers

Answer:

(

1

)

(

3

2

+

6

)

Step-by-step explanation:

Please helppppp!!!!!!

Answers

Answer:

$7.44

Step-by-step explanation:

4.96/8= .62 per ounce

.62 x 12 = $7.44

8% of x is 20.
Plz help

Answers

Answer: 250 im not sure if its correct though

Step-by-step explanation: 8% = 8/100  

8 /100  × x = 20

Multiplying both sides by 100 and dividing both sides by 8,

we have x = 20 ×  100 /8

x = 250

If you are using a calculator, simply enter 20×100÷8, which will give you the answer.

Can somebody help me out ? Please

Answers

Answer:

52 sq mm

Step-by-step explanation:

you can break it into a long rectangle in the middle with dimensions of 2(6+8) or 2(14) = 28 sq mm

the triangle on the bottom has a base of (8-4) x height of 3, which gives 6 sq mm (you have to divide by 2)

the upper left rectangle is 6 x 3 = 18 sq mm

add: 28 + 6 + 18 = 52

PLEASE ANSWERRRRRRRRRRRRRRRRRRRRRRRRR

Sara and 3 of her friends went to lunch one day. Each person paid for her own lunch, but they agreed to split the tip. If the tip amount was 15% of the total, and the 4 lunches totaled $60, what was the portion of each person’s tip amount?

Answers

Answer:

Step-by-step equation:

15% of 60 is nine.

Percentage is equivalent to the portion of a quantity present in the whole. The portion of each person’s tip amount shared by Sara and 3 of her friends is $2.65.

What is percentage?

A percentage is a value that indicates 100th part of any quantity.

To convert percentage into a fraction it is divided by 100.

Given that,

The amount of tip is 15% of the total amount A.

The total amount of 4 lunches = $60.

As per the question, the total amount can be written as,

15% of A = A - 60

=> 15 / 100 × A = A - 60  

=> A - (3 / 20) × A = 60

=> A - (3 / 20) × A = 60

=> (17 / 20) × A = 60

=> A = (60 × 20) / 17

=> A = 70.58

Now, the total amount of tip is,

15% of 70.58

(15 / 100) × 70.58 = 10.58

The tip shared by each friend = 10.58 ÷ 4

                                                 = 2.65

Hence, the portion of each person’s tip amount is $2.65.

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Jaden is saving money to buy a bike that costs $290. He has saved $140 so far. He plans on saving $25 each week. Write and solve an equation to determine in how many weeks (identify the question) Jaden will have enough money to buy the bike.

What does the variable in question 4a represent?

Answers

Answer:

25w+140=290

He will have enough money in 6 weeks

w represents the amount of weeks

Step-by-step explanation:

25w+140=290

$25 every week + the original $140 = the total needed $290

Answer:

140 + 25w = 290

w = 6

Step-by-step explanation:

Goal: $290

Currently have $140

Saving $25 each week (variable)

Start with your given amounts :

(base) 140 + 25w (variable solving for) = 290 (goal you want equation to equal)

w stands for the amount of weeks for the goal to be reached

Solve:

140 + 25w = 290

subtract 140

25w = 150

divide 25

w=6

Double check (optional but suggested)

140 + 25 (6) = 290

140 + 150 = 290

290 = 290

correct

B. Decide whether each quantity is constant or variable
1. The number of eggs in a dozen. 2*12 = 24 eggs
.
2. The number of a person's heartbeat per minute. 12d
3. The number of minutes in an hour.
4. The length of a meter.
5. The number of enrollees in your school each year.
maayos na sagot po...​

Answers

Answer:

ituturo ko ang sagot pero follow me muna sa brainly

plz answer the picture below fast and correctly!

Answers

Answer:

a) BOC = 80⁰

b) COD = 60⁰

Step-by-step explanation:

..................

Answer:

BOC is 80 and COD is 60

Step-by-step explanation:

If DOF is 120 you subtract 40 from it because of of AOB then COD is the remaining of 180

In this figure, angles R and S are complementary. Find the measure of angle S.
S
62°
R
PLEASE HELP ASAP

Answers

Answer:

Angle S is 28 degrees.

Step-by-step explanation:

You know angle R is 62 degrees and that angle Q is 90 degrees because the angle is marked by a teeny square (as I like to call it). You ten can add these two angles together and you will get the angle of 152 degrees. And as you should know that all angles of a triangle added together are  180 degrees you just take 180 degrees and subtract it with the two known angles added together. Thus you know that the final answer to S is 28 degrees.

Find the value of x.
2x
fi
80
27
60
x = [?]
Enter

Answers

the answer is x=18

hope that helped^^

HELP I NEED HELP ASAP

Answers

Answer:

I think the answer is letter C

i really need help wit this pleasee help and show work pleasee

Answers

Answer:

4000π cm^2

Step-by-step explanation:

first we change the 1.6m to cm:

1.6m = 160cm

Now we can use the formula:

V = πr^2h

where π is just π, r is the radius (not the diameter) and h is the height

V = π * 5^2 * 160 = 4000π cm

Answer:

Step-by-step explanation:

[tex]\text{They give you the equation for the volume.}\\ \\ V=\pi r^2h\\ \\ \text{You simply need to plug in the values given to you for r and h.}\\ \\ r=10/2=5cm,\ h=1.6m(100cm/m)=160cm\\ \\

V=\pi 5^2(160)\\ \\ V=160(25)\pi\\ \\ V=4000\pi cm^3\\ \\ V\approx 12566.37 cm^3[/tex]

28-3(2+4)+9


With explanation

Answers

Answer:

=19

Step-by-step explanation:

28-3*2+4)+9

28-3*6+9

28-18+9

=19

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