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1. The eigenvalues of matrix A are 2 and 3.

2. The bases for the eigenspaces of A are {(1, -1)} and {(3, 1)}.

3. A is diagonalizable because it has distinct eigenvalues and the sum of the dimensions of its eigenspaces is equal to the dimension of the matrix.

4. The matrix P is [1, 3; -1, 1], and the diagonal matrix D is [2, 0; 0, 3], such that P^(-1)AP = D.

5. A^23 is equal to 2^23, which can be written as 223.

6. The system of differential equations can be solved using the matrix equation X' = PX, where X is the vector [x1; x2] and P is the matrix [1, 2; 2, 1].

1. To find the eigenvalues of matrix A, we solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue. By calculating the determinant, we get (2-λ)(2-λ) - 1 * 1 = 0, which simplifies to λ^2 - 4λ + 3 = 0. Solving this quadratic equation, we find the eigenvalues λ = 2 and λ = 3.

2. To find the eigenspaces of A, we solve the equations (A - λI)X = 0, where X is a non-zero vector in the eigenspace corresponding to eigenvalue λ. For eigenvalue λ = 2, we have (A - 2I)X = 0, which gives the equation [0, 1; -1, 0]X = 0. The solution is X = [1, -1]. Similarly, for eigenvalue λ = 3, we have (A - 3I)X = 0, which gives the equation [-1, 1; -1, 1]X = 0. The solution is X = [3, 1].

3. A matrix is diagonalizable if it has a complete set of eigenvectors. In this case, since A has distinct eigenvalues and the sum of the dimensions of its eigenspaces (2) is equal to the dimension of the matrix (2x2), A is diagonalizable.

4. To find the matrix P and diagonal matrix D, we need to find the eigenvectors corresponding to the eigenvalues of A. The matrix P is formed by taking the eigenvectors as its columns, i.e., P = [1, 3; -1, 1]. The diagonal matrix D is formed by placing the eigenvalues on its diagonal, i.e., D = [2, 0; 0, 3]. Then, we can verify that P^(-1)AP = D.

5. A^23 means raising the matrix A to the power of 23, which is equivalent to raising each element of A to the power of 23. Since A is a 2x2 matrix, A^23 is represented as 223.

6. The system of differential equations can be solved using the matrix equation X' = PX, where X is the vector [x1; x2], X' is the derivative of X with respect to t, and P is the matrix [1, 2; 2, 1]. By solving this equation, we can find the solution for x1 and x2 as functions of t.

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Answer:

x=11/18 or 0.61

Step-by-step explanation:

Let x represent the blank

[tex]As\ x:11::1/3:6\ form\ a\ proportion,\ we\ may\ use\ the\ ratio\ method\ to\ find\ x.\\\\Hence,\\x:11::1/3:6\\6x=1/3*11\\x=11*1/3*1/6\\x=11*1/18\\x=11/18[/tex]

Answer:

19

Step-by-step explanation:

f(x) = 2x^2 + 1

Let x= 3

f(3) = 2 * (3)^2 +1

Exponents first

     = 2 * 9+1

Then multiply

     = 18+1

Add

   = 19

Answer:

THE ANSWER IS 19 JUST TOOK THE UNIT TEST

Step-by-step explanation:

Answer:

all are functions

Step-by-step explanation:

a function is when each x has a y

a relation is when 1 x has more than 1 y which makes it invalid therefore not a function

Answer:

(2x - 1)(2x + 1)

Step-by-step explanation:

Difference of Squares: (ax + b)(ax - b) = (ax² - b²)

Answer:

4×^2-1=(2× +1)(2× -1)

Step-by-step explanation:

using a^2 - b^2 =(a+b)(a-b)

Answer:

What kind of proof do you need?

M, Q, and N are collinear, with Q between M and N.

Triangle QPM is isosceles (PM=PQ).

That makes PN greater than PQ.

If you need a formal proof, it looks as if you can use trigonometry and the law of sines.

If you need a formal two-column proof using Euclidean geometry, I'm not sure how you would do it....

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Given that the graph of f(x) = ax² + 3 passes through the point (1,1). We are supposed to find the value of a.Since the point (1, 1) lies on the graph of the function, we can say thatf(1) = 1That is:a(1)² + 3 = 1a + 3 = 1a = 1 - 3a = -2

Therefore, the value of a is -2. Thus, the graph of the function f(x) = -2x² + 3 passes through the point (1, 1).The solution is done in 88 words.

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Answer:

15

Step-by-step explanation:

Its y2 - y1 over x2-x1

Answer:

25/27

Step-by-step explanation:

because

5/6÷15/3×2/3

in BODMAS =5/6×15/3×2/3

=150/54=25/27

Answer:

38.83 inches

Step-by-step explanation:

Jose: 52 1/2

Sister: 52 1/2 - 13 2/3

His sister is 38.83 inches

Answer:

38 5/6 inches

Answer:

An arithmetic sequence has first term 4 and common difference 8

Step-by-step explanation:

Answer:

17.45

Step-by-step explanation:

I just took the quiz good luck! :)

Answer:

17.45

Step-by-step explanation:

edge 2022

A. The arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone boothe.

B. The arrival rate per hour must increase by at least 1.6 customers per hour to justify a second telephone booth under the new criterion.

To get the how much arrival rate must increase, we must get the expected waiting time for a customer.

Assuming;

X is the number of customers who arrive per hour

Y is the length of a phone call in minutes.

Then, X follows a Poisson distribution with λ = 4 (since 4 customers per hour use the phone on average)

Y follows a negative exponential distribution with mean μ = 5 (since the mean length of a phone call is 5 minutes).

Total time is given as sum of waiting time and length of call;

T = W + Y

The waiting time W is the difference between the time a customer arrives and the time that the phone becomes available. waiting time follows a uniform distribution where mean= 1/λ (since the arrivals follow a Poisson process);

Then we have;

E(W) = 1/(2λ) = 1/8 hours

The expected total time T that a customer spends at the phone booth is:

E(T) = E(W) + E(Y) = 1/8 + 5/60 = 11/48 hours

For a second telephone booth to be justifiable, new customer that arrives must wait 3 minutes or longer for the phone.

E(W) ≥ 1/20

To get λ,

1/(2λ) ≥ 1/20

λ ≤ 10

This means that, the arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone booth.

b. Getting how much the arrival rate per hour must increase to justify a second telephone booth under the new criterion,

we need to find the probability that a customer has to wait at all.

Let P(W > 0) be the probability that a customer has to wait.

P(W > 0) = 1 - P(W = 0)

The waiting time W follows a uniform distribution with mean 1/λ, so we have:

P(W = 0) = 1 - λ/4

The length of a phone call Y follows a negative exponential distribution with mean 5 minutes = 1/12 hours, so we have:

P(Y > t) = e^(-μt) = e^(-t/12)

The probability that a customer has to wait is given as;

P(W > 0) = 1 - P(W = 0) = λ/4

To justify a second telephone booth, the probability of having to wait at all must exceed 0.6. so we have;

P(W > 0) > 0.6

λ > 2.4

The arrival rate per hour must increase by at least 2.4 - 4 = 1.6 customers per hour to justify a second telephone booth under the new criterion.

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Answer:

we use BODMAS

-4 x 4 /5÷ 4=-16/5÷4

=-16÷1[tex]1/4[/tex]

=-16 ÷ 5/4

=-16 x 4/5

=-64/5

=12[tex]4/5[/tex]

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Distance can't be negative (especially after using absolute value) so A and C are cancelled.

When you are trying to find the distance between the 2, you want to subtract to see how far they are away from each other.

That means B is cancelled and D is the only answer you have left :)

Answer: 62 units

Step-by-step explanation:

To find the key numbers of the inequality x² - 2x - 24 > 0, we need to determine the values of x that make the inequality true. The key numbers are the points where the expression changes sign. In this case, the key numbers are -4 and 6.

To find the key numbers, we can factor the quadratic expression x² - 2x - 24 > 0. The factored form is (x - 6)(x + 4) > 0. The inequality is satisfied when either both factors are positive or both factors are negative.

Setting each factor equal to zero, we get x - 6 = 0 and x + 4 = 0. Solving these equations, we find that x = 6 and x = -4.

Now, we need to determine the intervals on the number line where the inequality is true. We choose test values from each interval and substitute them into the inequality. For example, testing x = -5 gives (-5 - 6)(-5 + 4) > 0, which is true. Similarly, testing x = 0 gives (0 - 6)(0 + 4) < 0, which is false.

By considering the sign changes, we find that the inequality is true for x < -4 and x > 6. Therefore, the key numbers are -4 and 6, which divide the number line into three intervals: (-∞, -4), (-4, 6), and (6, ∞).

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Answer:

The answer is $97.35

Step-by-step explanation:

This because you would need to multiply 75x1.298 to get your answer and your conversion method is multiplying so your answer is $97.35

Hope this helps and have a great day!!

Answer:

r u indian??

Step-by-step explanation:

wow bro m an indian too

Answer:

34 and 6 =40

Step-by-step explanation:

40 divided by 2=20 20-14=6 14+20=34

Answer:840 hours

Step-by-step explanation:You have to Add to get your answer.This is how I got 840:

60+60=120

120+720=840

Your answer is:840 hours

hope this was helpful :)

Answer:

situation a and she bought 3 pounds

Step-by-step explanation:

Answer: I would say A because $10 per pound seems to much and laundry detergent to turn out as $16

16× X = 1.49

=> X = 1.49 ÷ 16

Answer:

Yes, the scale factor is 4.

Step-by-step explanation:

If you times the length, 3, and the width, 5, by 4, you'll get 12 as your length and 20 as your width.

Answer:

steps below but I recommend the graphing calculator on demos

Step-by-step explanation:

y= mx + b.......  y= 1/2x+ 0

our b is 0 so first plot that

our slope is 1/2 so go up one and to the right twice

keep doing that and you will have your line. USE DESMOS

Answer:

1.46

Step-by-step explanation:

Answer:

Solution steps:

Step 1: Locate and underline the whole number place (.) and look to the right (4):

1.456

Step 2: The digit to the right (4) is 4 or below. So, we replace it by a 0 (zero), then we get 1 as the answer.

In short: 1.456 rounded to the nearest whole number is 1.

Answer: the answer is X=-6

Step-by-step explanation:

5x-14=8x+4 - move variable to the left-hand side and change its sign

5x-8x-14=4  - first switch it you are going to have a better understanding

5x-8x= 4=14 move constant to the right-hand side and change its sign

-3x=4+14 collect like term

-3x=18 add the numbers/ then divide both sides of the equation by -3

x=-6