Solve the differential equation by variation of parameters. y + 2y' + y = e^-t ln t y(t)=

Answers

Answer 1

The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.

(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.

Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.

Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian

W(t) = e-2t, to derive the specific integral related to f(t) = e-t.

Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y

Obtain yp = (1/2)(t2)e-t for the given situation.

As a result, the general integral is provided by

y = C1e-t + C2te-t + (1/2)(t2)e-t.

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Related Questions

A meteorologist set up rain gauges at various locations around a city and recorded the rainfall amounts in the table below. Use data in the table to create a line plot using 1/8 inches.

Answers

The data of the rainfall amount in inches to the locations are used to plot the attached line plot created with MS Excel.

What is a line plot?

A line plot is a graph is the graphical display of data as check marks or points above a number line.

A line plot shows the frequency of the values in the data on the number line, using dots or check marks. The frequency of the data is shown above the specified locations on the graph of a line plot.

The line plot is therefore, indicative of how frequent particular values in the dataset are.

The possible data in the question are presented as follows;

Rainfall Amount; 1/8,[tex]{}[/tex] 3/8,  3/4,  3/4,     1/4,    1 1/4, 1/8,     1/4,    1,     1/8

Location;     [tex]{}[/tex]          1,    2,     3,      4,        5,       6,     7,       8,      9,    10

The frequency of the data in a tabular form are;

Rainfall        [tex]{}[/tex]  Frequency

1/8        [tex]{}[/tex]          3 locations

3/8        [tex]{}[/tex]         1 location

3/4        [tex]{}[/tex]         2 locations

1/4       [tex]{}[/tex]           2 locations

1 1/4       [tex]{}[/tex]         1 location

1        [tex]{}[/tex]              1 location

The above frequency values can be used to create the attached line plot created with MS Excel

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What is the revolution of the Earth and Moon?

Answers

The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes time of 365.24 days, and the Moon's revolution takes 27.32 days.

The revolution of the Earth and Moon is the path of the two celestial bodies around the Sun. The Earth takes 365.24 days to complete one revolution, which is also known as one year. The Moon, on the other hand, takes 27.32 days to complete one revolution, which is also known as one lunar month.

The revolution of the Earth and Moon refers to their orbits around the Sun, with the Earth taking 365.24 days and the Moon taking 27.32 days to complete one revolution.The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes 365.24 days, and the Moon's revolution takes time of  27.32 days.

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Mav is making pizzas for a pizza party. Each pizza requires 4/5 pound of cheese. How many pounds of cheese does she need to make 5 pizzas? Express your answer in simplest form.

Answers

Answer:

4 pounds of cheese

Step-by-step explanation:

4/5*5=4

The container has 1 gallon of water. Each bottle holds 1/8 of a gallon. How many bottles of water does the container hold?

Answers

The total quantity of water that the container would have to hold is given as 8.

How to find the total quantity of water

We know that the container holds 1 gallon of water, and that each bottle holds 1/8 of a gallon. To find out how many bottles the container can hold we need to divide the container size by the size of each bottle.

We can use the following formula to find the number of bottles:

Number of bottles = Container size / Size of each bottle

We can substitute the values into the formula:

Number of bottles = 1 / (1/8) = 8

So the container can hold 8 bottles of water.

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Latifa writes down a number
She says
If i find the cube root of that number and then quadruple the answer,I get 16
What number did Latifa write down?

Answers

Answer:

64?

Step-by-step explanation:

Basically the idea is we suppose the number she thinks of is "x"

She says that if she cube roots the number and then quadruples it (means multiply by 4 I think) she gets 16. We set this up as equation below:

[tex]4\sqrt[3]{x} = 16\\\sqrt[3]{x} = 4\\x = 4^{3}\\ x= 64[/tex]

This is my best guess, not totally sure sorry

Find the volume of the sphere. Leave your answers In terms of pi

Answers

Answer:

volume of the sphere

[tex] \frac{4}{3} \times \pi \times {r}^{3} \\ \frac{4}{3} \: \times \pi \times 1000 \\ 1333.333333333\pi {in}^{3} [/tex]

answer is option C

Lynn is a zoo keeper at mattock zoo.Her hourly rate is $6.85.she earns $328.80 every week.how many hours does she works in a week?show working

Answers

Answer:

48 hours

Step-by-step explanation:

you would divide the total by the part (328.80/6.85) and that would give you her hours. hope this helps

Answer:

48 hours

Step-by-step explanation:

328.80 ÷ 6.85=48 hours in a week

The mean of 4 5 6 7 8

Answers

Answer:

6

Step-by-step explanation:

The mean of 4 5 6 7 8

there are 5 numbers in sequence, you can solve at a glance by looking at the number in the middle, or add the numbers and divide them by their number, in any case the answer will be 6

4 5 6 7 8    (6 is central)

or

(4 + 5 + 6 + 7 + 8) : 5 =

30 : 5 =

6

Type answer here.

Mollie is playing a game where she is

throwing darts at a wall filled with shapes.

Her current results are circle 7, square 4,

triangle 7, and pentagon 3. Which of the

followings statements is true?

A She is more likely to hit a square

than a triangle

B She is less likely to hit a circle than

a square.

C She is just as likely to hit a

triangle as a circle.

D She is certain to hit a circle.

6

Answers

Taking into account, the number of successful throws into different shapes, Mollie is just as likely to hit a triangle as a circle. i.e option C.

What is probability?

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

What is the significance of probability?

Probability is an important method for comprehending and making judgments regarding uncertain occurrences in many disciplines, including statistics, finance, and science. It aids in quantifying and forecasting the probability of specific events, enabling us to make better educated choices and comprehend the degree of risk involved with various activities. In summary, probability is a key idea in decision-making and risk management because it is a potent instrument for comprehending and managing uncertainty.

Since, the number of throws of darts by Mollie is same for both the circle and triangle, there is equal likelyhood to hit the triangle as a circle. Which is the required true statement.

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Lorraine prepared a 1.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.5 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars
can Lorraine fill?
A.) 03 jars
B.)O4 jars
C.)05 jars
D.)O8 jars

Answers

If 1 gallon equals 4 quarts, Lorraine fill can 4 jars. Hence option B is the correct option.

What is the unit of an object?

The user can describe locations and dimensions in a wide range of various coordinate systems using unit objects. Every drawing is done in relation to a viewport, and the units determine the coordinate system to use there. "npc" is one example of a unit (coordinate system).

Given Lorraine filled a pot with tomatoes and the volume of the pot is 1.5 gallons.

She wants to fill the tomatoes in jars. The volume of the jar is  1.5 quarts.

1 gallon is equal to 4 quarts.

1.5 gallons is equal to 1.5 × 4 quarts = 6 quarts.

The number of jars that are filled with tomatoes is 6 quarts/ 1.5 quarts = 4.

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Uri buys two burgers and a soda for $\$2.10$, and Gen buys a burger and two sodas for $\$2.40$. How many cents does a soda cost

Answers

The cost of soda as calculated from the data given is found to be as 0.9 cents.

the price of 1 burger = x

the price of 1 soda =y

Therefore, the equation for Uri and Gen becomes,

2x + y = $2.10

x+ 2y = $2.40

On solving these two equations we will get the value of x and y which represents their cost.

on multiplying equation 2 with 2 , we will get ,

2x + 4y = 4.80

Therefore , on subtracting equation 1 and 2 ,

 2x + y = $2.10

- 2x + 4y = 4.80

=> -3y = - 2.7

=> y = 0.9

Therefore x will be ,

x+ 2y = $2.40

x+ 2(0.9) = $2.40

x + 1.8 = $2.40

x = 2.40 - 1.8

  = 0.60

Therefore, cost of soda is 0.9 cents.

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I need help please and thank you

Answers

Answer:

One possible equation is  2m+16 = 40

There are other possible equations to set up as well.

That equation solves to m = 12 which means both plans cost the same when you go 12 MB over the limit (using 27 MB total).

===============================================================

Explanation:

The unlimited plan costs $40 a month no matter how much data you use.

The second plan costs $16 a month, and there are no extra fees as long as you don't go over the limit of 15 MB. If you do exceed this limit, then you're charged an extra $2 per MB. That means an extra 2m dollars is tacked onto the 16 mentioned earlier,  where m is the amount of MB you've gone over the limit. Overall, the expression 2m+16 represents the cost of the second plan. If you don't go over the limit, then you'll use m = 0 for the second plan.

Set that expression equal to 40 to set up the equation. Solving the equation leads to...

2m+16 = 40

2m = 40-16

2m = 24

m = 24/2

m = 12

If you exceed the limit by 12 MB, then both plans cost the same at $40 per month.

Note: Going 12 MB over the limit means you've used 15+12 = 27 MB.

1. Find the median of the following set of data.
55, 46, 48, 57, 46, 53, 50, 47

Answers

Answer:

51.5

Step-by-step explanation:

i think not sure if there's an odd number of numbers you get the 2 numbers add them up and divide them by 2! hope this helps! good luck.

monica says since all squares are rectangles, all rectangles are squares is she correct explain

Answers

Answer:

no, rectangles have 2 sets of parallel sides but in a square all sides are parallel

Answer:

no

Step-by-step explanation:

She is not correct because in the hierarchy squares are last. All squares are rectangles but not all rectangles are squares.  Some rectangles do not have all the properties of a square.

Find the midpoint between these points.
(1,3) (5.1)
someone please help asap !!!

Answers

Answer:SOLUTION

The midpoint for two points P=(px,py) and Q=(qx,qy) is M=(px+qx2,py+qy2).

We have that px=1, py=3, qx=5, qy=1.

Thus, M=(1+52,3+12)=(3,2).

ANSWER

M=(3,2)A

Step-by-step explanation:

Answer:

The midpoint is (3, 2)

Step-by-step explanation:

To find the x-coordinate of the midpoint, average the x-coordinates 1 and 5:

          1 + 5

xm = ----------- = 3

              2

y-coordinate:

          1 + 3

ym = ----------- = 2

              2

The midpoint is (3, 2)

One-fifth of a bread loaf was shared equally among Herb, Dara, Mark, and Lily. What fraction of the original bread loaf did each person get?

Answers

Using the provided values and information, The answer is each person would receive 1/5 of the original bread loaf.

What do you mean by proportion?

A proportion is a mathematical statement that compares two ratios. It is an equation that states that two ratios are equal, such as "a/b = c/d." Proportions are often used to solve problems involving fractions, decimals, and percentages. For example, if you know that a particular recipe calls for two cups of flour for every one cup of sugar, you can use this proportion (2/1 = x/3) to figure out how much sugar you need if you want to triple the recipe. The proportion can also be written as 2:1 = x:3.

What do you mean by ratio?

A ratio is a mathematical comparison of two or more quantities, typically represented as a fraction. It is a way to compare the size of two or more things. For example, if a recipe calls for 2 cups of flour to 1 cup of sugar, the ratio of flour to sugar is 2:1. This means that for every 2 units of flour, there is 1 unit of sugar. Ratios can also be written using the colon symbol (:) or the word "to". For example, the ratio 2:1 can also be written as 2/1 or 2 to 1. Ratios can be simplified by dividing both the numerator and denominator by a common factor and can be used to compare quantities in different units.

Each person would get 1/5 of the original bread loaf. If the bread is divided equally among four people, then each person would receive 1/4 of the total amount. Since 1/5 is the same as 4/20, and 4 people are receiving the bread, then each person would receive 1/5 of the original bread loaf.

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Math! :( no links answer correct for brainliest!

Answers

90 squareroot 2
In decimal form it’s 127.27922

PLEEEEEEEEEEEASE HELP

Answers

Answer:

x=6

Step-by-step explanation:

x+54+5x=90

6x+54=90

6x=90-54

6x=36

x=36/6

x=6

plz mark as brainiest

Sally completely solves at least 7 calculus problems per hour and at most 10 calculus problems per hour. Based on this information, what is a possible number of calculus problems that Sally can completely solve in five hours?

Answers

Sally can solve minimum of 35 calculus problem and maximum of 50 calculus problem.

What does calculus mean in plain English?

Calculus is a branch of mathematics that focuses on rates of change, to put it simply. For instance, you might want to determine how quickly a car will slow down as it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is used by who?

Calculus is useful in many different fields, including engineering, medicine, biological research, economics, architecture, space science, electronics, statistics, and pharmacology.

minimum = 35

maximum=50

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5. The base of a rectangular prism has
an area of 23 square cm. The height of
the rectangular prism is 3 cm. What is
the volume of this rectangular prism?

Answers

Answer:

1. length×width × height

4×9×10

=360cm

2.base×height

36×65

=2340 inches

Grace was born in 1995. How old will she be in 2027

Answers

Answer:

Grace will be 32 years old in 2027.

Answer: she will be 32 years old.

Step-by-step explanation:

Hannah wants to simulate whether customers will choose a small, medium, or large drink, or no drink at a fast food restaurant.

Answers

Answer:

d. Some customers had more than one drink.

Step-by-step explanation:

The exact question is as follows :

Given - Hannah wants to simulate whether customers will choose a small, medium, or large drink, or no drink at a fast food restaurant. She decides to use digits from a random  number table to represent the drink option a customer will order (0=no drink, 1=small  drink, 2=medium drink, 3=large drink, ignore digits 4-9)

To find - Why does this NOT model the  situation?

a. The choices are not equally likely to occur.

b. Some of the digits were ignored.

c. The choice are independent of each other.

d. Some customers had more than one drink.

Solution -

The correct option is - d. Some customers had more than one drink.

Reason -

If Customer order more than one drink, then also he has to order either of the digits.

So, Hannah can not be sure about the order that he wants single order or wants to repeat the order.

The sum of two consecutive even numbers is 34. What numbers is it

Answers

Answer:

16 and 18

16 + 18 = 34 .......... .....

help please u^u no links thanks

Answers

Answer:

x = 24

Step-by-step explanation:

The angles of a triangle added together equal 180⁰. Set up a simple equation to solve for x.

90⁰ + 42⁰ + (2x)⁰ = 180⁰

90 + 42 = 132

2x = 180 - 132

2x = 48

x = 24

Answer:

x = 24

Step-by-step explanation:

2x + 42 + 90 = 180

2x + 132 = 180

2x = 48

48/2 = x

x = 24

Have a nice day!

#8 Please answer the question

Answers

Answer:

22°

Step-by-step explanation:

angles in a triangle sum upto 180°

100+58+<b=180

<b=180-158

<b=22°

The answer is B......

H) find the solution of the equation

In ( x + 2 ) = 4

how?

Answers

Answer:

x = 2

Step-by-step explanation:

If you look at the equation:

(x + 2) = 4

We just need to solve for x.

To solve for x, we can subtract the total by the addend, to get the variables value.

4 - 2 = 2

Therefore, the value of x is 2.

Answer: x = e^4 - 2

Explanation:
1. Since In(x) = b is equivalent to x = e^b,
convert the given equation to exponential form. It should be x+2 = e^4.

2. To solve for x subtract by 2 on both sides which should give you x = e^4 - 2.

I need Help with this​

Answers

I believe the answer to that is <

Answer:

<

Step-by-step explanation:

Negative 1 and 3/4 is less than negative -1 and 1/4 because if you were to put the points on a number line, -1 and 1/4 is on the right of negative 1 and 3/4. And right is the positive direction on a number line.

express √832 in the form 4n where n is the integral

Answers

We can express √832 as 4(2√13).

What is definite integral?

A definite integral of a function can be represented as the signed area of the region bounded by its graph.

Given is the root of 832 or √832.

Assume that {4n} is equal to {y}. So, we can write -

y = 4n

Squaring both sides, we get -

y² = (4n)² = (√832)²

y² = 16n² = 832

16n² = 832

n² = (832/16)

n² = 52

n = √52

n = 2√13

So, we can write (√832) as 4(2√13).

Therefore, we can express √832 as 4(2√13).

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What are 3 examples of perfect squares?

Answers

Three examples of perfect squares is 1) 9, as it is equal to 3 x 3.2) 16, as it is equal to 4 x 4.3) 25, as it is equal to 5 x 5.

What is perfect squares?

Perfect squares are numbers that can be expressed as the product of two equal integers, such as 4, 9, and 16. These numbers can be written as the square of a single number, such as 2² = 4, 3² = 9, and 4² = 16. Perfect squares are also known as whole squares, and they provide an easy way to find the square root of a number.

Perfect squares are numbers that are the result of multiplying a number by itself. For instance, 4 is a perfect square because it is equal to 2 x 2.

Similarly, 9 is a perfect square because it is equal to 3 x 3. Perfect squares can be easily identified by their square root, which is the number that can be multiplied by itself to produce the perfect square.

For example, the square root of 16 is 4, since 4 x 4 = 16.

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Help asap!!!!!!!!!!!

Answers

Answer:

hi there I am Madhumita a good time to explore new ways of learning and smart ways of learning and smart ways of earning a living the good work he is there a way to get lost in the given equation of state for the diagram

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