In this problem, y=c₁ece is a two-parameter family of solutions of the second-order DE y-y-0. Find a solution of the second-order TVP consisting of this differential equation and the given initial conditions. y(-1)=2 y(-1) = -2;

Answers

Answer 1

The solution of the second-order differential equation y'' - y' = 0 with the given initial conditions y(-1) = 2 and y'(-1) = -2 is y(x) = 2e^x - 4e^-x.

To find a solution to the second-order differential equation y'' - y' = 0, we first solve the characteristic equation by assuming a solution of the form y(x) = e^(rx). Plugging this into the differential equation, we get r^2e^(rx) - re^(rx) = 0. Factoring out e^(rx), we have e^(rx)(r^2 - r) = 0. This gives us two possible values for r: r = 0 and r = 1.

For r = 0, the corresponding solution is y₁(x) = c₁, where c₁ is a constant.

For r = 1, the corresponding solution is y₂(x) = c₂e^x, where c₂ is a constant.

To find the particular solution that satisfies the given initial conditions, we substitute the values of x = -1, y(-1) = 2, and y'(-1) = -2 into the general solution. This gives us the equations 2 = c₁ and -2 = c₂e^-1. Solving for c₁ and c₂, we find c₁ = 2 and c₂ = -2e.

Therefore, the solution to the second-order differential equation with the given initial conditions is y(x) = 2e^x - 4e^-x.

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Related Questions

Find the area. 14 m 4.5 m 4.5 m 9m 12 m 3 m 3 m

plzzz help meeee​

Answers

Answer:

52

Step-by-step explanation:

6) The cost of a computer system increases with increased processor speeds. The cost C
of a system as a function of processor speed is estimated as C = 1234 - 35 + 1900,
where S is the processor speed in MHz. Find the processor speed for which cost is at a
minimum. [4 marks]​

Answers

Answer:

The speed is: 0.0142MHz

Step-by-step explanation:

Given

[tex]C(s) = 1234s^2 - 35s + 1900[/tex]

Required

The processor speed when the cost is at minimum

First, differentiate C(s) with respect to s

[tex]C(s) = 1234s^2 - 35s + 1900[/tex]

[tex]C'(s) = 2468s - 35[/tex]

The cost is at minimum when [tex]C'(s) = 0[/tex]

So, we have:

[tex]C' = 2468s - 35 = 0[/tex]

[tex]2468s - 35 = 0[/tex]

Solve for s

[tex]2468s = 35[/tex]

[tex]s=\frac{35}{2468}[/tex]

[tex]s\approx0.0142[/tex]

Roger brought some sponges. The number of packages he bought was 14 less than the number of sponges per package. Roger bought 51 sponges in all. How many packages of sponges did roger buy?

Answers

Answer:

the number of sponges per package bought be 32.5

Step-by-step explanation:

Let us assume the number of sponges per package be x

So the number of packages he bought be x - 14

And, the overall he bought 51 sponges

So

the number of packages of sponges did roger buy is

x + x - 14 = 51

2x = 51 + 14

2x = 65

x = 32.5

So the number of sponges per package bought be 32.5

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Answers

Answer:

Infinitely many solutions

Step-by-step explanation:

7x - 11 = 5(x - 2) + 2x - 1

7x - 11 = 10x - 10 + 2x - 1

7x - 11 = 7x - 11

No matter what number you plugin, it will always be equal.

1) 7x-11 = 5(x-2)+2x-1

2) 7x-11=5x-10+2x-1

3)7x-11=7x-11

4)0=0

5)Would cancel each other out.

6) So I guess no solutions?

help pls first awnser get brainest

Answers

Answer:

124

Step-by-step explanation:

the top square is 16 by 6 which will give you an area of 124 the bottom square has dimensions of 2 by 14 which is 28 add those numbers together to get your answer.

The radius of a circle is 4 feet. What is the area?

r=4ft

Give the exact answer in simplest form.

Answers

Answer:

100.571429.

Step-by-step explanation:

2*22/7*(4)^2

=44/7*16

=100.571429

please please please help​

Answers

Answer:

I wanna say 16 but im not sure

Step-by-step explanation:

Which of the following is equivalent to the expression below?

Answers

Answer:

A. 7✓6 - 6x✓6

Explanation:

7✓6 - 5x✓6 - x✓6

= 7✓6 - (5x + x)✓6

= 7✓6 - 6x✓6

Which expression is equivalent

Answers

Answer:

the first one

Step-by-step explanation:

I think it’s the first one

5/7+1/2+3/4

i need help please

Answers

Answer:

1.96428571429

Step-by-step explanation:

Answer:

55/28

Step-by-step explanation:

5×2+7/14+3/4

17/14+3/4

68+42/56

110/56

55/28

5. How far can you get away from your little brother with a squirt gun filled point
with paint if you can travel at 3 m/s and you have 15 s before he sees you?"
45 m
5 m
2 m
20 m

Answers

Answer:

45 meters

Step-by-step explanation:

I hope this helps.

Find the area of ​​the painted part of the image below. (Units in m)

Answers

Answer:

11 meters square.

Step-by-step explanation:

if the painted area is the gray it would be 10m

if its the white area its 9m

what is m (angle) 2 if m (angle) 4 = 120°?​

Answers

Answer:

if 4 is 120° then 2 is also 180° since they are opposite angles.

The following data repite the resundew of students to short-zule test (out of 10) of cours Alb. X. and Cae). X 7 10 3 8 3 0 9 8 Sum 9 G 8 5 2 9 10 1. Calculate the correlation coeffici

Answers

The correlation coefficient between the scores of students in courses Alb. X and Cae is approximately -0.333.

Correlation refers to the strength of the relationship between two variables while coefficient refers to the numerical value that measures the strength of the correlation.

To calculate the correlation coefficient between the scores of students in courses Alb. X and Cae, we need to first organize the data into two separate lists or arrays representing the scores in each course. Let's denote the scores in Alb. X as X_scores and the scores in Cae as C_scores:

X_scores: 7, 10, 3, 8, 3, 0, 9, 8

C_scores: 8, 5, 2, 9, 10, 1

Next, we need to calculate the mean (average) of both sets of scores.

Mean of X_scores (denoted as X_mean):

X_mean = (7 + 10 + 3 + 8 + 3 + 0 + 9 + 8) / 8

X_mean = 48 / 8

X_mean = 6

Mean of C_scores (denoted as C_mean):

C_mean = (8 + 5 + 2 + 9 + 10 + 1) / 6

C_mean = 35 / 6

C_mean ≈ 5.83

Now, we calculate the covariance between the two sets of scores using the formula:

cov(X_scores, C_scores) = Σ((X_i - X_mean) * (C_i - C_mean)) / (n - 1)

where Σ denotes the sum, X_i and C_i are individual scores, X_mean and C_mean are the means calculated above, and n is the number of scores.

Let's calculate the covariance:

cov(X_scores, C_scores) = ((7-6)(8-5.83) + (10-6)(5-5.83) + (3-6)(2-5.83) + (8-6)(9-5.83) + (3-6)(10-5.83) + (0-6)(1-5.83) + (9-6)(8-5.83) + (8-6)(0-5.83)) / (8-1)

cov(X_scores, C_scores) ≈ -3.39

Next, we calculate the standard deviations of both sets of scores:

Standard deviation of X_scores (denoted as X_std):

X_std = √(Σ(X_i - X_mean)² / (n - 1))

Let's calculate X_std:

X_std = √(((7-6)² + (10-6)² + (3-6)² + (8-6)² + (3-6)² + (0-6)² + (9-6)² + (8-6)²) / (8-1))

X_std ≈ 3.20

Standard deviation of C_scores (denoted as C_std):

C_std = √(Σ(C_i - C_mean)² / (n - 1))

Let's calculate C_std:

C_std = √(((8-5.83)² + (5-5.83)² + (2-5.83)² + (9-5.83)² + (10-5.83)² + (1-5.83)²) / (6-1))

C_std ≈ 3.18

Finally, we can calculate the correlation coefficient (r) using the formula:

r = cov(X_scores, C_scores) / (X_std * C_std)

Let's calculate r:

r ≈ -3.39 / (3.20 * 3.18)

r ≈ -3.39 / 10.176

r ≈ -0.333

Therefore, the correlation coefficient between the scores of students in courses Alb. X and Cae is approximately -0.333.

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Identify the type of conic that follwoing equation represents and write the standard form of each equation.

25x² + 100y² - 450x - 400y - 75 = 0

Answers

The standard form of the equation for the ellipse is ((x - 9)²/376) + ((y - 2)²/94) = 1.

The given equation represents an ellipse. The standard form of the equation is ((x-h)²/a²) + ((y-k)²/b²) = 1, where (h,k) is the center of the ellipse, 'a' is the semi-major axis, and 'b' is the semi-minor axis.

To determine the type of conic represented by the equation, we examine the coefficients of the x² and y² terms. In the given equation, both the x² and y² terms have positive coefficients, indicating that it represents an ellipse.

To write the equation in standard form, we need to complete the square for both the x and y terms. Let's rearrange the equation:

25x² - 450x + 100y² - 400y = 75

Now, we group the x and y terms and complete the square separately:

25(x² - 18x) + 100(y² - 4y) = 75

To complete the square for the x term, we take half of the coefficient of x (-18/2 = -9) and square it to get 81. Similarly, for the y term, we get 4.

25(x² - 18x + 81) + 100(y² - 4y + 4) = 75 + 25*81 + 100*4

Simplifying further:

25(x - 9)² + 100(y - 2)² = 9400

Dividing both sides by 9400, we get:

((x - 9)²/376) + ((y - 2)²/94) = 1

Therefore, the standard form of the equation for the ellipse is ((x - 9)²/376) + ((y - 2)²/94) = 1.

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Bryan is a waiter. He waits on a table of 4 whose bill comes to $110.31. If Bryan receives a 15% tip, approximately how much will he receive?

Answers

If Bryan receives a 15% tip, then he will receive an amount of approximately $16.55 as a tip.

In order to calculate the tip-amount, we need to multiply the total-bill by the tip percentage. In this case, the "bill-amount" is $110.31, and the tip percentage is 15%.

To find the tip amount, we can use the formula:

Tip amount = (Total bill) × (Tip percentage),

Simplifying further,

We get,

Tip amount = $110.31 × 0.15,

= $16.5465 (rounded to the nearest cent)

Therefore, Bryan will receive approximately $16.55 as a tip.

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A telephone company representative estimates that 40% of its customers have call-waiting service. To test this hypothesis, she selected a sample of 100 customers and found that 37% had call waiting. At α-0.01 , is there enough evidence to reject the claim?

Answers

Using the null-hypothesis to calculate the test-statistic at a significance level of 0.01, there is not enough evidence to reject the claim that 40% of the telephone company's customers have call-waiting service based on the sample data.

Is there enough evidence to reject the claim?

To test the hypothesis that 40% of the telephone company's customers have call-waiting service, we can conduct a hypothesis test.

Let's set up the null and alternative hypotheses:

Null hypothesis (H₀): The proportion of customers with call-waiting service is 40%.

Alternative hypothesis (H₁): The proportion of customers with call-waiting service is not 40%.

We can use the t-test for proportions to perform the hypothesis test. The test statistic is given by:

z = (p - p₀) / √((p₀ * (1 - p₀)) / n)

where p is the sample proportion, p₀ is the hypothesized proportion, and n is the sample size.

In this case, p₀ = 0.40, p = 0.37, and n = 100.

Calculating the test statistic:

z = (0.37 - 0.40) / √((0.40 * (1 - 0.40)) / 100)

z = -0.03 / √(0.24 / 100)

z = -0.03 / 0.049

z = -0.612

To determine if there is enough evidence to reject the null hypothesis, we compare the calculated z-value with the critical z-value at a significance level of α = 0.01.

The critical z-value for a two-tailed test at α = 0.01 is approximately ±2.576.

Since -0.612 falls within the range of -2.576 to 2.576, we fail to reject the null hypothesis.

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Is 0.25 greater or less than 0.03?

Answers

Answer:

0.25 is greater than 0.03

Step-by-step explanation:

You can solve this simply by looking for the position of the decimal point.

For example, 0.30 is greater than 0.25, but 0.03 is less than 0.25

0.25  >  0.03

Answer:

Step-by-step explanation:

se desea constrir una barda utilizando block . las dimensiones de la barda son 25 m de largo y 2 m de altura . si se requieren 12 blocks para cada metro cuadrado de barda ¿ cuantos blocks se usaran en su construcción?​



respuesta urgente !!!

Answers

Answer:

I don't understand the language

Step-by-step explanation:

am not form Paris



[tex](2 \div 2 \sqrt{2) ^{2} } [/tex]
what is the answer ​

Answers

Hopes this helps:

Answer: 2

Right triangle EFG it is known that the side opposite of acute angle F has a length of 18 inches and the leg adjacent to F has a length of 14 inches. Which of the following is closest to angle F
1. 38° 2. 65° 3. 52° 4. 72°

Answers

Answer:

3

Step-by-step explanation:

The closest angle to F in the triangle is 52 degrees.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that Right triangle EFG it is known that the side opposite of acute angle F has a length of 18 inches and the leg adjacent to F has a length of 14 inches.

We can use the tangent function to find the measure of angle F:

tan(F) = opposite/adjacent = 18/14

we can find the inverse tangent of this value:

F = tan⁻¹(18/14)

= tan⁻¹(1.28)

F= 52.15°

Hence, the closest angle to F in the triangle is 52 degrees.

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If angle A=320∘, what is the radian measure of A? Give your answer as an exact fraction in terms of π.

Answers

The radian measure of angle A is (16/9)π.

To convert degrees to radians, we use the conversion factor:

[tex]1\ degree = \pi /180\ radians[/tex]

Given that angle A is 320 degrees, we can calculate its radian measure as follows:

Angle A in radians = (320 degrees) * (π/180 radians/degree)

                    = (320π)/180 radians

                    = (16/9)π radians

Therefore, the radian measure of angle A is (16/9)π.

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6.18 heart transplant success. the stanford university heart transplant study was conducted to determine whether an experimental heart transplant program increased lifespan. each patient entering the program was officially designated a heart transplant candidate, meaning that he was gravely ill and might benefit from a new heart. patients were randomly assigned into treatment and control groups. patients in the treatment group received a transplant, and those in the control group did not. the table below displays how many patients survived and died in each group.22 control treatment alive 4 24 dead 30 45 suppose we are interested in estimating the difference in survival rate between the control and treatment groups using a confidence interval. explain why we cannot construct such an interval using the normal approximation. what might go wrong if we constructed the confidence interval despite this problem?

Answers

We cannot construct a confidence interval using the normal approximation in this case because the sample sizes of the control and treatment groups are relatively small (less than 30), and the data does not meet the assumptions required for the normal approximation.

The normal approximation assumes that the data follows a normal distribution, and for sample sizes less than 30, the distribution of the sample mean may not be well approximated by a normal distribution. In addition, the normal approximation assumes that the observations are independent, which may not hold true in this study due to the nature of the treatment and control groups.

If we constructed a confidence interval despite these problems, the interval may not accurately reflect the true difference in survival rates between the control and treatment groups. The interval could be biased or too wide/narrow, leading to incorrect conclusions about the effectiveness of the heart transplant program. Therefore, it is important to use appropriate statistical methods that account for the specific characteristics of the data and study design in order to obtain reliable estimates and valid inferences.

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Aubrey has a new art box in the shape of a rectangular prism. The box is 12\text{ cm}12 cm12, start text, space, c, m, end text by 20\text{ cm}20 cm20, start text, space, c, m, end text by 5\text{ cm}5 cm5, start text, space, c, m, end text. The only thing in the art box is a new pink eraser with the dimensions shown below.

Answers

Answer:

1196 cm3

Step-by-step explanation:

Answer:

1196

Step-by-step explanation:

Freddie is reading a book that has
440 pages. He has already read
140 pages. What decimal
describes the part of the book that
Freddie has already read?

PLEASE HELP ME

Answers

Answer:

140÷440(you can write it as a fraction)

=0.318181882

=0.32

Angle W is shown in the diagram.
w
400
What is the measure of Angle w in degrees?

Answers

Answer:

The measure of Angle w in degrees is 50°

Step-by-step explanation:

We know that in a straight line, 180°

So,

90° + 40° + w = 180°

130° + w = 180°

w = 180° - 130°

w = 50°

Thus, The measure of Angle w in degrees is 50°

-TheUnknownScientist

what weight is shown

Answers

Answer:

325 grams is the weight.

Please answer correctly! I will mark you as Brainliest

Answers

Answer:

Choice D

Step-by-step explanation:

Choice D, 3072ft^2 is the correct answer.

Here's how! The length AND width are both 24, so we know that 24 * 24 is our start. Then the height of the pyramid is 16, which now makes our equation 24 * 24 * 16. When finding the volume of a pyramid, you must divide by 3, so now the answer is (24 * 24 * 16) / 3. Making the answer 3072ft^2.

Hope this helped!

Answer:

3072

Step-by-step explanation:

volume =(1/3) hight ×width×length

v=(1/3) × 16 × 24 × 24

v=3072

Find the distance between the points (7,–9) and (–2,–4).

Answers

The answer would be √106

Which expression is equivalent to 1/4m + 3/4m- 3/8(m+1)?

Answers

Answer:

5/8m-3/8

Step-by-step explanation:

thats prolly it

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