Theorem: Finding portions of the basin of attraction for a critical point at the origin

Answers

Answer 1

The origin is an unstable node. In these cases, the basin of attraction is not well-defined.

How to find portions of the basin of attraction for a critical point at the origin?

The theorem for finding portions of the basin of attraction for a critical point at the origin is as follows:

Suppose we have a system of differential equations given by:

dx/dt = f(x,y)

dy/dt = g(x,y)

And a critical point at the origin, (0,0). Suppose further that the Jacobian matrix evaluated at the origin has distinct eigenvalues λ1 and λ2, with corresponding eigenvectors v1 and v2.

Then the basin of attraction for the critical point at the origin can be divided into three parts as follows:

The origin is a stable node if both eigenvalues are negative. In this case, the basin of attraction includes all initial conditions in the quadrant containing the origin that are not on the eigenvectors.

The origin is a stable spiral if both eigenvalues are complex with negative real part. In this case, the basin of attraction includes all initial conditions that spiral towards the origin, excluding those on the eigenvectors.

The origin is a saddle point if the eigenvalues have opposite signs. In this case, the basin of attraction is divided by the eigenvectors into two regions, one containing initial conditions that approach the origin and the other containing initial conditions that move away from the origin.

Note that if the eigenvalues are complex with positive real part, the origin is an unstable spiral, and if both eigenvalues are positive, the origin is an unstable node. In these cases, the basin of attraction is not well-defined.

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Related Questions

the screenshot is below for the question
Simplify.

4+37x−2−27x




6+57x

2+17x

6−17x

2−57x

the screenshot is below for the questionSimplify.4+37x227x6+57x2+17x617x257x

Answers

Answer:

2+1/7x

Step-by-step explanation:

I didn't realize there were fractions in the numbers

The simplification of the expression 4 + 3x/7 -2 - 2x/7 is 2 + x/7.

The correct answer is B.

What is an expression?

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

We have the expression,

4 + 3x/7 -2 - 2x/7

Simplifying,

4 + 3x/7 -2 - 2x/7

= 3x/7 - 2x/7 + 4 -2

= (3x-2x)/7 + 2

= x/7 + 2

Therefore, 2 + x/7 is the value of the expression.

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What is the circumference of a circle with a diameter of 10 in? (NO LINKS PLS)

Answers

Answer:

10π or 31.4159265359

Step-by-step explanation:

Step-by-step explanation:

radius is 5

C = 2πr

C = 2(5)π

= 10π

= 31.42in

The boys and girls soccer clubs are trying to raise money for new uniforms.​

The boys and girls soccer clubs are trying to raise money for new uniforms.

Answers

Answer: the answer you chose was correct x+y <1000

                                                                       x=<75

Step-by-step explanation:

first they are selling 3 dollar and 4 doallar items to get above 1000 dollars

then they sayed at least 75 bags of hot chips so it has to be 75 or higher

consider the number 2.18 in the estimate column and budget row in the table. is it sensible to interpret this number? if not, explain why we can't give meaning to this number. otherwise, explain (1) why we can give meaning to this number and (2) what it means in this context.

Answers

Answer:

Step-by-step explanation:

HOW MUHPOINTS U GON GIVE ME?

Please hurry! This is due soon.

Please hurry! This is due soon.

Answers

Hi!

We can see here that this is a composition question.

And since the composition of g of f of x is x, we can conclude that g(x) is the inverse of f(x) (if you're confused, search up the definition of an inverse function).

To find an inverse function, we can take the f(x) function and change the positions of the x and y variables.

\(f(x)=\frac{e^7^x+\sqrt{3}}{2}\)

\(y=\frac{e^7^x+\sqrt{3}}{2}\)

\(x=\frac{e^7^y+\sqrt{3}}{2}\)

\(2x=e^7^y+\sqrt{3}\)

\(e^7^y=2x-\sqrt{3}\)

\(7y=ln(2x-\sqrt{3})\)

\(y=\frac{ln(2x-\sqrt{3})}{7}\)

Which is answer choice A, to check your work, you can solve the composition of g(f(x)), which will get you x.

\(g(f(x))\)

\(g(\frac{e^7^x+\sqrt{3}}{2})\)

\(\frac{ln(2(\frac{e^7^x+\sqrt{3}}{2})-\sqrt{3}}{7}\)

2s cancel.

\(\frac{ln(e^7^x+\sqrt{3})-\sqrt{3}}{7}\)

The natural log and e cancel.

\(\frac{7x+\sqrt{3}-\sqrt{3}}{7}\)

\(\sqrt{3}\)s cancel.

\(\frac{7x}{7}\)

7s cancel.

\(x\)

Hope this helps!

the soccer teams sells pizza and drinks during football games to raise money for their club . 50 slices of pizza and 100 drinks for $275. 100 slices of pizza and 60 drinks will sell for $270. How much does each slice of pizza sell for ?

Answers

Answer:

$1.5

Step-by-step explanation:

From the given problem, we would set up two equations to solve for the cost of each slice of pizza;

 Let the cost of a slice of pizza  = P

 Let the cost of a drink  = D

  50 slices of pizza and 100 drinks for $275

          50p + 100D  = 275 ----- i

 100 slices of pizza and 60 drinks will sell for $270  

           100p + 60D  = 270 ----- ii

  The two equations:

         50p + 100D  = 275 ----- i

        100p + 60D  = 270 ----- ii

Multiply equation i by 3 and equation ii by 5

        150p + 300D  = 825      ----iii

        500p + 300D  = 1350   ---- iv

Now,

Subtract iii from iv;

               350p  = 525

                   p = $1.5

A personal pizza recipe calls for 4 ounces of sauce and 5 ounces of cheese. How many ounces of sauce are there for every ounce of cheese?

Answers

Answer:

taco Tuesday way chamaco

Step-by-step explanation:

What is 36/81
in simplest form? HELP!

Answers

Answer:

4/9

Step-by-step explanation:

To simplify this fraction, we can find the factors for each number and then take an equal amount out (divide).

Two factors that make up 36 are 4 and 9. Two factors that make up 81 are 9 and 9. Therefore, because 9 is a common factor between the two, we can divide both terms by 9 and simplify the fraction.

36/9 = 4

81/9 = 9

The new fraction is 4/9.

A function f(x) is graphed on the coordinate plane.


What is the function rule in slope-intercept form?



Enter your answer in the box.

A function f(x) is graphed on the coordinate plane.What is the function rule in slope-intercept form?Enter

Answers

Answer:

y = -4x - 2

Step-by-step explanation:

y-intercept: -2

Slope: -4

18) Both x and y coordinates of a point in quadrant 1 are negative.

Answers

Answer:

false

Step-by-step explanation:

the first quadrant of a coordinate plane is the upper right corner

this means that both x and y coordinates of a point would have to be positive

therefore it's false

hope this helps!

how many degrees would the minute hand on a clock have to turn from 6am to reach 12pm​

Answers

akeeeeeeeeeeeeeeeeeeetseeeeeeeeeeebe

Answer:

180° is the accurate correct answer

Step-by-step explanation:

mark me as brainliest

do u know which symbol makes 6 15/28 ____ 6 5/9

Answers

Answer:

The "less than" sign

6 15/28 < 6 5/9

Explanation:

The value of

\(6\frac{15}{28}=6.536\)

The value of

\(6\frac{5}{9}=6.556\)

Since 6.536 is less than 6.556, we use the "<" sign.

I know its not alot of point but please help me and no essay you will get brainliest if ur answer was first and correct

I know its not alot of point but please help me and no essay you will get brainliest if ur answer was

Answers

60 feet; because the length goes down by one each time so it is (6•4)+(5•4)+(4•4)

Solve the inequalities please

Solve the inequalities please

Answers

\(\huge\text{Answer:}\)

Inequality number 1: x≥7

Inequality number 2:  x<3

Inequality number 3: x≤-2

Inequality number 4: x≤7

\(\huge\text{Solution:}\)

1. 3x+12-6x≤-9

3x-6x+12≤-9

Subtract the x's:

-3x+12≤-9

-3x≤-9-12

-3x≤-21

3x≥21

x≥7

2. x+5x-6<12

6x-6<12

Move 6 to the right, using the \(\bold{\underline{opposite ~operation}}\):

6x<12+6

6x<18

Now, divide both sides by 6:

x<3

3. 5(x+8)-7≤23

Use the Distributive Property:

5x+40-7≤23

5x+33≤23

5x≤23-33

5x≤-10

x≤-2

4. 4x-6≥6x-20

4x-6x≥-20+6

-2x≥-14

2x≤14

x≤7

___________________________

Note:

If we divide both sides of the inequality by a negative variable, we flip the inequality sign.

___________________________

Hope you find it helpful.

Feel free to ask if you have any doubts.

#1

3x+12-6x≤-9-3x+12≤-9-3x≤-213x≥21x≥7

#2

x+5x-6<126x<18x<3

#3

5(x+8)-7≤235x+40≤305x≤-10x≤-2

#4

4x-6≥6x-20-2x≥-14x≤7

Find the area of hexagon DEFGHI.

Find the area of hexagon DEFGHI.

Answers

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Find the area of hexagon DEFGHI.

PLS HELP ASAP(100 POINTS)

The following tree heights were recorded on a school campus:


61, 72, 84, 88, 77, 67, 76, 79, 63, 79, 69, 70, 86, 78, 82, 82, 80, 73, 87, 90, 73, 76, 79, 71, 75, 79, 76, 83, 84, 87, 72, 81, 89, 74, 77, 78, 81, 84


A science teacher wants to choose a data display that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. Which display will present the information in this way?

Bar chart
Dot plot
Circle graph
Histogram

Answers

A plot that will present the information that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. : histogram

In this question, we have been given the tree heights recorded on a school campus.

A science teacher wants to choose a data display that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc.

We need to find a correct plot that will present the information in this way.

We know that in bar charts, each bar represents one value(category). And  in a histogram, each bar will represent a continuous data

Therefore, a plot that will present the information that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. : histogram

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Answer:

Step-by-step explanation:

A plot that will display information highlighting the number of trees in a range of heights, such as 60-64, 65-69, and so on: histogram

We were provided the tree heights reported on a school grounds in this question. A science instructor needs to select a data presentation that will show how many trees are in a given height range, such as 60-64, 65-69, and so on. We must find a suitable plot to portray the data in this manner. We know that each bar on a bar chart represents one value (category). And each bar in a histogram represents continuous data.

i need help with this!!

i need help with this!!

Answers

Answer:

16x^2-12x+9

explanation:

64x^3-27 by 4x-3 = 16x^2-12x+9

A recipe calls for 1/3 of a cup of sugar per batch. Elena user 6 1/6 cups of sugar to make multiple batches of cookies. How many batches did she make?

Answers

Answer:

18 1/2

Step-by-step explanation:

6 1/6 ÷ 1/3 = 18 1/2

A number doubled plus ten. (Expression)

Answers

Ok, ok, ok, and ok njkkjvjkhjbgggbn.

what does 130°30' mean

Answers

130 degrees and 30 minutes

That's minutes as in arc-minutes, a sub-division of a degree. 1 degree is made up of 60 minutes.

So 130°30' is the same as 130° + 30/60° = 130.5°.

Why is [3, ∞) the range of the function?

Why is [3, ) the range of the function?

Answers

The range of the graph is [3, ∞), because it has a minimum value at y = 3

Calculating the range of the graph

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an absolute value graph

The rule of a graph is that

The domain is the x valuesThe range is the f(x) values

Using the above as a guide, we have the following:

Domain = All real values

Range = [3, ∞), because it has a minimum value at y = 3

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A stew recipe states that of the whole stew should be beef. Marika made her stew with 4 pounds of beef. What was the total
weight of the stew if she followed the recipe?

Answers

Answer:

10 pounds.

Step-by-step explanation:

In this scenario, we can use the Rule of Three to solve for the whole weight of the stew. This rule is used for ratio problems. You simply need to multiply the available diagonal values together and then divide by the remaining value to get the value of the single variable in the ratio. Like so...

40%   <=====>  4 pounds

100%  <=====>  x pounds

(100 * 4) / 40 = x pounds

400 / 40 = x pounds

10 = x pounds

Finally, we can see that the total weight of the stew if she followed the original recipe would be 10 pounds.

55 ÷ -------- +5 × _____× 2 =195

u can only use numbers 11,19,2,29,4

Answers

Answer:

55 ÷ 11 +5 × 19 × 2 =195

If you take turns in filling each gap then at one point you can get the answers.

Brainliest pls if it is correct! And hope it helps!

Evaluate

-3 (2) (-1) (4)

Answers

64854755555557427382675

It is 24

Explanation: (-3) • (2)= -6
-6 • -1 = 6
6 • 4 = 24

Would any three squares
form the sides of a right
triangle? Explain.

Answers

The sum of the areas would be two small squares so no

Three squares of sides 15 units, 9 units, and 12 units can form a

right-angled triangle.

What is a triangle?

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Given, We have to form a right-angled triangle that has side lengths of

3 different squares.

Let, The first square has a side length of 9 units, and let this be the height of the right-angled triangle.

Another square has a side length of 15 units and this is the hypotenuse.

Therefore, the base of the triangle must be 15² - 9² = 225 - 81 = 144 = 12 units.

So, The third square must have a side length of 12 units.

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Would any three squaresform the sides of a righttriangle? Explain.

between clock skew and clock jitter, which is preferable and why? group of answer choices jitter is preferred because it is predictable jitter is preferred, because it increases max frequency skew is preferred, because it is more predictable and can sometimes increase max frequency skew is preferred because it is unpredictable

Answers

Between clock skew and clock jitter, skew is preferred because it is more predictable and can sometimes increase max frequency. This makes it easier to manage in electronic systems and can provide benefits in certain scenarios.

Jitter is preferred because it is predictable. Clock jitter refers to the variability of the clock signal and can be predicted and compensated for. On the other hand, clock skew refers to the difference in arrival time of the clock signal at different points in the circuit and can sometimes increase maximum frequency. However, skew is preferred because it is more predictable and can be compensated for, while jitter is preferred because it is unpredictable and can't be compensated for. Therefore, in general, jitter is considered more preferable than skew.

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A new health drink has ​% of the recommended daily allowance​ (RDA) for a certain vitamin. The RDA for this vitamin is mg. How many milligrams of the vitamin are in the​ drink?

Answers

Answer:

git to be honest with you i dont know

Step-by-step explanation:

The reading group checked out 36 library books. 17 books are fiction, 10 are biographies, and some are science. How many books are science?​

Answers

17+10=27
36-27= 9
so 9 books are science

Answer:

9 science books

Step-by-step explanation:

Step 1) 36 - 17 = 19

Step 2) 19 - 10 = 9

Calliope Is going to buy a television for $1349. If sales tax is 8%, find the price of the television including tax.

Answers

Answer:

The price including tax is $1,456.92

Step-by-step explanation:

First we need to convert our percentage into a decimal.

0.08

Now we need to multiply our price by the sales tax.

$1,349.00 × 0.08 = $107.92

Our sales tax is $107.92.

Added to our price it's $1,456.92.

Samuel wants to eat at least 15grams of protein each day. Let x represent the amount of protein he should meat each day to meet his goal. Which inequality represents this situation?

Answers

Answer:

\(x\geq 15\)

Step-by-step explanation:

Samuel wants at least 15 grams

Let's expand on "at least 15"

It means that Samuel wants no less than 15, but 15 or more

It could be 16, but not 14

To create an inequality, 15 or more can be written as \(x\geq 15\) (x is 15 more more)

The answer is \(x\geq 15\)

Hope this helps :)

Have a nice day!

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