The matrix A has eigenvalues X₁ = 3 and X₂ = 4 with associated eigenvectors 2 V₁ = and v2 [A] Use this information to find the solution to the initial value - [³] Y' = AY where Y (0) = [ (0)] - [8] - [ 2₂ ] 1 problem = Give your answer as x(t) and y(t). y
Answers
The solution to the initial value problem is:
x(t) = \((1/4) * e^{(3t)} - (1/4) * e^{(4t)}\) and y(t) = \(e^{(3t)} + (1/6) * e^{(4t)}\)
To find the solution to the initial value problem Y' = AY, where A is the matrix with eigenvalues and eigenvectors given, we can use the eigenvalue-eigenvector method.
Let's denote the eigenvectors as v₁ and v₂:
v₁ = [2]
[8]
v₂ = [-3]
[2]
The general solution to the system of linear differential equations can be written as:
Y(t) = \(c_1 * e^{(X_1t)} * v_1 + c_2 * e^{(X_2t)} * v_2\)
where c₁ and c₂ are constants.
Substituting the given eigenvalues and eigenvectors:
Y(t) = c₁ * \(e^{(3t)\) * [2] + c₂ * \(e^(4t)\) * [-3]
[8] [2]
Simplifying further:
Y(t) = [2c₁ * \(e^{(3t)\) - 3c₂ * \(e^{(4t)\)]
[8c₁ * \(e^{(3t)\) + 2c₂ * \(e^{(4t)\)]
To find the specific solution that satisfies the initial condition Y(0) = [0] and [8], we can substitute t = 0 into the general solution:
Y(0) = [2c₁ - 3c₂]
[8c₁ + 2c₂]
Equating this to the initial condition:
[2c₁ - 3c₂] = [0]
[8c₁ + 2c₂] [2]
Solving this system of equations will give us the values of c₁ and c₂:
2c₁ - 3c₂ = 0 ----(1)
8c₁ + 2c₂ = 2 ----(2)
Multiplying equation (1) by 4 and adding it to equation (2), we get:
16c₁ = 2
Solving for c₁, we find:
c₁ = 1/8
Substituting c₁ back into equation (1), we can solve for c₂:
2(1/8) - 3c₂ = 0
1/4 - 3c₂ = 0
3c₂ = 1/4
c₂ = 1/12
Therefore, the specific solution to the initial value problem is:
x(t) = \((1/8) * e^{(3t)} * 2 + (1/12) * e^{(4t) }* (-3)\)
y(t) = \((1/8) * e^{(3t)} * 8 + (1/12) * e^{(4t)} * 2\)
Simplifying further:
x(t) = \((1/4) * e^{(3t)} - (1/4) * e^{(4t)}\)
y(t) = \(e^{(3t)} + (1/6) * e^{(4t)}\)
Therefore, the solution to the initial value problem is x(t) = \((1/4) * e^{(3t)} - (1/4) * e^{(4t)}\) and y(t) = \(e^{(3t)} + (1/6) * e^{(4t)}\).
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Related Questions
the mail arrival time to a department has a uniform distribution over 0 to 60 minutes. what is the probability that the mail arrival time is more than 20 minutes on a given day?
Answers
The probability that the mail arrival time is more than 20 minutes on a given day is 2/3.
How do we find the probability?It's nearly impossible to predict the outcomes of many events with a hundred percent certainty. However, we can still tell how likely the events are to happen.
Probability is how likely something is to happen. Probability can also mean a number that indicates the chance or likelihood that a particular event will occur. Probability is always between zero and one. Zero means impossible while one means certain. In most cases, the probability of something to happen is greater than zero and less than one.
Mathematically, we can express probability as P(A) = f/N where
P(A) represents the probability of an event (event A),f represents frequency or number of ways an event can occur, andN represents the total number of possible outcomes.Let P(A) represent the probability that the mail arrival time is more than 20 minutes on a given day, f represent the frequency (60 - 20), and N represent total number of possible outcomes, which is 60.
P(A) = (60 - 20)/60
P(A) = 40/60
P(A) = 4/6
P(A) = 2/3
There you have it! The probability is two-thirds.
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Jahnay is following this recipe to make cakes.
Jahnay uses 600 g of sugar.
How many cakes is Jahnay making?
Recipe: Makes 1 Cake
120 g butter
150 g sugar
200 g flour
2 eggs
Answers
Answer: Jahnay makes 4 cakes bc 120g butter u times by 4 and gets u 360g and u get 4 cakes
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
All the square numbers between 20 and 50
Answers
it is 3 numbers all together and they are 25, 36 and 49.
can someone help please I really need help
Answers
Answer:
angle 1 corresponds with angle 7
Step-by-step explanation:
mark brainliest thanks
Answer:
Angle 1 corresponds with Angle 7
Explanation:
Angle 1 is the corresponding angle to Angle 7
Line m has an equation of y = 3x + 2
Identify the slope:
What is the slope of a line that is parallel to m?
What is the slope of a line that is perpendicular to m?
Answers
Answer:
y = 3x-2
Step-by-step explanation:
Write and solve a proportion to answer the question.
72 is what percent of 45?
Answers
Answer:
160% is for 72 of 45
There are 12 players on a soccer team, 10 girls and 2 boys. What is the ratio
of girls to boys on the soccer team?
Answers
Answer: 5:1
Step-by-step explanation:
So, I would start by writing this out:
G:B
Girls to Boys, as that is the order in the question.
Then;
G:B
10:2
As there are 10 girls and 2 boys.
Then, you need to simplify it.
10/2=5
2/2=1
Answer:
G:B
10:2
5:1
I hope this helps.
pls helpp ..................
Answers
Answer:
The answer is B
Step-by-step explanation:
Because x -intercept is -2 y-intercept is 4
2 1/3% as a mixed number in simplest form
Answers
Answer:
71
Step-by-step explanation:
a young person with no initial capital invests k dollars per year in a retirement account at an annual rate of return 0.05. assume that investments are made continuously and that the return is compounded continuously. a) write a differential equation which models the rate of the change of the sum s(t) with t in years (this will involve the parameter k). b) Use part a) to determine a formula for the sum S(t) c) What value of k will provide 3500000 dollars in 41 years?
Answers
The differential equation that models the rate of change of the sum S(t) with respect to time t is given by dS/dt = k * e^(0.05t). The formula for the sum S(t) is S(t) = (k/0.05) * e^(0.05t) + C. It is not possible to determine the exact value of k that will result in $3,500,000 in 41 years.
(a) The differential equation that models the rate of change of the sum S(t) with respect to time t is given by dS/dt = k * e^(0.05t), where k represents the annual investment amount and e^(0.05t) represents the continuous compounding growth factor.
(b) To determine a formula for the sum S(t), we need to integrate the rate of change equation from part (a). Integrating both sides with respect to t, we have ∫dS = ∫k * e^(0.05t) dt. Integrating the left side gives S(t), and integrating the right side gives (k/0.05) * e^(0.05t) + C, where C is the constant of integration. Thus, the formula for the sum S(t) is S(t) = (k/0.05) * e^(0.05t) + C.
(c) In order to find the value of k that will provide $3,500,000 in 41 years, we can use the formula derived in part (b) and substitute the given values. The equation becomes 3500000 = (k/0.05) * e^(0.05*41) + C. To determine the value of k, we need to know the constant of integration C or have additional information about the initial conditions. Without this information, it is not possible to determine the exact value of k that will result in $3,500,000 in 41 years. However, with the given equation, you can solve for the value of k by rearranging the equation and solving numerically using methods such as iteration or numerical approximation techniques.
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Using the Remainder Theorem, which of the following is NOT a factor of x^4-x^3-7x^2+x+6
Answers
Answer:
X-2
Step-by-step explanation:
1 -1 -7 1 6
O -1 2 5 -6
1 -2 -5 6 0
+1
1 -1 -7 1 6
0 1 0 -7 -6
1 0 -7 -6 0
-1
1 -1 -7 1 6
0 2 2 10
1 1 5
-2
1 -1 -7 1 6
0 -2 6 -2 -2
1 -3 -1 1 4
+2
Between +2and -2 demos
HELP ASAP ITS EASY BUT IM BLANKING AND ITS 20 POINTS PLUS BRAINLIEST
This table shows values that represent an exponential function.
what is the average rate of change for this function for the interval from x=2 to x=4?
Answers
Answer:
Subtract the two Y values of X = 2 and X = 4 to find the total difference, then divide by the difference between X=2 and X =4
When X = 2 Y = 9
When X = 4 Y = 64
Difference between the two Y values = 64 -9 = 55
Difference between the two X values = 4-2 = 2
The rate of change = difference in Y divided by difference in X:
55/2 = 27.5
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I'm not really sure if I'm getting this right. please correct me if I'm wrong
Answers
Answer:
D
Step-by-step explanation:
The area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × \(\frac{80}{360}\)
= π × 0.9² × \(\frac{8}{36}\)
= 0.81π × \(\frac{2}{9}\)
= 0.09π × 2
= 0.18π in² → D
(08.01 mc) sue wants to know how many families in her small neighborhood of 50 homes would volunteer to help at a neighborhood animal shelter. she put all the addresses in a bag and drew a random sample of 25 addresses. she then asked those families if they would volunteer to help at the shelter. she found that 18% of the families would volunteer to help at the shelter. she claims that 18% of the neighborhood families would be expected to help at the animal shelter. is this a valid inference?
Answers
Answer:
Yes, this is a valid inference because she took a random sample of the neighborhood.
Step-by-step explanation:
As we can see, Sue's survey was perfectly random and without any prejudice.
18% of the families, according to her research, would volunteer at the shelter. According to her, 18% of the local households should be required to volunteer at the animal shelter.
Therefore, given that she chose a representative sample of the area, her conclusion is valid.
Estephania has 24 video games. She distributes them equally among her 3 younger siblings. How many video games does each sibling receive?
Answers
Answer:
6
Step-by-step explanation:24 divided by 4
Answer:
Each sibling receives 8 video games.
Step-by-step explanation:
24 : 3 = 8
The total cost of x pounds of ham and 4 pounds of turkey is given by
the function below, where F(x) represents the total cost in dollars.
F(x)=8(x+4)
Which statement best interprets this function?
The ham and turkey together cost a total of $32.
The ham costs a total of $8, and the turkey costs a total of $4.
The ham costs $8 per pound, and the turkey costs $4 per pound.
The ham and turkey each cost $8 per pound
Answers
The ham and turkey each cost $8 per pound
inscribed angles. I need answers asap, thank you!
Answers
Answer:
60°
Step-by-step explanation:
The whole circunference is 360° from a central angle
so from an inscribed angle is 180°
notice that arc ABC + arc ADC make the whole circunference
so the inscribed angles that support those arc together must add to 180°
120°+b=180
b=60
from here we deduce that a cyclic quadrilateral (a quadrilateral that his points are on a circunference) oposite angles add up to 180
urgent I don't have time pllllllllzzzzzzzzzz
thhhxx
Answers
What is the value of 2(5b - 7) in terms of y if b = 3y ?
Answers
2(5(3y)-7) —> 2(15y-7) —> 30y -14
—> 30y = 14 —> y = 14/30 —> y = 4.6667
Jane wants to measure the amount of precipitation in her backyard for the month of January. Which weather instrument should Jane use?
Answers
Answer:
rain gauges
Step-by-step explanation:
Earth is approximately 9.3 × 107 miles from the sun. Saturn is approximately 8.87 × 108 miles from the sun. About how much farther is Saturn from the sun than Earth is? A. 7.94 × 107 miles B. 7.94 × 108 miles C. 4.3 × 107 miles D. 4.3 × 108 miles
Answers
Answer:
B. 7.94 × 10^8 miles
Step-by-step explanation:
Given that
Earth is approximately 9.3 × 107 miles from the sun.
Saturn is approximately 8.87 × 108 miles from the sun.
We need to find out how much farther is saturn from the sun than earth is
So,
Earth - Sun = 9.3 × 10^7 miles
Saturn - Sun = 8.87 × 10^8 miles
Now
= 8.87 × 10^8 - 9.3 × 10^7
= 88.7 × 10^7 - 9.3 × 10^7
= 79.4 × 10^7
= 7.94 × 10 ^8
= 794,000,000 miles
Hence, saturn is 7.94 × 10^8 miles farther from Sun than Earth is
The number of stories in a Manhattan building is 22. Does the data come from a discrete or continuous data set?
Group of answer choices
a. A continuous data set because there are infinitely many possible values and those values can be counted.
b. A discrete data set because the possible values can be counted.
c. A continuous data set because there are infinitely many possible values and those values can be measured.
d. The data set is neither continuous nor discrete.
Answers
Discrete-data is a category of quantitative information that has countable or finite values.
This indicates that there are no intermediate values between the precise numerical values that can be used to convey the data; only those values can be used. The number of siblings a person has, the number of pets a home has, and the number of individuals in a room are all examples of discrete data.
Numerous statistical methods, such as measures of central tendency like the mean, median, and mode, as well as measures of dispersion like range and standard deviation, can be used to analyse discrete data. Additionally, discrete data can be displayed graphically using tools like bar charts and frequency histograms.
A discrete data set is the number of stories in a skyscraper in Manhattan. A continuous data set, on the other hand, can be divided into ever-smaller pieces and can take on any value within a range. Therefore (b), "A discrete data set because the possible values can be counted."
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Can you guys answer these questions please i have allot of work and im trying to do multiple things answer will get brainliest
Answers
Answer:
first one - 30%
second - 15%
third - 40%
fourth - 20%
fifth - 75%
sixth - 70%
seventh - 88%
eighth - 25%
sorry but the last question is too blurry, can you type it and I can help you answer it?
Hope this helps.
n a second run of the data, it was determined that the sample mean was actually 37 miles instead of the originally reported 35 miles. how will this affect the width of the confidence interval? a. the new interval would be wider. b. the new interval would be narrower. c. there would be no change in the interval width.
Answers
There would be no change in the interval width that is Option-C is correct when the sample mean was discovered to be 37 miles rather than the first reported 35 miles after a second run of the data.
Given that,
The sample mean was discovered to be 37 miles rather than the first reported 35 miles after a second run of the data.
We have to find how will this impact the confidence interval's width.
We know that,
Therefore, There would be no change in the interval width that is Option-C is correct when the sample mean was discovered to be 37 miles rather than the first reported 35 miles after a second run of the data.
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PLEASE HELP ME ASAP Given the following polynomial function, find f(-1): 2x^3 - 3x^2+7x-10
F(-1)=?
Answers
Answer:-22
Step-by-step explanation:Just put the value -1 wherever there is x.
Answer:
f(-1) = -22
Step-by-step explanation:
f(x): 2x^3 - 3x^2 + 7x - 10
Repace x = -1
f(-1) = 2(-1)^3 - 3(-1)^2 + 7(-1) - 10
f(-1) = -2 - 3 - 7 - 10
f(-1) = -22
can someone help me pls
Answers
Answer:
160
Step-by-step explanation:
Marian asked 25 students the following questions in a survey.
1. Are you male or female?
2. Do you wear glasses?
Marian's results are shown below.
There were a total of 15 female students who were surveyed.
• There were 17 students who wear glasses.
Answers
Answer:
Step-by-step explanation:
30 POINTS!!!
Suppose f(x) = x2 and
g(x) = (1/3)^2. Which statement best compares the graph of g(x) with the graph of f(x)?
Image attached
Please help!!!
Answers
Answer:
A. The graph of g(x) is vertically compressed by a factor of 3.
Step-by-step explanation:
When there is a fraction, that means that there is a veritcal dilation.
Hope this helps! Good luck!
Consider the partially completed one-way ANOVA summary table.Source Sum of Squares Degrees of Freedom Mean Sum of Squares F Between 270Within 18 Total 810 21The number of factor levels being compared for this ANOVA procedure is
Answers
The degrees of freedom for the between groups would be 4-1 = 3 and the degrees of freedom for the within groups would be 24-4 = 20.
What do you mean by factor ?A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
The number of factor levels being compared for this ANOVA procedure cannot be determined from the given information. The degrees of freedom for the between and within groups are provided, but the number of factor levels is not directly given.
In general, the number of factor levels in a one-way ANOVA refers to the number of groups being compared. Each group represents a level of the factor being studied.
To find the number of factor levels, we need to know the degrees of freedom associated with the between and within groups. The degrees of freedom for the between groups is equal to the number of groups minus one, while the degrees of freedom for the within groups is equal to the total number of observations minus the number of groups.
For example, if we had 4 groups and 24 total observations, the degrees of freedom for the between groups would be 4-1 = 3 and the degrees of freedom for the within groups would be 24-4 = 20.
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Please helpppp!!,!,
Jaime's dad put 12 gallons of gasoline in his car. The gasoline costs $3.25 a gallon.
How much did Jaime's dad pay for the gasoline?
Answer options with 4 options
A. $9.75
B. $15.25
C. $36.00
D. $39.00
Answers
Answer:
Step-by-step explanation:
To find the total cost of the gasoline, we can multiply the number of gallons of gasoline by the cost per gallon.
12 gallons * $3.25/gallon = $<<12*3.25=39>>39.00
So the correct answer is D. $39.00.
Answer:
choice D. $39.00
Step-by-step explanation: