points): Consider the planar linear system X' = AX, where [2 - A = 3 2 Find the general solution. Sketch the phase plane and determine its type. J Find the solution X(t) satisfying X (0) = [-2].
Answers
The matrix exponential eAt can be expressed as:
eAt = (5/4)*e^(3t/2) * [1 3/5; 2/5 1]
Sketching the phase plane, we can see that it represents a spiral source. The solution X(t) satisfying X(0) = [-2] can be found by substituting
t=0 and X(0) = [-2] in the general solution as follows:
X(t) = e^(3t/2) * [1 3/5; 2/5 1] * [-2]X(t) = [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)]
Hence, the solution X(t) satisfying
X(0) = [-2] is X(t) = [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)].
Given system of differential equation is
X'
= AX, where [2 - A
= 3 2
We need to find the general solution, sketch the phase plane and determine its type.The general solution is given by: X(t)
= eAt X(0)
Where eAt is the matrix exponential. Since A is a 2x2 matrix, we can find eAt by using the formula:
eAt
= (I + tA + (t^2/2!)A^2 + (t^3/3!)A^3 + ....)
The matrix exponential eAt can be expressed as:
eAt
= (5/4)*e^(3t/2) * [1 3/5; 2/5 1]
Sketching the phase plane, we can see that it represents a spiral source. The solution
X(t) satisfying X(0)
= [-2]
can be found by substituting t
=0 and X(0)
= [-2] in the general solution as follows:
X(t)
= e^(3t/2) * [1 3/5; 2/5 1] * [-2]X(t)
= [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)]
Hence, the solution X(t) satisfying
X(0)
= [-2] is X(t)
= [-2e^(3t/2)*(3/5) + 2e^(3t/2); -4e^(3t/2)/5 + 2e^(3t/2)].
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Related Questions
a check or quadrangle is defined by the intersection of pairs of
Answers
A check or quadrangle is defined by the intersection of pairs of diagonals of a parallelogram.
What is a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides are parallel and have the same length. The opposite angles of a parallelogram are equal. A parallelogram is a unique type of quadrilateral with specific characteristics.
What is a check or quadrangle?A quadrangle or check is defined as the intersection of pairs of diagonals of a parallelogram. In other words, it is the area inside the parallelogram that is divided into four triangles, each of which shares a common vertex in the center of the parallelogram.
The diagonals of a parallelogram are the line segments that connect the opposite vertices of a parallelogram. When these diagonals intersect, they form four triangles, which are also known as the parallelogram's "sub-triangles." The point where the diagonals intersect is called the center of the parallelogram, and it divides each diagonal into two equal parts.
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Wich sign makes the statement ture
1 1/14 1/4
Answers
The sign that makes the statement as true is minus.
For the statement 1 1/4 [sign] 1/4, we need to determine whether the missing sign should be a plus or a minus. To do this, we need to perform the arithmetic calculation that the sign represents.
If we insert a plus sign between 1 1/4 and 1/4, we would be adding the two fractions together. To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 4 and 14 is 28.
Therefore, we can rewrite the statement as 1 7/28 = 1.25.
This is not true, since 1 1/4 is equal to 1.25, and 1.25 plus 1/4 would be greater than 1 1/2.
On the other hand, if we insert a minus sign between 1 1/4 and 1/4, we would be subtracting the second fraction from the first. We can find a common denominator as before and rewrite the statement as
1 3/28 = 1.1071. This is true, since 1 1/4 minus 1/4 is equal to 1.
Therefore, the sign that makes the statement true is the minus sign.
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I need the help
On the problems with it and what is the answer
Answers
please answer
4. Suppose that for 3MA Forecast, my Mean Absolute Deviation (MAD) is \( 3.0 \) and my Average Error (AE) is \( -2.0 \). Does my forecast fail the bias test? a. Yes b. No
Answers
The answer is: a. Yes, the forecast fails the bias test.
To determine whether the forecast fails the bias test, we need to compare the Average Error (AE) with zero.
If the AE is significantly different from zero, it indicates the presence of bias in the forecast. If the AE is close to zero, it suggests that the forecast is unbiased.
In this case, the Average Error (AE) is -2.0, which means that, on average, the forecast is 2.0 units lower than the actual values. Since the AE is not zero, we can conclude that there is a bias in the forecast.
Therefore, the answer is:
a. Yes, the forecast fails the bias test.
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Peyton invested $300 into a savings account. The equation
A = 300(1.005)12t models the amount in Peyton's account A after t
years. How much will be in Peyton's account after 7 years?
Answers
First let’s plug in 7 for t. 300(1.005)12(7), 12*7= 84
300*1.005= 301.5
301.5*84= 25,326
Peyton will have $25,326 in her account after 7 years.
A bag contains 20 brown, 16 orange, 4 navy, and 13 purple marbles. A marble is drawn at random. What is the theoretical probability of drawing a brown marble?
Answers
20/53 chance or 0.38 probability.
can someone help me with this problem and explain how to do it please I don't really under stand this
justify each step
1.44-2(3x+4)=-18x
Answers
Step-by-step explanation:
You want to solve for x:
First, distribute -2 into the parenthesis, you will end up with 44 - 6x - 8 = -18x
Next, combine like terms, you will end up with 36 - 6x = -18x
Next, add 6x to both sides, you will end up with 36 = -12x
Finally, divide both sides by -12, you will end up with x = -3
27. Albright Motors is expected to pay a year-end dividend of \( \$ 3 \) a share \( \left(D_{1}=\$ 3.00\right) \), then a divivend of \( \$ 5 \) in 2 years \( \left(\mathrm{D}_{2}=\$ 5.00\right) \), a
Answers
Albright Motors is expected to pay a year-end dividend of $3 per share \((\(D_1 = \$3.00\))\), followed by a dividend of $5 in 2 years \((\(D_2 = \$5.00\))\). To calculate the present value of these future dividends, we can use the concept of discounting to determine the current value of the expected dividends.
The present value of future dividends can be calculated using the formula:
Present Value = \(\(\frac{{D_1}}{{(1 + r)^1}} + \frac{{D_2}}{{(1 + r)^2}}\)\)
where \(\(D_1\) and \(D_2\)\) are the future dividends and \(\(r\)\) is the required rate of return or discount rate.
In this case, the dividend \(\(D_1\)\) is $3 and the dividend \(\(D_2\)\) is $5. To find the required rate of return \((\(r\))\), we need additional information such as the stock price or market value of Albright Motors' shares. Without that information, we cannot determine the exact value of the required rate of return or calculate the present value of the dividends.
Once the required rate of return is known, we can substitute the values into the formula to calculate the present value of the future dividends. The present value represents the current value of the expected dividends, taking into account the time value of money.
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Jaime created the list of factors of 32 below.
32: 1, 2, 4, 6, 8, 16, 32
Which number should be removed from this list to make the list accurate?
Answers
Step-by-step explanation:
The number 6 is not a factor of 32. Hope this helps. So remove that one
How many solutions does this equation have? –2f + 2f = 0
Answers
Answer:
an infinite number
Step-by-step explanation:
The equation is true for any value of f, so there are an infinite number of solutions.
Marvin is playing a solitaire game with marbles. There are n bowls (for some positive integer n), and initially each bowl contains one marble. Each turn, Marvin may eitherremove a marble from a bowl, orchoose a bowl A with at least one marble and a different bowl B with at least as many marbles as bowl A, and move one marble from bowl A to bowl B.The game ends when there are no marbles left, but Marvin wants to make it last as long as possible.Prove that the game must end after at most n(n+1)/2 turns.Prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns.Marisa comes along and asks to join the game. Marvin and Marisa revise the rules: they will alternate taking turns, starting with Marisa. When the game ends, whoever took the last turn is the winner.Prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.
Answers
Among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.
For the first part of the problem, we can prove that the game must end after at most n(n+1)/2 turns by induction. Base case: When there is only one bowl, Marvin can remove the single marble in one turn, so the game ends after one turn.
Inductive step: Suppose the game ends after at most k(k+1)/2 turns when there are k bowls. We will show that the game ends after at most (k+1)(k+2)/2 turns when there are k+1 bowls. If Marvin removes a marble from a bowl, then the number of bowls decreases by one and the game must end after at most k(k+1)/2 turns by the inductive hypothesis.
If Marvin moves a marble from bowl A to bowl B, where bowl A has at least one marble and bowl B has at least as many marbles as bowl A, then the number of marbles in bowl A decreases by one and the number of marbles in bowl B increases by one. Since bowl B has at least as many marbles as bowl A, the number of bowls remains unchanged. Thus, the game must still end after at most k(k+1)/2 turns.
In either case, the game ends after at most k(k+1)/2 turns, so the game must end after at most (k+1)(k+2)/2 turns when there are k+1 bowls, as desired.
For the second part of the problem, we can prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns by constructing a strategy.
Suppose Marvin wants to make the n-bowl game last for at least kn turns. He can do this by making sure that there are always at least k marbles in each bowl. To do this, Marvin can start by placing k marbles in the first bowl, k-1 marbles in the second bowl, and so on, down to 1 marble in the nth bowl.
On each turn, Marvin can choose a bowl with at least k marbles and move one marble to a bowl with fewer than k marbles. For example, if there are k+1 marbles in the first bowl and k marbles in the second bowl, Marvin can move one marble from the first bowl to the second bowl. This keeps the number of marbles in each bowl at least k. Since Marvin can take at least one turn per bowl, the game will last for at least kn turns.
For the third part of the problem, we can prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.
Let n be a positive integer. We will show that either Marvin has a winning strategy for the n-bowl game or Marisa has a winning strategy for the (n+1)-bowl game.
If Marvin has a winning strategy for the n-bowl game, then he can win the n-bowl game by following his winning strategy.
If Marvin does not have a winning strategy for the n-bowl game, then Marisa has a winning strategy for the n-bowl game. In this case, Marvin can adopt Marisa's winning strategy for the n-bowl game as his own winning strategy for the (n+1)-bowl game.
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I » The temperature when Spencer arrived at school was a very chilly -4°F. By the time school got out, the temperature had risen 13°F. 1) What was the temperature when school got out?
Answers
Answer:
ur answer would be 9!
Really don’t understand this one
Answers
Answer:
(3,8)
Step-by-step explanation:
First, you need to graph a triangle using the points given.
Then reflect across y = x
R is (3,0) which when reflected across y = x is (0,3)
S is (3,3) which when reflected across y = x is (3,3)
R is (4,0) which when reflected across y = x is (0,4)
How do I Answer this question ? using the following directions.
Answers
Answer:
12-2n
Step-by-step explanation:
Difference means to subtract
Times means to multiply
A number would be the variable
In the equation, y = 3x + 7 what is the range when the domain is 8.
15
45
31
24
Answers
Answer:
31 is your answer.
I HOPE IT WILL HELP YOU.
Thank you.
^ - ^
1. do people who drink the caffeine equivalent of at least two cups of coffee (group a) do worse on tests than those who drink less than one cup (group b)? 2. do people do better on tests when they drink the caffeine equivalent of at least two cups of coffee (condition a) than when they drink less than one cup (condition b)? notice that both studies described are getting at the same research question (does drinking at least two cups of coffee worsen tests results?). but, the first example studies two different populations (those people who drink the caffeine equivalent of at least two cups of coffee and those people who drink less than one cup), while the second example studies the same people twice, under two different conditions or treatments (first when people drink the caffeine equivalent of at least two cups of coffee, and then when they drink less than one cup). statement advantage not an advantage the repeated-measures t test can handle categorical data. in the repeated-measures t test the participants in one treatment are not substantially different from the participants in another. the repeated-measures t test can handle more than two conditions. the repeated-measures t test uses half the number of participants.
Answers
The repeated measures t-test uses half the number of participants is
Statement 1: Advantage
The repeated measures t-test can handle categorical data.
This makes the experiment more efficient, the validity of the results higher, and to keep the variability low.
Statement 2: Advantage
In the repeated measures t-test, the participants in one treatment are not substantially different from the participants in another, because the same subjects are used in both and throughout our study. This makes the researcher get a reliable statistical conclusion even with a small set of subjects.
Statement 3: Not an advantage.
The repeated measures t-test can handle more than two conditions. This is a disadvantage compared to other designs, where the subjects are exposed to more than one treatment.
Statement 4: Advantage.
The repeated measures t-test uses half the number of participants. This method requires minimal subjects. With that, we can get significant results for the given sample.
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What is a secure line of credit? a. A line of credit offered only to individuals with excellent credit ratings. B. A line of credit offered to a business or corporation. C. A line of credit backed by the government. D. A line of credit backed by collateral. Please select the best answer from the choices provided A B C D.
Answers
Answer:
d. A line of credit backed by collateral.
Step-by-step explanation:
i just took the test
answer?
i have been searching and i still have gotten one please help if you can
Answers
Answer:
7 ft/yr
Step-by-step explanation:
Answer:
7 ft/yr!
Step-by-step explanation:
Find the common difference of the arithmetic sequence -6,2, 10,
Answers
Answer:
the common ratio is +8
10 - 2 = 8
2 - (-6) = 8
is it function or non function?
Answers
Answer:
function
Step-by-step explanation:
Answer:i Believe its a. non Function sorry if. Im. Wrong
please help, this is due tonight
Answers
Answer:
It's B
Step-by-step explanation:
Just divide y by x. For example: 6.6 / 6 = 1.1. This would be B! Hope this helps!
J.W. is an artist and sells hisnpottery each year at a local Renaissance Festival. He keeps track of his sales and the 7.75% sales tax he collects by making notations in a ledger. Every evening he checks his records by counting the total money in his cash drawer. After a day of selling pottery, the cash totaled $1253.68. How much is from the sale of the merchandise and how much is sales tax? Round your answer to the nearest cent.
Answers
The amount from tax is $97.16 while the amount from sales is $1156.52
Tax is a compulsory sum levied on the sales of goods and services
Taxes increases the price of a good
The price of J.W.'s pottery would be 7.75% higher as a result of the tax
Amount of tax collected = percentage of sales tax x total of cash
0.0775 x $1253.68 = $97.16
Amount from the sale = total cash - taxes
$1253.68 - $97.16 = $1156.52
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Thomas spent $3.30 for 3 ice cream cones. Dan spent 2.50 for 2 ice cream cones. How much less did Dan or Thomas spend?
A. $0.25
B. $0.05
C. $0.15
D.$0.10
Answers
Answer: Thomas spent .15 less
Step-by-step explanation:
Dan: 2.50/2=1.25
Thomas: 3.30/3=1.1
1.25-1.1=.15
Answer:
C
Step-by-step explanation:
Each cone they bought was 1.10 each and 1.25 each
1.10<1.25
1.25-1.10=0.15
Choose the point-slope form of the equation below that represents the line that
passes through the points (-6, 4) and (2, 0). (2 points)
1) y - 4 =-1/2 (x+6)
2) y - 4 = 2(x + 6)
3) y+6=-1/2(x - 4)
4) y + 6 = 2(x - 4)
Answers
\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the Concept of the Straight lines.
Since the slope of the line, m = -1/2
and we know that, line equation is, y=mx+c
so the answer is, option 1.)
1.) y-4 = -1/2 (x+6)
a strain of peas has 3 green and one yellow for every four peas. if 12 peas are rendomly selected, what is the probability that exactly 8 peas are green? provide your answer to three decimal places
Answers
The probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.
We can use the binomial probability formula to solve this problem.
The formula is given as; $$P(X=k)={n\choose k}p^k(1-p)^{n-k}$$
Where;
n= sample size=12
k= number of green peas=8
p= probability of getting a green pea=3/4
q= probability of getting a yellow pea=1/4
Since we want the probability of exactly 8 green peas out of 12 peas,
we will plug in the values in the formula to get;
$$P(X=8)={12\choose 8}(\frac{3}{4})^8 (1-\frac{3}{4})^{12-8}$$$$
P(X=8)={12\choose 8}(\frac{3}{4})^8(\frac{1}{4})^{4}$$$$P(X=8)=495
(0.3164)(0.0039)$$$$P(X=8)=0.4749$$
Therefore, the probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.
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Kelvin has $1842. He wants to save 1/2 of the money and use the rest to buy a new bike. How much money will Kelvin save
Answers
Answer:
Kelvin will save (1/2) × $1,842 = $921.
The length of the curve y=sinx from x=0 to x=3π4 is given by(a) ∫3π/40sinx dx
Answers
The length of the curve y = sin(x) from x = 0 to x = 3π/4 is (√2(3π - 4))/8.
The length of the curve y = sin(x) from x = 0 to x = 3π/4 can be found using the arc length formula:
\(L = ∫(sqrt(1 + (dy/dx)^2)) dx\)
Here, dy/dx = cos(x), so we have:
L = ∫(sqrt(1 + cos^2(x))) dx
To solve this integral, we can use the substitution u = sin(x):
L = ∫(sqrt(1 + (1 - u^2))) du
We can then use the trigonometric substitution u = sin(theta) to solve this integral:
L = ∫(sqrt(1 + (1 - sin^2(theta)))) cos(theta) dtheta
L = ∫(sqrt(2 - 2sin^2(theta))) cos(theta) dtheta
L = √2 ∫(cos^2(theta)) dtheta
L = √2 ∫((cos(2theta) + 1)/2) dtheta
L = (1/√2) ∫(cos(2theta) + 1) dtheta
L = (1/√2) (sin(2theta)/2 + theta)
Substituting back u = sin(x) and evaluating at the limits x=0 and x=3π/4, we get:
L = (1/√2) (sin(3π/2)/2 + 3π/4) - (1/√2) (sin(0)/2 + 0)
L = (1/√2) ((-1)/2 + 3π/4)
L = (1/√2) (3π/4 - 1/2)
L = √2(3π - 4)/8
Thus, the length of the curve y = sin(x) from x = 0 to x = 3π/4 is (√2(3π - 4))/8.
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Find the equation of the line use exact numbers y=
Answers
I WILL TAKE THE POINTS (0,7) AND (2,1) FROM THW GRAPH AND USE THEM TO GET THE GRADIENT.
\(m \frac{y2 - y1}{x2 - x1} \\ = \frac{1 - 7}{2 - 0} \\ m = \frac{ - 6}{2} \\ m = - 3\)
I WILL USE THE POINT (0,7) TO FIND THE VALUE OF C IN THE GENERAL EQUATION.
\(7 = - 3(0) + c \\ c = 7\)
THE EQUATION IS
\(y = - 3x + 7\)
ATTACHED IS THE SOLUTION
Subtract 3/16 minus 3/9
Answers
Answer: 3/16 - 3/9 = -7/48
Step-by-step:
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(3/16, 3/9) = 144
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(3/16×9/9)−(3/9×16/16)=?
Complete the multiplication and the equation becomes
27/144−48/144=?
The two fractions now have like denominators so you can subtract the numerators.
Then:
27−48=−21
144=144
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 21 and 144 using
GCF(21,144) = 3
−21÷3=-7
144÷3=48
Therefore:
3/16−3/9=−7/48
Hi today im going to be giving a -lot of point so if u dont get points dont worry cuz im going to be doing 5 times.
Im going to be giving them away at the same time!!!!!!!!!
Good luck!!
Answers
Answer:
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Thanks So MUCH!!!
Step-by-step explanation:
Answer: omg, thank you so much!!!!!!!
Step-by-step explanation: