Find the solution of the given initial value problem y'+2/ty=cost/t^2

Answers

Answer 1
[tex]y'+\dfrac2ty=\dfrac{\cos t}{t^2}[/tex]
[tex]t^2y'+2ty=\cos t[/tex]
[tex](t^2y)'=\cos t[/tex]
[tex]t^2y=\sin t+C[/tex]
[tex]y=\dfrac{\sin t+C}{t^2}[/tex]

Related Questions

What number is the solution of the inequality of 10.6 < b

Answers

it can be any number as long as it is greater than 10.6
Any number less than 10.6 is a solution. example: 8, 4, -1000, ...

Karen is riding her bike at 4 miles per hour she wants to show this on a graph what should she draw

Answers

Graph needs to be labeled. I labeled it as shown on picture. It also needs a title. The title can be up to you. :) you can title it “Karen riding her bike”

What are fissures and how are theu created by land subsidence?

Answers

as the land above subsides due to gaps in the soil underneath due to tectonic activity, the area above that sinks to a lower level, requires soil to cover that horizontal hole.

as soil is pulled in to this location, it has to come from somewhere and it comes from the nearby land mass, whilst covering that sink-hole made by this one gap underneath, the land mass splits on other parts where the extra soil came from, causing the fissure.

so the fissure is made from the extra soil used to cover the sink-hole, whilst covering the sink-hole made by the underneath gap, making another gap on the surface above, and that is what the fissure ends up as.

in a sense, the gap underneath kinda tranferred to above at the surface.

20 randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions - all on the same material. the professor was interested in determining which type of questions the students scored higher. this experiment is an example of a one sample test of means. a two sample test of means. a paired t-test. a test of proportions.

Answers

I think that this an example of a paired t test. Since each student (subject) is given 2 treatments of the same material. 

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

Answers

(-2,6) this is the coordinates of the vertex

Answer:

The coordinates of the vertex are [tex] (-2, -6)[/tex]

Step-by-step explanation:

The graph of this function is a parabola that opens up in the Cartesian plane. We can find like this:

[tex]y = (x ^ 2 + 4x +4) +6 = (x + 2) ^ 2 +6[/tex], where,  [tex](y - 6) = (x + 2) ^ 2[/tex]

In the canonical equation of the parabola:

[tex](y - k) = (x + h) ^ 2[/tex], with the point (h, k) as the vertex, [tex]h = -2[/tex] and [tex]k = 6[/tex].

Conclusion: the coordinates of the vertex are [tex](-2, -6)[/tex]

The manager of a plant nursery bought 120 lb of soil to use for potting plants. The manager can put 5 lb into each of the small pots and 12 lb into each of the large pots. The manager made a sketch to show the line representing the different combinations of pots that can be used. The x-axis represented the number of small pots and the y-axis represented the number of large pots. The manager labeled only the intercepts.

Which points did the manager label?



(0, 12) and (5, 0)
(0, 10) and (24, 0)
(0, 24) and (10, 0)

(0, 5) and (12, 0)

Answers

Set up the equation. The equation is: 5x + 12y = 120. Solve for both variables (x and y). The answer will give you the intercepts.

(0,10) and (24,0) is the final answer.
Yeah the answer is C.

a garden table and a bench cost $1,000 combined the cost of a garden table is three times the cost of the bench what is the cost of the bench.

Answers

it shold be something like 834 or something liek that

The average person lives for about 78 years. Does the average person live for at least 1,000,000 minutes? (Hint: There are 365 days in each year, 24 hours in each day, and 60 minutes in each hour.)

Answers

Okay. so, there are 1,440 minutes in one day. 1,440 * 365 is 525,600. There are 525,600 minutes in one year. 525,600 * 78 is 40,996,800. The average person lives 40,996,800, which is without a doubt way over 1 million minutes, so yes. The average person lives over 1 million minutes. Living 1 million minutes or less would mean that you would live less than 2 years. That's just barely starting to enter the toddler years.

Answer:

cool kkdkdkkdkkfkkfkfkd

In 34 pound of a spice mix, there is 5/6 cup of cinnamon. How much cinnamon does the spice mix contain per pound? a 5/8 cup b ​ 9/10 ​ cup c ​ 1 1/9 ​ cups d ​ 1 3/5 ​ cups

Answers

Answer:

c. 1 1/9 cups

Step-by-step explanation:

To find cups per pound, divide cups by pounds.

  (5/6 cup)/(3/4 pound) = (5/6)/(3/4) cup/pound

  = (5/6)×(4/3) cup/pound . . . . . . . invert the denominator and multiply

  = 20/18 cup/pound = 10/9 cup/pound = 1 1/9 cup/pound

Solving Equations with Variables on Both Sides

1. (g+4) - 3g = 1 + g

g = 1
g = 4
no solution
identity

2. -6a + 3 = -3(2a - 1)

a=5
a=10
no solution
identity

3. 0.5b + 4 = 2(b+2)

b=0
b=0.5
no solution
identity

4. 8 -(3 + b) = b - 9

7
8
no solution
identity

Answers

1)
g+4-3g=1+g
subtracting g from both sides
4-3g=1
subtracting 4 from both sides
-3g=-3
g=1
2)
-6a+3=-3(2a-1)
extending the right side
-6a+3=-6a+3
adding 6a to both sides
3=3
which is an identity
3)
0.5b+4=2(b+2)
extending the right side
0.5b+4=2b+4
subtracting 0.5 b from both sides
4=1.5b+4
subtracting 4 from both sides
0=1.5b
b=0
4)
8-(3+b)=b-9
subtracting 8 from both sides
-(3+b)=b-17
extending the left side
-3-b=b-17
adding b to both sides
-3=2b-17
adding 17 to both sides
14=2b
b=7

A TV has a listed price of $607.95 before tax. If the sales tax rate is 8.75% , find the total cost of the TV with sales tax included.

Answers

Answer:

  $661.15

Step-by-step explanation:

The addition of tax causes the price to be multiplied by (1+0.0875), so the final price is ...

  $607.95×1.0875 ≈ $661.15

3x-2=x
show work and check

Answers

Solving for the variable x boils down to isolating it, so we need to collect all of our x's on one side of the equation and "undo" any operations being performed on it.

First, we'll move the 2 over to the right side ("undoing" the subtraction on the left side by adding 2 to both sides):

(3x-2)+2=x+2
3x=x+2

Next, we'll subtract x from both sides to collect all of the terms on the left side of the equation:

3x-x=(x+2)-x
2x=2

Finally, "undo" the multiplication being performed on x by dividing both sides of the equation by 2:

(2x)/2=2/2
(2/2)x=2/2

2/2 is, of course, another form of 1, so simplifying, we get:

x=1

Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes y= 1/2 x− 3/2

Answers

The x-intercept would be, (3,0). And the y-intercept would be, (0,-3/2).


 

When converted to speeds, which list is in order from slowest to fastest?
17 miles in 2 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes;
60 miles in 8 minutes
17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
33 miles in 6 minutes;
26 miles in 4 minutes;
60 miles in 8 minutes;
17 miles in 2 minutes
60 miles in 8 minutes;
33 miles in 6 minutes;
26 miles in 4 minutes;
17 miles in 2 minutes

Answers

speed = distance / time

17 miles in 2 minutes ....17/2 = 8.5 miles per minute
26 miles in 4 minutes.....26/4 = 6.5 miles per minute
33 miles in 6 minutes.....33/6 = 5.5 miles per minute
60 miles in 8 minutes.....60/8 = 7.5 miles per minute

slowest to fastest : 
(1) 33 miles in 6 minutes
(2) 26 miles in 4 minutes
(3) 60 miles in 8 minutes
(4) 17 miles in 2 minutes
I believe that is answer C

Answer:

When converted to speeds, the list which is in order from  slowest to fastest is:

  1)      33 miles in 6 minutes

  2)      26 miles in 4 minutes

  3)      60 miles in 8 minutes

  4)       17 miles in 2 minutes

Step-by-step explanation:

We know that speed is defined as the ratio of distance and time.

Here we are given distance and time in each of the options and we will check the speed of each and arrange them in increasing order.

1)

33 miles in 6 minutes

The speed is:

[tex]\dfrac{33\ \text{miles}}{6\ \text{minutes}}=5.5\ \text{miles\ per\ minute}[/tex]

2)

26 miles in 4 minutes

The speed is:

[tex]\dfrac{26\ \text{miles}}{4\ \text{minutes}}=6.5\ \text{miles\ per\ minute}[/tex]

3)

60 miles in 8 minutes

The speed is:

[tex]\dfrac{60\ \text{miles}}{8\ \text{minutes}}=7.5\ \text{miles\ per\ minute}[/tex]

4)

17 miles in 2 minutes

The speed is:

[tex]\dfrac{17\ \text{miles}}{2\ \text{minutes}}=8.5\ \text{miles\ per\ minute}[/tex]

Since,

[tex]5.5\ \text{miles\ per\ minute}<6.5\ \text{miles\ per\ minute}<7.5\ \text{miles\ per\ minute}<8.5\ \text{miles\ per\ minute}[/tex]

Hence, the increasing order of speed is:

           1→2→3→4

How much does mike earn at fresh foods if he works 20 hours ? 40 hourss ? 60 hours ? when mike gets paid 10 per hour

Answers

Hey there,
1 hour = $20
20 hours = $ 20 x 20
               = $400
40 hours = $20 x 40
               = $800
60 hours = $20 x 60
               = $1,200

Hope this helps :))

~Top

at a school pep rally, the ratio of students who wore red to those who wore yellow is 7 to 3. There are 300 students at the pep rally, and each student wore either red or yellow. How many more students wore red?

Answers

300 total, divided by 10 is 30. 30 x each part of ratio gives:
30 x 7 = 210 - red
30 x 3 = 90 - yellow
210 - 90 = 120 more students
120 more students


I hope this helps and have a wonderful day filled with joy!!

3.1666666667 as a fraction

Answers

31666666667/10000000000
Recognize that 0.16666666..... is equivalent to 1/6.  Try dividing 6 into 1 on your calculator and see what y ou get.

Then 3.166666666666 ...  = 3 1/6   =>  19/6 (as a fraction).

−2 is less than or equal to w , and 8 is greater than or equal to w Use w only once in your inequality.

Answers

Attached the solution.

a recipe makes a total of 5 cups a serving of pudding is 3/4 cup how many servings of pudding does the recipe make?

Answers

Final answer:

To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. The recipe makes approximately 6.67 servings of pudding.

Explanation:

To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. In this case, the recipe makes 5 cups and each serving is 3/4 cup. So, to find the number of servings, divide 5 cups by 3/4 cup: 5 cups ÷ (3/4 cup) = 5 cups × (4/3 cup) = 20/3 servings

Therefore, the recipe makes approximately 6.67 servings of pudding.

Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable

Answers

multiply 365 by 8

365 * 8 = 2920

so yes it is reasonable

2,920”divided”by 8 = 365so yes

The photography club has 28 members .there are 12 boys in the club . What is the ratio of boys to girls in simplest form?

Answers

First, find the # of girls.  28 total members, less 12 boys, leaves 16 girls.
Write the ratio boys/girls as 12/16.  Reduce this to 3/4.

A person standing 20 feet from a street light casts a 10 foot shadow. How many times taller is the streetlight than the person? Assume the triangles are similar.

Answers

check the picture below.

they're at a 3:1 ratio, thus, 3 times.

circle P had a circumference of approximately 75 inches. what is the approximate of the radius ,r? use 3.14 for

Answers

circumference=2πr=75
2×3.14×r=75
6.28 r=75
r=75/6.28=11.943=12 inch (nearly)

Answer:

1)  12in

Step-by-step explanation:

The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.

Will Reward Brainliest!

Answers

Hey there!

So, I solved it for you but I couldn't type it here because they don't have everything I need :) . Please see the pictures below  for the answer.

Best of luck!

If you need help in the future, just send me a message then I'll help you out :)

Garebear~


Jane can pack 48 shirts into each box. round to the nearest compatible numbers to estimate how many boxes she will need to box 1,453 shirts

Answers

1400 would be the answer i belive 

Answer: There are 30 boxes for 1453 shirts.

Step-by-step explanation:

Since we have given that

Number of shirts = 48

Number of box for 48 shirts = 1

We need to adjust number of boxes she will need to box 1453 shirts.

So, number of boxes would be

[tex]\dfrac{1453}{48}\\\\=30.27\\\\\approx 30[/tex]

Hence, there are 30 boxes for 1453 shirts.

One of the angles formed by two intersecting lines is 42°. What is the measure of the other three angles?

Answers

okay, so first lets think about the angle next to the 42 degree angle.
we know that those two angles must add to 180 degrees, so lets form an equation to figure out the other angle
42 + x = 180
subtract 42 from both sides
x = 138
so 138 degrees is the first AND the 3rd angle
the opposite angle from the 42 degree angle also happens to be 42 degrees

this is because there are two lines in total right?? if you draw out the 42 degree angle and the 138 degree angle, flip that upside down, the angles are the same!!

i hope this helps!! 

Answer:

42, 138, 138

Step-by-step explanation:

A pond at a hotel 4,290 gallons of water. The groundskeeper drains the pond at a rate of 78 gallons of water per hour. How long will it take to drain the pond?

Answers

divide total gallons by rate:

4290 / 78 = 55 hours

For a circle of radius 3 feet, find the arc lengths subtended by a central angle of 57 degrees.

Answers

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=3\\ \theta = 57 \end{cases}\implies s=\cfrac{57\cdot \pi \cdot 3}{180}[/tex]

Answer: The length of an arc is 2.98 feet.

Step-by-step explanation:

Since we have given that

Radius of a circle = 3 feet

Angle subtended at the centre = 57°

We need to find the length of an arc:

As we know the formula for "Length of an arc":

[tex]Length=\dfrac{\theta}{360^\circ}\times 2\pi r\\\\Length=\dfrac{57}{360}\times 2\times \dfrac{22}{7}\times 3\\\\Length=2.98\ feet[/tex]

Hence, the length of an arc is 2.98 feet.

Let c be parametrized by x = et sin (10t) and y = et cos (10t) for 0 ≤ t ≤ 2. find the length l of
c. l = 2 correct: your answer is correct.

Answers

Final answer:

To find the length of the curve c parameterized by given equations, we differentiate these equations with respect to t, find the magnitude of the derivative vector, and integrate this magnitude from t = 0 to t = 2.

Explanation:Finding the Length of Parametrized Curve

To find the length L of a curve c parametrized by x = et sin(10t) and y = et cos(10t) for 0 ≤ t ≤ 2, we use the formula for the arc length of a curve given in parametric form. The formula is L = ∫ |c'(t)| dt, where |c'(t)| represents the magnitude of the derivative of the parametric equations. The integral is evaluated over the given interval of t.

Step-by-step Explanation

First, compute the derivatives of the parametric equations: dx/dt and dy/dt.Next, find the magnitude of the velocity vector |c'(t)| = sqrt((dx/dt)^2 + (dy/dt)^2).Finally, integrate |c'(t)| from t = 0 to t = 2.

Using this approach, we find that the length L of the curve c over the interval from 0 to 2 is indeed 2, as verified by the calculus of parametric functions.

Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:20 to 1:55? (Hint: Find the number of degrees per minute first.)

Answers

There are 12 five minutes in one hour and 1 hour correspond to 360°, then each 5 minutes represents 360/12 = 30°

From 1:20 to 1: 55 we have 35 minutes or 7 x 5 minutes or

7 x 30° = 210° 

To convert degree into radian, we apply the following formula:

degree/180° = radian/π

210/180 = r/π or (cross multiplication) →Radian = (π x 210/180

→ Radian = 7π/6 (simplify by 30)

Answer:

Part 1:

In order to find how many radians the minute hand moves from 1:20 to 1:55, we need to remember that there are 60 minutes in an hour (clock) and there are 360 degrees in the clock since the clock is a circle. After dividing 360 by 60, we find that each minute is equal to 6 degrees. After that, we can subtract the times, which tells us that there are 35 minutes between 1:20 and 1:55. Using this we can just multiply this out, to get 35 times 6, which is equal to 210 degrees. We can get our final answer by converting this into degrees. Since one 1 degree is about 0.0174, we can set up a proportion. After solving, we will get that the minutes hand moves 3.555 radians in total.

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In the story Little Women, one family brings breakfast to a cold and hungry family on Christmas morning. Read this passage and then answer the question that follows: My girls, will you give them your breakfast as a Christmas present?" They were all unusually hungry, having waited nearly an hour, and for a minute no one spoke, only a minute, for Jo exclaimed impetuously, "I'm so glad you came before we began!" "May I go and help carry the things to the poor little children?" asked Beth eagerly. "I shall take the cream and the muffins," added Amy, heroically giving up the article she most liked. Meg was already covering the buckwheats, and piling the bread into one big plate. "I thought you'd do it," said Mrs. March, smiling as if satisfied. What can you infer about Mrs. March from this text? The Lovin' Lemon Company sells a 4-gallon jug of lemonade for $24. The Sweet and Sour company sells an eight-pack of one quart bottles of lemonade for $16. Which company has a higher price? Explain your answer. A relation is a function if _____.there is exactly one input for each outputthere is exactly one output for each inputthere is more than one input for each outputthere is more than one output for each input In milgram's experiment, _____ of the students administering the shocks turned the lever all the way to "danger: severe shock." none some most all Parrino corporation has announced that its net income for the year ended june 30, 2008, is $1,824,214. the company had an ebitda of $5,174,366, and its depreciation and amortization expense was equal to $1,241,790. the company's average tax rate is 34 percent. what is the amount of interest expense for the firm? Congratulating yourself and feeling a sense of satisfaction relates to which step in p.o.w.e.r. learning? organize evaluate work rethink Lowering the top note in a major interval by one half-step creates which of the following?A.a major intervalB.a minor intervalC.a tonic toteD.an octave leapTHIS IS MUSIC BTW HELP asap Compounds may be represented by chemical formulas. In the chemical formula for water which is H20, the 2 which represents the number of hydrogen atoms is called_______? A) the reactant. B) the subscript. C) the coefficient. D) the atom factor. it takes sami 10 minute to shovel the snow 20 m2 area. he charges 5 dollars for half an hour . how much will he charge to shovel the snow of a sidewalk that has a dimensions of 2m x 40m. Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After reading for 4 hours, he had 330 pages left to read. how long is the book? Fermentation reactions generally occur under conditions of: give the number of protons, electrons, and neutrons in the following atoms a. 90Zr b. 202Hg c. 58Ni d.222Rn The u.s. supreme court is composed of ____ members that are ________?a. 7; appointed for 8 year termsb. 9; appointed for lifetime termsc. 9; elected by the voters during the presidential electiond. 10; recommended by congress Someone please help me Find the value of x .A) 80 B) 100C) 130 D)120 Plzzzzzzzzzz help me What is the literary term for a brief story added to an autobiography to offer a glimpse into the authors life You need to create the directory /var/oracle/database/9i. only the directory /var currently exists. from the root of the filesystem, which command will create the directory path ____ as 9 hundreds is 9 thousands Improving your ove physical health should focus on what 3 areas? Greg is opening a car wash. He estimates his cost equation as C = 9000 + 0.09x and his revenue equation as R = 1.85x, where x is the number of cars washed in a six-month period. Find the number of cars that must be washed in a six-month period for Greg to make a profit. Steam Workshop Downloader