Theorem 9.6.2: When the origin is an unstable critical point. Conditions for instability
Answers
This indicates that there is no clear direction in which the system moves, and higher-order terms in the Taylor series may cause it to move away from the origin.
What is the conditions for instability when the origin is an unstable critical point?Theorem 9.6.2 provides conditions for instability when the origin is an unstable critical point. The statement of the theorem is as follows:
Suppose that the system of differential equations given by
dx/dt = f(x,y)
dy/dt = g(x,y)
Has an unstable critical point at the origin, (0,0). That is, the origin is a critical point, but it is not stable. Then the following conditions must hold for the system to be unstable at the origin:
At least one eigenvalue of the Jacobian matrix evaluated at the origin is positive.
The eigenvector corresponding to the positive eigenvalue points away from the origin.
Alternatively, if the Jacobian matrix evaluated at the origin has a repeated eigenvalue of zero, then the system may also be unstable. In this case, we need to examine the higher-order terms in the Taylor series expansion of the system near the origin to determine its stability.
Intuitively, the conditions for instability tell us that if there is any direction in which the system moves away from the origin, then the origin is unstable. This can happen if the eigenvalues of the Jacobian matrix have a positive real part, which causes the system to move away from the origin in that direction. It can also happen if the Jacobian matrix has a repeated eigenvalue of zero, since this indicates that there is no clear direction in which the system moves, and higher-order terms in the Taylor series may cause it to move away from the origin.
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Related Questions
Evaluate each of the following given that f(x) =2x+10, find:f(-3)
Answers
Answer:
4
Step-by-step explanation
Which of the following below is a solution to y=4x-3
(2,5)
(5,5)
(4,5)
(3,5)
Answers
\( \fbox{(2,5)}\)
Step-by-step explanation:Hello, substitute all the given coordinates & see if RHS match with LHS
given equation,
y = 4x-3
First coordinate,
(x,y) = (2,5)
5= 4×2-3
5=5
Hence, first solution satisfies the given equation,
let's solve for rest other cordinates,
second coordinate,
(x,y) = (5,5)
5= 4×5-3
5 ≠ 17
does not satisfy,
third coordinate,
(x,y) = (4,5)
5= 4×4-3
5 ≠ 13
does not satisfy,
fourth coordinate,
(x,y) = (4,5)
5 = 4×3-3
5 ≠ 9
does not satisfy.
Hence the correct answer is (2,5)
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Cab A charged $5x + 20 for a ride to the
airport from the mall and Cab B charged
$4x+ 50 for the same ride. Which cab
charged more? How much more?
Answers
Answer:
Cab B charged more
It charged $(30-x) more
Step-by-step explanation:
Here, we want to know which of two cabs charged more for a ride from the airport to the mall.
To know the cab that charged more, we shall be substituting any same value of x in both of the fees
Let’s say x is 10
Thus 5x + 20 becomes 5(10) + 20 = 50 + 20 = 70
while 4x + 50 becomes 4(10) + 50 = 40 + 50 = 90
Clearly we can see that 4x + 50 is greater then 5x + 20, so we can conclude that 4x + 50 is a greater fee
Now since we know the one that’s higher, we can now know the value by which it is higher
That would be (4x + 50)-(5x + 20)
= 4x + 50 -5x -20
= 4x-5x + 50-20
= -x + 30 or simply 30-x
An account earns simple annual interest. $925 at 2.3% for 2.4 years. Find the balance of the account.
Answers
The balance of the account after 2.4 years is 975.22.
To find the balance of the account, we need to calculate the interest earned over 2.4 years and add it to the initial principal of 925.
The formula for simple interest is:
I = P × r × t
where:
I = interest earned
P = principal (initial amount of money)
r = annual interest rate (as a decimal)
t = time (in years)
Plugging in the values given in the problem, we get:
I = 925 × 0.023 × 2.4
I = 50.22
Therefore, the interest earned over 2.4 years is 50.22.
To find the balance of the account, we need to add the interest earned to the initial principal:
Balance = Principal + Interest
Balance = 925 + 50.22
Balance = 975.22
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1) One angle is 28° larger than the other. The sum of the measures of two angles is 90°. Find the measure of each angle.
X=_____
Equation:______
Answers
Answer:
62
Step-by-step explanation:
Equation: x +28 =90
x = 59°
Measure of one angle = 59°
Measure of another angle = 31°
Equation to calculate the measurement: x + x - 28 = 90Given,
What is angle?In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.
Given,
Sum of two angles = 90°
One angle is 28° larger than other
Let the measurement of one angle is x
then other angle = x - 28°
But,
x + x - 28° = 90°
2x - 28° = 90°
2x = 90° + 28°
x = 118°/2
x = 59°
one angle = 59°
other angle = 59° - 28° = 31°
Hence, 59° is measure of one angle
and 31° is measure of other angle.
x + x - 28 = 90 is the Equation to calculate the measurement.
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i need help with this ?
Answers
Answer:
Range: [-5, 0]
General Formulas and Concepts:
Algebra I
Range is the set of y-values that are outputted by function f(x)Step-by-step explanation:
According to the graph, the line's y-values span from -5 to 0. Since both are closed dot, they are inclusive in the range:
[-5, 0] or -5 ≤ y ≤ 0
hi pls help: a dress is on sale for $600, if that is 75% of the regular price, then what is the regular price of the dress.
Answers
Answer:
800
Step-by-step explanation:
orginal price x 75% = 600
600/75% = original price
Pedro has a student loan of $62,845. This loan has a simple interest rate of 7% per year. What is the amount of interest that Pedro will be charged on this loan at the end of the year?
Answers
P=62,845
R=0.07 or 7%
T=1 year period
So overall your equation is 62845*0.07*1=$4,399.15
Now at this point the interest is added onto the principal amount to figure out some new amount after one year so:
62845.00+4399.15=$67,244.15
Farmer TC is drinking 17 cups of tea by the sea. His cows are grazing behind him, and he notices that the square of the fifth root of the number of cows he has is 1 less than the number of cups of tea he is drinking. How many cows does TC have?
Answers
We can determine that TC owns one cow using exponential calculations.
Exponential equations: what are they?Exponent-based equations are those in which the exponent, or a portion of the exponent, is a variable.
For illustration, \(3^{x}\) = 81.
In the question given,
TC is drinking no. of cups = 17
Let no. of cows TC has = x
Now according to the question, we can for the equation as:
\((\sqrt[5]{x} )^{2}\) = 17 -1
⇒ x = \(\sqrt[5]{4}\)
⇒ x = 1.319
⇒ x ≈ 1
Hence, TC owns 1 cow.
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Erin is rolling a six-sided number cube repeatedly. Her goal is to roll a prime number 12 times. How many times should Erin expect to have to roll the number cube to result in a prime number 12 times
Answers
The number of times to roll the number cube to result in a prime number 12 times is 24
How to determine the number of times?The given parameters are:
Number cube = 6 sides
Number of times= 12
The probability of obtaining a prime number in a six-sided die is:
P(Prime) = 3/6
The number of times (n) is then calculated as:
p * n = 12
Substitute known values
3/6 * n = 12
Evaluate the fraction
1/2 * n = 12
Multiply both sides by 2
n = 24
Hence, the number of times is 24
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Answer:
24
Step-by-step explanation: I took the test
write 10 rational numbers between -1/3 and 1/3
Answers
Step-by-step explanation:
-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4
a fair die is tossed, and the up face is noted. if the number is even, the die is tossed again; if the number is odd, a fair coin is tossed. consider the following events: a: 5a head appears on the coin.6 b: 5the die is tossed only one time.6 a. list the sample points in the sample space. b. give the probability for each of the sample points. c. find p ( a ) and p ( b ). d. identify the sample points in ac , bc , a b, and a b. e. find p1ac 2, p1bc 2, p1a b2, p1a b2, p1ab2 , and p1b a2 . f. are a and b mutually exclusive events? independent events? why?
Answers
a) Sample space: {1,2,3,4,5,6} for the first toss of the die. If the result is even, then another toss is made, resulting in the sample space {2,4,6} for the second toss. If the first toss is odd, a coin is tossed, resulting in the sample space {H, T} for the coin toss.
b) Each outcome in the sample space has an equal probability of 1/6, except for the outcomes in {2,4,6}, which have a probability of 1/18 for the second toss.
c) P(a) = P(H) = 1/6, P(b) = 1/2.
d) ac: {5H}, bc: {1,3,5}, ab: { }, a∪b: {1,3,5,H}.
e) P(ac) = 1/6, P(bc) = 3/6 = 1/2, P(a∩b) = 0, P(a∪b) = 4/6 = 2/3, P(a|b) = P(ab)/P(b) = 0/1/2 = 0, P(b|a) = P(a∩b)/P(a) = 0/1/6 = 0.
f) a and b are not mutually exclusive events because there is a possibility that both events can occur together. They are not independent because the outcome of the first toss affects the likelihood of the second toss or coin toss.
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Which side of ADEF is the longest?
Answers
Answer:
B: EF
Step-by-step explanation:
This is a right triangle. In a right triangle there are always 2 legs and 1 hypotenuse. The hypotenuse is the side opposite the right angle and is always the longest side. Therefore, EF is the longest side.
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A set of pencils sells for $1.85 and costs $0.60 to make. Twenty percent of
the profit (the difference between the purchase price and the amount it
costs to make) from each set of pencils goes to a school.
If 600 sets are sold, what is the amount of money that will go to the school?
Answers
Answer:
i believe its 150
Step-by-step explanation:
Question
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and
the average number of customers per hour. Create an inequality in standard form that represents the restaurant
owner's desired revenue.
Type the correct answer in each box. Use numerals instead of words.
____x^2 + ____x + ____ > or equal to ____
Answers
To calculate the hourly revenue from the buffet after x $1 increases, we need to multiply the price paid by each customer by the average number of customers per hour.
Let's assume the original price of the buffet is $P and the average number of customers per hour is C. After x $1 increases, the new price becomes $P + x.
The revenue per customer is ($P + x) and the total revenue per hour can be calculated as (C * ($P + x)).
To represent the restaurant owner's desired revenue as an inequality in standard form, we need to specify the minimum desired revenue. Let's assume the desired minimum revenue is R.
The inequality representing the restaurant owner's desired revenue is:
Cx(P + x) ≥ R
Expanding and rearranging the terms, we get:
CxP + Cx^2 ≥ R
Therefore, the inequality in standard form representing the restaurant owner's desired revenue is:
Cx^2 + Cx - R ≥ 0
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If a person consumes a 2500 kcal daily diet, of which 35% is from proteins, the individual would consume approximately grams of protein. (round to the nearest gram)
Answers
Approximately 109 grams of protein would be consumed on a 2500 kcal daily diet, with 35% of the calories coming from proteins.
Protein intake is an important aspect of a healthy diet, as it plays a vital role in various bodily functions. To calculate the grams of protein consumed, we start by determining the total calorie intake and then find the proportion of calories that come from proteins. In this case, the daily diet consists of 2500 kcal. To find the protein calories, we multiply this by the percentage of calories from proteins, which is 35%. This gives us 0.35 * 2500 = 875 kcal from proteins.
Next, we need to convert these calories into grams of protein. Each gram of protein provides approximately 4 calories. Therefore, we divide the protein calories (875 kcal) by 4 to get the grams of protein consumed, which is 875 / 4 ≈ 218.75 grams. Rounding this to the nearest gram, the individual would consume approximately 219 grams of protein on a 2500 kcal daily diet with 35% of the calories coming from proteins.
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What is the domain of the function graphed below?
Answers
Answer:
The domain is the set of x values for which the function resides in.
In this graph, it is unclear as to if the function goes on to infinity, but if it does, the answer is quite easily:
(-2, 4] and [7, ∞)
since the function starts on the left at -2 then continues to the right, with a pause, then indefinitely after.
dogs are inbred for such desirable characteristics as color; but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. a 1992 study of bull terriers (by strain and others, as reported in the veterinary journal) found the following: (i) 50% of the studied bull terriers are white. (ii) 11% of the studied bull terriers are deaf. (iii) 20% of the white bull terriers are deaf. what is the probability that a randomly chosen bull terrier is white and deaf?
Answers
A 1992 study of bull terriers found the following: (i) 50% of the studied bull terriers are white. (ii) 11% of the studied bull terriers are deaf. (iii) 20% of the white bull terriers are deaf. The probability that a randomly chosen bull terrier is white and deaf is 0.1, or 10%.
To find the probability that a randomly chosen bull terrier is white and deaf, we can use the given information from the study:
(i) 50% of the studied bull terriers are white (P(White) = 0.5)
(iii) 20% of the white bull terriers are deaf (P(Deaf|White) = 0.2)
Now, we can apply the conditional probability formula to find the probability of a bull terrier being both white and deaf:
P(White and Deaf) = P(Deaf|White) * P(White)
P(White and Deaf) = 0.2 * 0.5
P(White and Deaf) = 0.1
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A company sells widgets. The amount of profit, y, made by the company, is related to
the selling price of each widget, x, by the given equation. Using this equation, find out
the maximum amount of profit the company can make, to the nearest dollar.
y = -4x2 + 141x – 703
Answers
Answer:
b
Step-by-step explanation:
The maximum amount of profit the company can make is $543
Let y represent the amount of profit and x represent the selling price.
The relationship between x and y is:
y = -4x² + 141x – 703
The maximum profit is at dy/dx = 0, hence:
dy/dx = -8x + 141
-8x + 141 = 0
8x = 141
x = 17.625
The maximum profit is:
y = -4(17.625)² + 141(17.625) – 703 = 543
The maximum amount of profit the company can make is $543
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Annika sells 6 inch pies for $5.00 and 8 inch pies for $9.00 each. Last week she sold twice as many 6 inch pies as she did 8 inch pies. She made $133.00 from her sales. Annika defined x as the number of 6 inch pies she sold and y as the number of 8 inch pies she sold. She wrote the system below.
6 x + 8 y = 133. 2 x = y.
Which statements about the system are true? Check all that apply.
Since the cost for each pie is $5 and $9, the first equation should be 5 x + 9 y = 133.
Since the 8 inch pies are 2 inches larger, the second equation should be x + 2 = y.
Since there are fewer 8 inch pies, the second equation should be x = 2 y to balance the values.
The first equation is correct because 6x represents the money earned for 6 inch pies and 8y represents the money earned for 8 inch pies.
The second equation is correct because there are more 6 inch pies and 2 times a number is always more.
Answers
Answer:
See below!
Step-by-step explanation:
Only the first choice is accurate.
The second choice is incorrect since it doesn't accurately represent the situation described.
The third choice is incorrect since it also doesn't accurately represent the situation described.
The fourth choice is incorrect since the equation is meant to show the cost of the pies, not the size.
While the fifth choice is correct in that the second equation is accurate, the reasoning is inaccurate.
Answer
Only option 1 is correct
helllpppp!!!!!!!!!!!
Answers
Answer:
m∠1 = 148° and m∠2 = 32°
Step-by-step explanation:
m∠1 + m∠2 = 180° (supplementary angles)
4x° + (x - 5)° = 180 (substitution)
4x + x - 5 = 180
5x - 5 = 180
5x = 185
x = 37
m∠1 = 4(37)° =148° and m∠2 = (37 - 5)° = 32°
Three pens cost £1.05. How much would seven pens cost in pence
Answers
Answer:
The cost of 7 pens is Rs. 60, so 2.45
Step-by-step explanation:
find the cost of 7 pens. so 3 divided by 1.05 = 0.35 then multiply by 7 = 2.45 hope this helps can i get brainlyesti tried my best;]
Question 5 (20 points) Circle L is shown. Line segments K L and M L are radii. The length of K L is 12. Angle M L K is 60 degrees. Sector M L K with a 60 degree angle is shaded. What is the area of the sector that is not shaded? a 24π square units b 120π square units c 12π square units d 144π square units
Answers
Answer:
b) is correct 120π square units
Step-by-step explanation:
The sector that is not shaded froms a 300 degree angle. The area of that sector and its angle are proportional with the area of the entire circle and its angle, which is 360 degrees.
We start by computing the area of the circle. Since the radius is 12 units, then the area of the circle is 12² * π = 144π square units. Therefore, the area of the non shaded area is
144π * 300/360 = 120π square units
as option b) suggests.
Answer:
C. 120pi units^2
Step-by-step explanation:
Just took the Unit Test on Edg (2021)!!
solve the pair simultaneous equations
2x+y=7
x -2y=1
Answers
Answer:
y = 1
x = 3
Step-by-step explanation:
y = 7 - 2x
x - 2y = 1
5x - 14 = 1
y = 7 - 2x
x = 3
y = 7 - 2x
y = 1
The graph of y = e^x is transformed as shown in the graph below. Which equation represents the transformed
function?
Answers
y=e^x+3.
The given graph of the function y = e^x
he transformation occur when we add c to the parent function y = e^x giving us a vertical shift c unit in the same direction as the sign.
The y axis of a coordinate plane is the vertical axis. When a function shifts vertically, the value of y changes.
The given parent function: y = e^x,
we can now graph the vertical shift alongside i.e, c=3
Then, the upward shift function is, y = e^x + c
Substitute the value of c=3,
then, the transformed equation becomes, y = e^x + 3
as it goes through (0,4).
∴The equation y = e^x + 3 represents the transformed function.
Answer:
y=e^x+3.
Step-by-step explanation:
the z-index will be ignored if an element is set to which of the following position values? relative fixed absolute static
Answers
The z-index property determines the stacking order of elements on a webpage. If an element is set to the position value "static," the z-index property will be ignored.
1. However, if the element is set to "relative," "fixed," or "absolute," the z-index property will take effect, allowing the element to be positioned in front of or behind other elements based on its assigned value.
2. In HTML and CSS, the z-index property is used to control the vertical stacking order of elements on a webpage. It determines which elements appear in front of or behind others. By default, elements are positioned as "static," meaning they flow in the order they appear in the HTML document and the z-index property is ignored.
3. However, when an element is set to "relative," "fixed," or "absolute" position, it becomes a positioned element. In these cases, the z-index property becomes effective, allowing the element to be positioned in front of or behind other elements based on the assigned value. The higher the z-index value, the closer the element will appear to the viewer, overlapping elements with lower z-index values or default stacking order.
4. Therefore, if an element is set to the position value "static," the z-index property will have no effect, and the element will follow the default stacking order.
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Both please please………
Answers
Answer:
Step-by-step explanation:
First one - Because it says 2 years ago, you can do 60000-4% for one year and then take the answer and - another 4% for the second year to get her income from 2 years ago. (I commented on this)
Second one - 1/3 - Take 1/6*200%=1/6*2=2/6, 2/6=1/3. So 1/3 or 2/6 of the students have a engineering major
Josiah is in the business of manufacturing phones. He pays a cost of $150 per phone produced for materials and labor and also must pay a daily fixed cost of $300 to rent the building and equipment. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
Answers
Answer: C=150p+300
Step-by-step explanation:
find the answers for 45. and 46. please my grade is horrible in math and i need to raise it!!
Answers
The upper and lower values of the range of the dataset are: Option E: -12 and 104
How to find the range of the data set?The range of a dataset is defined as the difference between the highest and lowest values of that dataset when arranged in ascending or descending order.
The dataset is given by:
36, 45, 40, 36, 84, 72, 20, 53, 32, 45, 64, 76
The lowest value = 20
Highest value = 84
Thus:
Upper value of range will be: 80 + 24 = 104
Lower value of range will be: 20 - 32 = -12
There is no outlier
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can someone pls help me solve this
