Consider the system of linear differential equations
x_1’(t) = -3x_1(t) + 10 x _2 (t)
x_2’(t) = 1x_1(t) + 6x^2(t)
We want to determine the stability of the origin.
a) This system can be written in the form X'=AX where X(t) = x_1 (t)/x_2(t) and
A= ______
b) Find the eigenvalues of A. List them separated by semicolons.
Eigenvalues: _______
c) From (b), we can conclude that the origin is
O unstable
O stable
o because all eigenvalues are negative
o at least one of the eigenvalues is positive.
o the absolute value of each eigenvalue is less than one
o both of the eigenvalues have the same sign
o all the eigenvalues are non-positive with at least one of them null
Answers
The origin is unstable. Hence, the correct answer is option (b) unstable.
a) The given system of differential equations can be written in the form X'=AX
where X(t)
= x1(t)/x2(t) and
A= [−3,10x2x21,6x2]
.b) The matrix A= [−3,10x21,6x2] has two eigenvalues which are given as below:
Eigenvalues: λ1= −1.459, λ2
= 2.46
c) As we can see from the above calculation that the eigenvalues of the matrix A are given as λ1= −1.459 and
λ2= 2.46, and both of them have opposite signs, one negative and one positive.
So, we can conclude that the origin is unstable. Hence, the correct answer is option (b) unstable.
Note that the origin is stable if all the eigenvalues have negative real part, but in this case, one of the eigenvalues has positive real part, so the origin is unstable.
To know more about unstable visit:
https://brainly.com/question/30894938
#SPJ11
Related Questions
Anna is painting the outside of cardboard box for an art project. The box is a rectangular prism that has a lenght of 24 inches, a width of 24 inches, and a height of 30 inches. Fine the Surface area of the cardboard box.
Answers
SA = 2016^3 inches
Step-by-Step-Explanation
SA = lw(2) + wh(2) + hl(2)
SA = 24(24) + 24(30) + 30(24)
SA = 576 + 24(30) + 30(24)
SA = 576 + 720 + 720
SA = 1296 + 720
SA = 2016^3 inches
please help! super urgent!
Answers
Answer:
A. square root of 3 times 5
Step-by-step explanation:
can someone pls help me with this? i’d really appreciate it :)
Answers
Answer:
y = 2x - 12 or A
Step-by-step explanation:
6x - 3y = 36 Subtract 6x from both sides.
-3y = 36 - 6x Divide by - 3
-3y/-3 = 36/-3 - 6x/-3
y = -12 + 2x
The answer is A
At a dry cleaning store, it costs $1.79 to clean a man’s dress shirt and 6 times as much to clean a suit. Choose the answer that correctly completes the statement.
It would cost_________to dry clean one shirt and one suit.
Answers
You have to multiply 1.79 times 6 then add 1.79
Answer:
Step-by-anation:
flight time from london to chicago can be classified as________ data continious discrete independent variable dependent variable
Answers
Time is a continuous data type, meaning it can take any value within a range. For example, the flight time from London to Chicago could range from 6 to 8 hours.
Continuous data is a type of data that can take any value within a range. As opposed to discrete data which can only take certain values, continuous data can take any value within a range. An example of continuous data is time. The flight time from London to Chicago could range from 6 to 8 hours. This time can be measured in any unit, such as seconds, minutes, hours, or days. This type of data is useful in many fields such as mathematics, engineering, and economics. Continuous data provides a more accurate representation of real-world phenomena that often follow a certain pattern or trend. This type of data is also important for analyzing relationships between variables and for making predictions about the future.
Learn more about data here
https://brainly.com/question/14893265
#SPJ4
HAIIIIIII PLS HELPPPPPP
dis is confusing -_-
Miguel has $30. He spends $8.00 on a movie ticket, $3.85 for snacks and $1.00 for bus fare each way.
How much money does Miguel have left?
Miguel has_____dollars left
Answers
Answer:
$16.5
Step-by-step explanation:
$30-$8-$3.85-$1-$1 = $16.5
Round 7.4304909778 to the nearest millionth.
Answers
Answer:
7.430491
Step-by-step explanation:
Round the number based on the sixth digit. That is the millionth.
What is another way to write
3
×
(
4
+
5
)
=
27
Answers
Answer:
3 * 9 = 27
Step-by-step explanation:
Suppose a store examines a sample of n =100 purchases and observes 48 customers used a debit card. what is the probability of a sample proportion of 0.48 or less if the true population proportion is 0.60?
Answers
There is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less.
To find the probability of a sample proportion of 0.48 or less if the true population proportion is 0.60, we can use the sampling distribution of the sample proportion and the z-score.
Given:
Sample size (n) = 100
Observed sample proportion ) = 0.48
True population proportion (p) = 0.60
To find the probability, we need to standardize the observed sample proportion using the z-score formula:
z = ( - p) / √(p * (1 - p) / n)
Substituting the values:
z = (0.48 - 0.60) / √(0.60 * (1 - 0.60) / 100)
= -0.12 / √(0.24 / 100)
= -0.12 / √0.0024
= -0.12 / 0.049
Using a standard normal distribution table or a statistical calculator, we can find the probability associated with the z-score.
The probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is the probability to the left of the z-score obtained.
P ≤ 0.48) = P(z ≤ -0.12)
Using a standard normal distribution table, we find that the probability of z ≤ -0.12 is approximately 0.4522.
Therefore, the probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is approximately 0.4522 or 45.22%.
This means that there is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less, if the true population proportion is 0.60.
To know more about randomly refer here:
https://brainly.com/question/13319968#
#SPJ11
Write the slope intercept of the equation of the line through the given points. Through (-2,-4) and (-3,-5)
Answers
The slope between two(2) points;
\(\begin{gathered} P(x_1,y_1)_{} \\ \text{and Q(x}_2,y_2) \end{gathered}\)is given as:
\(m=\frac{y_2-y_1}{x_2-x_1}\)From the question, the given points are:
\(\begin{gathered} (-2,-4)\text{ and (-3,-5)} \\ \Rightarrow x_1=-2,y_1=-4 \\ \Rightarrow x_2=-3,y_2=-5 \end{gathered}\)Thus, the slope, m, is:
\(\begin{gathered} m=\frac{-5-(-4)}{-3-(-2)} \\ m=\frac{-5+4}{-3+2} \\ m=\frac{-1}{-1} \\ m=-1 \end{gathered}\)The equation of a line with two(2) given points is given as:
\(m=\frac{y-y_1}{x-x_1}\)Thus,
\(\begin{gathered} -1=\frac{y-(-4)}{x-(-2)} \\ -1=\frac{y+4}{x+2} \\ \text{cross}-\text{multiply} \\ y+4=-1(x+2) \\ y+4=-x-2 \\ y=-x-2-4 \\ y=-x-6 \end{gathered}\)Hence, the slope-intercept form of the equation of the line through the given points is:
\(y=-x-6\)I need help with this question
Answers
The length of the legs of the right triangle are 2.83 units.
How to find the side of a right triangle?A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the legs of the triangle can be found using trigonometric ratios.
Hence,
sin 45 = opposite / hypotenuse
sin 45 = a / 4
cross multiply
a = 4 × 0.70710678118
a = 2.83 units
Therefore,
cos 45 = b / 4
cross multiply
b = 0.70710678118 × 4
b = 2.82842712475
b = 2.83 units
Therefore, the legs are 2,83 units
learn more on right triangle here: https://brainly.com/question/29285631
#SPJ1
21 m
15 m
Which is closest to the length of XY?
Answers
Answer:
18.0 i think
Step-by-step explanation:
find x=, if x-7=11 HURRY!!
Answers
Answer:
X = 18
Step-by-step explanation:
X - 7 = 11
Add 7 to both sides
X - 7 + 7 = 11+7
X = 18
3. predict the difference in the cooking quality of cheddar cheese compared to that of fat-free cheddar cheese. why do you expect these outcomes?
Answers
The difference in the cooking quality of cheddar cheese compared to that of fat-free cheddar cheese is Fat-free cheddar cheese does not melt as well as regular cheddar cheese.
What is the main source of protein in cheddar cheese?Cheddar cheese's main source of protein is casein.
Cheddar cheese without fat does not melt as well as cheddar cheese with fat. When heated to a high temperature, fat-free cheddar cheese separates more readily than conventional cheddar cheese. Additionally, since fat-free cheese has more protein than conventional cheese, it will become difficult when heated. Regular cheese, on the other hand, would experience a stronger oiling off action, resulting in a glossier surface on the cooked cheese product.
Learn more about cooking quality here:
https://brainly.com/question/15207581
#SPJ4
Explain how the distributive property and the commutative property of addition are used in the Example to show that 2(x 1 1) 1 2x is equivalent to 4x 1 2.
Answers
Answer:
Step-by-step explanation:
\(2(x+1)+2x=4x+2\)
\(2(x+1)+2x\)
\(2(x)+2(1)+2x\)
\(2x+2+2x\) (combine liked terms)
\((2x+2x)+2\)
\(4x +2\)
Hope this helps!
what is the formula used to determine whether or not two events are independent
Answers
P(A and B) = P(A) × P(B) is the formula used to assess if two events are independent (B).
P(A) is the chance that event A will occur.
The chance that event B will occur is marked as P(B).
If the chance of both occurrences happening at the same time, P (A and B), equals the product of the individual probabilities of each event, P(A) x P(B), the events are called independent.
If, on the other hand, the chance of both occurrences occurring simultaneously is less than the product of the individual probabilities of each event, the events are deemed dependent.
Learn more about the independent events at
https://brainly.com/question/12619550
#SPJ4
using the binomial theorem expression, what is the expansion of (x+3y)^5
Answers
Answer:
x^5+15x^4y^1+90x^3y^2+270x^2y^3+405x^1y^4+243y^5
what is the equation of the line that contains the point (2,3) and has a slope of - 3/2
Answers
equation of line
y=mx+b
If m=-3/2
we have
\(\begin{gathered} y=mx+b \\ y=-\frac{3}{2}\cdot x+b \end{gathered}\)From points (2,3), we find b
\(\begin{gathered} y=-\frac{3}{2}\cdot x+b \\ 3=-\frac{3}{2}\cdot2+b \\ 3=-3+b \\ b=6 \end{gathered}\)Therefore
\(y=-\frac{3}{2}\cdot x+6\)Yoko made $15,000 in taxable income last year. Suppose the income tax rate is 15% for the first $850Cplus 19% for the amount over $8500 How much must Yoko pay in income tax for last year?
Answers
Answer:
$2510Step-by-step explanation:
Amount of tax on $8500:
$8500*15/100 = $1275Amount of income over $8500:
$15000 - $8500 = $6500Amount of tax on $6500:
$6500*19/100 = $1235Total tax is:
$1275 + $1235 = $2510Find the measure of each angle
m
m
Answers
(10x-7)=133
Five friends went to an amusement park. The group wanted to calculate the total cost, so Kathie wrote the expression 5x + 70. Each of her friends wrote expressions, too.
Determine which friends' expressions are equivalent to Kathie's. Show or explain your reasoning.
Kathie: 5x+70
Stephanie: 3(x+30)+2x−20
Jon: 3x+30+2x−20
Mary: 5(x+14)
Nicole: 3(x+30−20)+2x
Answers
Answer:
Stephanie Mary and Nicole
Step-by-step explanation:
the ages of students at a university are normally distributed with a mean of 20. what percentage of the student body is at least 20 years old?
Answers
The percentage of the student body that is at least 20 years old is 50%.
The ages of students at a university are normally distributed with a mean of 20. To find the percentage of the student body that is at least 20 years old solution to the is as follows: As the Mean of ages of students at a university, μ = 20. Age is normally distributed so it will be divided into two groups Therefore, the mean age is equal to the median age. As the age is normally distributed, 50% of the population will have an age greater than or equal to 20 years old. Thus, the percentage of the student body that is at least 20 years old is 50%. Hence, the required percentage of the student body that is at least 20 years old is 50%.
To learn more about "Normally distributed": brainly.com/question/14916937
#SPJ11
Jutin chooe a function o that when he ue the number 7 a an input, the output i 20. Which function could he ue?
A. F(x)=2x5
B. G(x)=x^2-19
C. H(x)=13-x
D. J(x)=3x-1
HELP PLEASE!!!
Answers
Jutin chooses a function J(x) = 3x - 1 that when he uses the number 7 as an input, then the output is 20.
As per the given data, Jutin chooses a function in which he uses the number 7 as an input, then the output is 20.
Here we have to determine which function Jutin has to use.
Now we have to substitute the value that x = 7 in all the given functions.
First function:
F(x) = 2\(x^{5}\)
F(7) = 2 \((7)^{5}\)
F(7) = 2 (16807)
F(7) = 33614 which is not equal to 20.
Second function:
G(x) = \(x^{2}\) - 19
F(7) = \((7)^{2}\) - 19
F(7) = 49 - 19
F(7) = 30 which is not equal to 20.
Third function:
H(x) = 13 - x
H(7) = 13 - 7
H(7) = 6 which is not equal to 20.
Fourth function:
J(x) = 3x - 1
J(7) = 3(7) - 1
J(7) = 21 - 1
J(7) = 20
The correct function is J(x) = 3x - 1
For more questions on substitution method
https://brainly.com/question/28663522
#SPJ4
x - y = 1
x+y=3 please using graphical method
Answers
Answer:
X is 2, Y is 1.
Step-by-step explanation:
say x is 2 and y is 1.
2 - 1 = 1
2 + 1 = 3
Answer:
(2, 1)
Step-by-step explanation:
To solve this using the graphical method, you want to graph each equation. Once you have graphed the equations, you need to locate the point of intersection. This is the solution to the system of equations.
To graph these equations, you can write the equation as is or convert to slope-intercept form: y = mx + b.
x - y = 1
Add y to both sides.
x = y + 1
Subtract 1 from both sides.
x - 1 = y
or
y = x - 1
x + y = 3
Subtract x from both sides.
y = -x + 3
These are your two equations.
Plug these into a graphing calculator or an online grapher.
From the graph, we can see that the point of intersection is at the coordinate (2, 1).
This is your solution.
Hope this helps!
The population of a town was 25000 in the 2000 census and and 30000 in 2010 census. By what percent did the population increase
Answers
Answer: This means that the population increased a 20% between the year 2000 and the year 2010.
Step-by-step explanation:
In this case, we have that 25,000 is the 100%.
Now we want to know which percentage represents 30,000
Let's suppose that the percentage is X.
Then we can have a system of equations:
30,000 = X
25,000 = 100%
To find the value of X, we can take the quotient of these two equations:
30,000/25,000 = X/100%
(30,00/25,000)*100% = X = 120%
Then in the 2000 we had a 100%, and in the 2010 there was a 120%.
The difference is:
120% - 100% = 20%
This means that the population increased a 20% between the year 2000 and the year 2010.
Annabella rolls two number cubes, each with sides that are labeled 1 to 6. What is the probability that the first cube shows a one and the second one shows a one?
Answers
I hope this is correct
Mandy has 1 drink and Karl has 2 Mandy takes all of Karl's drinks
Answers
Answer:
What is this question asking? If you give me a question to answer I can help you.
Step-by-step explanation:
Write the following as a number: minus one thousand, eight hundred and five point nine six.
Answers
The final number is a decimal number which is equal to -1805.96.
It is given to us that the set of expression is given by -
minus one thousand, eight hundred and five point nine six.
We have to write the given expression as a number.
According to the given information we see that there is a "point" word in the expression. This implies that the final number will be a decimal number.
So, from the given information, we can represent the number as -
-1805.96
Thus, the final number is a decimal number which is equal to -1805.96.
To learn more about decimal numbers visit https://brainly.com/question/4708407
#SPJ4
(3^4)^2 as a product question below help
Answers
The expression (3⁴)² in repeated multiplication is (3⁴) * (3⁴)
How to rewrite the expression as products?From the question. the expression is given as
(3⁴)²
The task is that we rewrite the expression as products i.e. repeated multiplication
This in other words means that:
We rewrite the (3⁴)² as repeated multiplication
To do this, we apply the exponent rule of indices
This rule states that:
a^m = a * a * a .... in m places
So, we have
(3⁴)² = (3⁴) * (3⁴)
Hence, the equivalent expression is (3⁴) * (3⁴)
Read more about repeated products at
brainly.com/question/28771184
#SPJ1
Assuming that y is the dependent variable, find the general solution to the equation. (4t + 4y + 1)dt - dy=0 (Ignore lost solutions, if any.) a. y(t) = t – ½ + C e^4t
b. y(t) = -t – 1/2 + C e^4t c. y(t) = -t – 1/2 + C e^-4t d. y(t) = -t – 3/2 + C e^-4t
Answers
The general solution is y(t) = -t - 1/2 + C e^-4t
Determine general solutionsThe general solution to the equation (4t + 4y + 1)dt - dy=0 is given by y(t) = -t - 1/2 + C e^-4t. This can be derived by solving the equation as follows:
1: Rearrange the equation in the form of dy + (4t + 4y + 1)dt = 0
2: Separate the variables and integrate both sides with respect to t
3: Solve for y
Therefore, the general solution is y(t) = -t - 1/2 + C e^-4t, where C is an arbitrary constant.
Learn more about equation at
https://brainly.com/question/10724260
#SPJ11