Consider the initial value problem D'=13_), zo = [ 2] y(0) = a. Find the eigenvalue 1, an eigenvector v1, and a generalized eigenvector v2 for the coefficient matrix of this linear system. - l= , Vj = -- b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. y(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = ya(t) =
Answers
The solution to the initial value problem is yı(t) = ya(t) = [a e^(13t) - (e^(13t) - 1)] (1, 0).
Given information:Consider the initial value problem D' = 13_, zo = [ 2] y(0) = a.To find the eigenvalue 1, an eigenvector v1, and a generalized eigenvector v2 for the coefficient matrix of this linear system.Step-by-step explanation:The given differential equation isD' = 13_Y = [ 2] y(0) = a.The coefficient matrix A for this system is:A = [13]The eigenvalues λ1, λ2 are obtained by solving the characteristic equation:det(A - λI) = 0where I is the 2x2 identity matrixdet(A - λI) = (13 - λ)(-λ) - 2(0) = λ(λ - 13)This equation has two roots:λ1 = 0, λ2 = 13.The corresponding eigenvectors v1 and v2 are obtained by solving the equations:(A - λ1I) v1 = 0, (A - λ2I) v2 = 0. For λ1 = 0, we have(A - λ1I) v1 = (13 0) (v1[1])= (0 0) (v1[2])which implies that v1[1] = 0 and v1[2] is free. Therefore, v1 = (0, 1). For λ2 = 13, we have(A - λ2I) v2 = (0 0) (v2[1])= (0 -13) (v2[2])which implies that v2[1] is free and v2[2] = 0. Therefore, v2 = (1, 0).The generalized eigenvector v3 for λ1 = 0 is obtained by solving the equation:(A - λ1I) v3 = v2For this equation, we have(13 0) (v3[1])= (0 0) (v3[2])which implies that v3[1] is free and v3[2] = 0. Therefore, v3 = (1, 0).b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers.The general solution of the system is given byy(t) = c1 e^(0 t) (0, 1) + c2 e^(13t) (1, 0) + c3 (t e^(0 t) (0, 1) + e^(0 t) (1, 0))Therefore, the most general real-valued solution to the linear system of differential equations is given byy(t) = c1(0, 1) + c2 e^(13t)(1, 0) + c3 (t(0, 1) + (1, 0))c. Solve the original initial value problem.To solve the given initial value problem, we need to determine the coefficients c1, c2, and c3 that satisfy the initial conditions:y(0) = a = c1(0, 1) + c2(1, 0) + c3(0, 1) + (1, 0)c1 = 0, c2 = a - 1, and c3 = 0Therefore, the solution to the initial value problem is given byy(t) = (a - 1) e^(13t) (1, 0) + (1, 0) = [a e^(13t) - (e^(13t) - 1)] (1, 0) = y1(t)The solution to the initial value problem is yı(t) = ya(t) = [a e^(13t) - (e^(13t) - 1)] (1, 0).
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Related Questions
PLEASE HELP!
Please don't spam or send me any links. Questions are in the screenshot below
Please don't add any useless information to get points (THOSE WHO DO WILL GET REPORTED)
Thank you
Answers
Part 1
Ying is correct while Jabbar is incorrect. The polar form would have cosine listed first, then sine later. The sine term always has the imaginary 'i' attached to it. It's fairly easy to mix these trig functions up. One way to remember is to think alphabetical order (C is before S, cosine before sine). Other than this difference, the two students have identical steps.
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Part 2
Ying made the error this time. Jabbar is correct. When using a unit circle, you should find that
cos(pi/2) = 0
sin(pi/2) = 1
The point (x,y) on the unit circle that corresponds to the angle theta will help us see this. Note how x = cos(theta) and y = sin(theta).
Side note: Jabbar now has the correct order of cosine and sine (see part 1 above).
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Part 3
Ying made the error of adding the r values. Instead, you should multiply them like Jabbar did. The theta angle values are the terms we add up. An interesting thing to notice is that Ying computed cos(pi/2) = 0, which contrasts to the mistake made in part 2.
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Part 4
Ying is correct. You divide the r values, and the order of division is important. The order of division is from left to right. We have 7 on the left and -2 on the right, so that's why Ying ended up with the correct new r value of -7/2. Jabbar swapped the order incorrectly. The same issue shows up when subtracting the theta values. Keep in mind that the order of subtraction is important. Something like 2-3 = -1 is not the same as 3-2 = 1. Ying has the correct order of subtraction for those theta values.
Please explain to me how to do this!
I don't have much time to get it in please help!
Answers
Answer:
y = mx + b
Step-by-step explanation:
so you first put the points on the graph and connect them with a slanted line.
Next, for your equation start of with y =
then, your going to find your slope, after you find it put it in front of x (slope x) (Ex; if the slope was 3 then it would look like this 3x)
finally you write + and the y intercept (at which point the line goes through the y axis)
the equation together should look like y = slope x + y intercept
how can oliver convert 1 red brick into 5 red bricks in six steps
Answers
Step 1: grab the brick
Step 2: use something to cut the brick
Step 3: cut the brick horizontally 2 times
Step 4: cut the brick vertically through the middle 1 time
Step 5: get rid of 1 brick piece
Step 6: now you have 5 brick pieces
There are other methods such as cutting the brick 4 times vertically and much more but this is what I came up with
Please answer (IN school) 32.4-0.78
Answers
Answer: 31.62
Step-by-step explanation:
(Used calculator)
An event is considered to be ________, if all possible outcomes of a random experiment are included in the events.
Answers
The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set.
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.
The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The potential ordered outcomes, or sample points, are listed as elements in a set that is used to represent a sample space.
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Adding and subtracting rational expressions, What is the difference? 2x+5/x^2-3x - 3x+5/x^3-9x - x+1/x^2-9?
Answers
After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9 .
We first simplify each expression inside the parentheses :
that means :
⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;
⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³) ;
⇒ (x + 1/x² - 9) = (-9 + x + 1/x²) ;
Now we substitute these expressions into original equation/expression :
we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)
Simplifying further ,
we get ;
⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x² ;
On Combining the like terms, we get ;
⇒ 4x - 4/x² - 5/x³ + 9
Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.
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The given question is incomplete , the complete question is
Adding and subtracting rational expressions, Simplify the rational expression (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9) .
Carmen has a sign with dimensions 5 ft x 7.5 ft. She wants to reduce it to make a postcard. The postcard sizes are 3.5 in x 5 in., 4 in. x 6 in., and 4.25 in. x 6 in. Which size postcard should she use?
Answers
Answer:
7.5 / 5 = 1.5
5/ 1.5 = 3.33
6 / 1.5 = 4
Only 4in X 6in has the same relative dimensions
What is the value of f(–2)of the polynomial f(x) = –x^3 + x +1 ? What does this mean about the linear binomial (x + 2)?
Answers
Answer:
2nd option
Step-by-step explanation:
Given f(x) divided by (x - h) then f(h) is the remainder
If f(h) = 0 then (x - h) is a factor of f(x)
f(- 2) = - (- 2)³ + (- 2) + 1 = - (- 8) - 2 + 1 = 8 - 1 = 7
Since f(- 2) ≠ 0 then (x - 2) is not a factor of f(x)
The value of the given polynomial function is -9.
The given function is f(x) = –x³ + x +1.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Put x=-2 in the given function
That is, f(-2)=(-2)³+(-2)+1
=-8-2+1
=-9
Here, x+2 is not a factor of given polynomial function.
Therefore, the value of the given polynomial function is -9.
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i just need an answer pls
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The area of the regular octogon is 196.15 square inches.
How to find the area?For a regular octogon with apothem A and side length L, the area is given by:
area =(2*A*L) * (1 + √2)
Here we know that:
A = 7in
L = 5.8 in
Replacing these values in the area for the formula, we will get the area:
area = (2*7in*5.8in) * (1 + √2)
area = 196.15 in²
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h(x) = –24x + 53 + 3x2
Answers
Answer:
h=
3x2−24x+53 orver x
Step-by-step explanation:
A pizza maker determined an annual profit in dollars
2
from selling pizzas using f(n) = 65n -0.04n² where
n is the number of pizzas sold. What is the annual
profit if the pizza maker sells 300 pizzas?
A. $18,500
B. $3,600
C. $7,800
D. $15,900
Answers
Answer:
Given, the annual profit equation is f(n) = 65n - 0.04n².
When the number of pizzas sold, n = 300, the annual profit will be:
f(300) = 65(300) - 0.04(300)²
= 19500 - 0.04(90000)
= 19500 - 3600
= $15,900
Therefore, the annual profit if the pizza maker sells 300 pizzas is $15,900. Answer: D.
Step-by-step explanation:
Help please thanks I need help asap
Answers
Hope this helped!! :)
Find half of the time that Arnold skied without falling, and write inequalities to compare it with the times others in the family skied without falling
Answers
The half of the time that Arnold skied without falling is 712 as 2 x 356=712>223 .
Inequality is a mathematical statement that illustrates the connection between two expressions by using the inequality symbol. The phrases on both sides of an inequality sign are distinct. It indicates that the left expression should be larger or smaller than the right expression, or vice versa. When the link between two algebraic expressions is expressed using inequality symbols, literal inequalities arise.
The discrepancy represents the incident in which Kelvin skied for more than twice as long as anybody else in his family:
2f < 223
Here 223 is the time for Kelvin.
Check for Lori as follows:
2f < 223
2 x 55=110 < 223
Kelvin skied without falling more than twice as long as Lori.
Check for Vanessa as follows:
2f < 223
2 x 265=530>223
Check for Arnold as follows:
2f < 223
2 x 356=712>223
Kelvin skied without falling less than twice as long as Arnold.
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Complete question:
Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.
Lori 55
Vanessa 265
Devon 172
Celia 112
Arnold 356
PLEASE HELP I WILL MARK BRAINLIEST!!!! :)
Answers
Explanation:
(75 + 90)/250 = 0.66 = 66% of students are 11 or 12
5/250 = 0.02 = 2% of students are 10
(90 + 70)/250 = 0.64 = 64% of students are 12 or 13
10/250 = 0.04 = 4% of students are 14
Graph the solution set of the following linear inequality:3 - 3y > 21 - 3xAnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.Choose the type of boundary line:Dashed -O Solid (-) OsEnter two points on the boundary line:10-5$-5Select the region you wish to be shaded:ОАOB101
Answers
Explanation
To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line
\(3-3y>21-3x\)
Step 1
a)change the "> " for a "=" and then isolate y
\(\begin{gathered} 3-3y>21-3x \\ \text{swap the sign} \\ 3-3y=21-3x \\ \text{subtract 3 in both sides} \\ 3-3y-3=21-3x-3 \\ -3y=-3x+18 \\ \text{divide both sides by -3} \\ \frac{-3y}{-3}=\frac{-3x+18}{-3} \\ y=\frac{-3x}{-3}+\frac{18}{-3} \\ y=x-6 \end{gathered}\)b) now, graph the line
to do that, we need points
so
I) for x=0
\(\begin{gathered} y=x-6 \\ y=0-6 \\ y=-6 \end{gathered}\)so,the coordinate is ( 0,-6)
ii) when x = 6
\(\begin{gathered} y=6-6 \\ y=6-6 \\ y=0 \end{gathered}\)so, the coordinate is (6,0)
c) finally, draw a dotted line that passes trought (0,-6) and (6,0), as we are lookinjg for the y-values greater than the line, let's isolate y in the inequality to check what area to shade, so
\(\begin{gathered} 3-3y>21-3x \\ \text{subtract 3 in both sides} \\ 3-3y-3>21-3x-3 \\ -3y>-3x+18 \\ \text{divide both sides by (-3),remember swap the sign } \\ \frac{-3y}{-3}<\frac{-3x+18}{-3} \\ yso, we need to find all the values smaller than the line, so we need to shade de area under the line
Divide.Enter the quotient in simplest form
7/10 divided by 4/5
Answers
Answer:
7/8
Step-by-step explanation:
7/10 divided by 4/5 = 7/10 x 5/4 = 35/40 divided by 5/5 = 7/8
What is the axis of symmetry of
the function y = −3(x − 2)² +1?
CX= 1
Dx=2
Ax=-3
B x= -2
Answers
The axis of symmetry is the one in option D, x = 2-
What is the axis of symmetry of the line?For a quadratic equation whose vertex is (h, k), the axis of symmetry is:
x = h
Here we have the quadratic equation:
y = −3(x − 2)² +1
We can see that the vertex is (2, 1) because the equation is in vertex form, and thus, we can conclude that the axis of symmetry of the equation is:
x = 2
So the correct option is D.
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Which statement best defines a circle?
OA. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
OB. the set of all points that are the same distance from a given point called the center
c.
the set of all points in a plane that are the same distance from a given point called the center
OD.
points in a plane that surround a given point called the center
Answers
Of the choices, the best definition for a circle is:
OA. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
Some key points in this definition:
1) It refers to a set of points, indicating it is a geometric shape.
2) The points are in a plane, showing it is a 2D shape.
3) The points have the same distance from each other, indicating they lie on a curve.
4) There is a given center point, showing the points surround the center point.
5) The points surround the center point, indicating it is a closed shape.
So choice OA captures all these key aspects in defining a circle. The other choices are too vague or incomplete.
Use the data points representing Clothes-4-You shoe sales, where x is the average temperature and y is the number of shoes sold. (5, 66), (8, 54), (11, 63), (18, 70), (24, 51), (32, 68), (36, 60), (44, 73), (50, 55) Is the sale of 90 shoes a reliable prediction when the temperature is 80°F?.
Answers
Based on the given data points, the sale of 90 shoes when the temperature is 80°F is not a reliable prediction.
Looking at the given data points, there is no specific trend or pattern observed between temperature and the number of shoes sold. The sales figures vary considerably even with similar temperature values. For example, at 5°F and 32°F, the number of shoes sold is 66 and 68 respectively, which suggests that temperature alone is not a strong indicator of shoe sales.
Additionally, there is no data point available near the temperature of 80°F to establish a clear relationship between temperature and shoe sales in that specific range. Without a more comprehensive dataset covering a wider range of temperatures and corresponding sales figures, it is difficult to accurately predict the number of shoes sold at 80°F. Therefore, relying solely on the given data points, the sale of 90 shoes at 80°F cannot be considered a reliable prediction.
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In what ways are the line of reflection and the line of symmetry the same?
Answers
Answer:
A shape has reflection symmetry if there exists a line of reflection that carries the shape onto itself. This line of reflection is called a line of symmetry. In other words, if you can reflect a shape across a line and the shape looks like it never moved, it has reflection symmetry.
Step-by-step explanation:
THIS IS KINDA HARD I NEED HELP
Answers
Answer:
4
Step-by-step explanation:
Looking at the stem and leaf plot, we have 4 zoos that have less than 18 sloths, with one zoo having 3, one having 16, and two having 17.
the diameter of a circle is 5.3 cm. What is the circumference
Answers
Answer:
16.642cm
Step-by-step explanation:
Diameter of a circle = 5.3cm
Circumference of a circle = π(d)
= π x 5.3
= 3.14 x 5.3
= 16.642cm
Answer:
C= pi x diameter
= 5.3pi
Answer is 16.65cm to 2 d.p
Hope this helps!
in the scientific method, which of the following is true about a hypothesis? group of answer choices the same hypothesis may not be tested more than once. research studies are designed to prove a hypothesis. a specific hypothesis is generated based on an established theory. a hypothesis both explains and predicts a phenomenon.
Answers
For the scientific method , the true statement about the hypothesis is (b) research studies are designed to prove a hypothesis.
The term Hypothesis is defined as the observation which is proposed as the possible outcome or results of an experiment .
we know that ; in order to prove a hypothesis, the experiments are designed and after that they are performed based on given hypothesis.
That is how the experiments are designed based on a previous idea which may result in a particular outcome.
So , any hypothesis is dependent on a specific experiment( research studies) .
Therefore , the correct option is (b) .
The given question is incomplete , the complete question is
In the scientific method, which of the following is true about a hypothesis?
(a) the same hypothesis may not be tested more than once.
(b) research studies are designed to prove a hypothesis.
(c) a specific hypothesis is generated based on an established theory.
(d) a hypothesis both explains and predicts a phenomenon.
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Hexadecimal numbers use the 16 "digits": 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. a) What is the base 10 value of the 3-digit hexadecimal number 2E5? Show your work. b) Find the probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters, like ACC. (Note: Part (b) has nothing to do with part (a) of this problem.) Write your answer as a simplified fraction, not a decimal or percent. Explain briefly how you got it.
Answers
The base 10 value of the 3-digit hexadecimal number 2E5 is 741. The probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters is 27/512.
a) To convert a hexadecimal number to its decimal equivalent, you can use the following formula:
(decimal value) =\((last digit) * (16^0) + (second-to-last digit) * (16^1) + (third-to-last digit) * (16^2) + ...\)
Let's apply this formula to the hexadecimal number 2E5:
(decimal value) = \((5) * (16^0) + (14) * (16^1) + (2) * (16^2)\)
= 5 + 224 + 512
= 741
Therefore, the base 10 value of the 3-digit hexadecimal number 2E5 is 741.
b) To find the probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters, we need to determine the number of valid options and divide it by the total number of possible 3-digit hexadecimal numbers.
The number of valid options with only letters can be calculated by considering the following:
The first digit can be any letter from A to F, giving us 6 choices.The second digit can also be any letter from A to F, including the possibility of repetition, so we have 6 choices again.The third digit can also be any letter from A to F, allowing repetition, resulting in 6 choices once more.Therefore, the total number of valid options is 6 * 6 * 6 = 216.
The total number of possible 3-digit hexadecimal numbers can be calculated by considering that each digit can be any of the 16 possible characters (0-9, A-F), allowing repetition. So, we have 16 choices for each digit.
Therefore, the total number of possible 3-digit hexadecimal numbers is 16 * 16 * 16 = 4096.
The probability is then calculated as:
probability = (number of valid options) / (total number of possible options)
= 216 / 4096
To simplify the fraction, we can divide both numerator and denominator by their greatest common divisor, which in this case is 8:
probability = (216/8) / (4096/8)
= 27 / 512
Therefore, the probability that a 3-digit hexadecimal number with repeated digits allowed contains only letters is 27/512.
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Use an appropriate substitution to solve 2yy' + x^2 + y^2 + x = 0.
Answers
The general solution to the differential equation is y = [-(1/4)x^2 - (1/3)x + (C/4)]^(1/3).
To solve 2yy' + x^2 + y^2 + x = 0 using an appropriate substitution, we can substitute u = y^2. Taking the derivative of u with respect to x, we get du/dx = 2yy'. We can then rewrite the original equation as 2(u^(1/2))(du/dx) + x^2 + u + x = 0.
This is now a separable differential equation, where we can move the u term to the right side and the x terms to the left side: 2(u^(1/2))du/u = -(x^2 + x)dx. Integrating both sides, we get 4/3u^(3/2) = -(1/3)x^3 - 1/2x^2 + C, where C is the constant of integration.
Substituting back u = y^2, we get 4/3y^3 = -(1/3)x^3 - 1/2x^2 + C.
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What is the value of the function f(x)=x2−5x+2 evaluated at x=−3.5 ??
Answers
Answer:
31,75
Step-by-step explanation:
at x = -3,5 => f(x) = (-3,5)^2 - 5.(-3,5) + 2 = 31,75
Answer:
f(x)=31.75
Step-by-step explanation:
I need help, I need to find the value of a
Answers
Answer:
4
Step-by-step explanation:
which explains whether 18/24 and 63/84 are equivalent fractions
Answers
Answer:
Yes they are.
Step-by-step explanation:
18/24 * 3.5/3.5 (which equals 1) = 63/84
so yes
Area of the right triangle 15 12 10
Answers
Answer: Can you give me a schema of the triangle please ?
To calculate the area of a triangle you need to calculate:
(Base X Height ) ÷ 2
Step-by-step explanation:
Answer:
Step-by-step explanation:
A right triangle would have side 15 12 and 9
and its area is 1/2 * 12 * 9
= 54 unit^2
matthew wants to estimate the mean height of students attending his college. he records the heights of 635 randomly selected students attending the college. what is the population?
Answers
The population in order to calculate the mean height will be all the students attending the college.
The population is the entire group of individuals being studied. In this case, the population is all the students who goes to the college.
Every member of a group constitutes a population. It is the inverse of a sample, which is a percentage or proportion of a group. It is sometimes possible to poll every member of a group. The U.S. Census is a quintessential example of a population, as it is required by law that every member of the U.S. population reply. In most circumstances, surveying everyone is unfeasible in statistics.
Consider how long it would take you to phone every dog owner in the United States to find out what brand of dog food they preferred. Furthermore, people may choose not to respond or may forget to respond, resulting in incomplete censuses. By definition, incomplete censuses become samples.
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