Mathematics College

Find the general solution of
dy/dx + 2y =6​

Answers

Answer 1

Answer:

ye^(2x) - 3e^(2x) = C or (y - 3)e^(2x) = C

Step-by-step explanation:

dy/dx + 2y = 6

This is a first order linear ODE.

p(x) = 2

Integrating factor: I(x) = e^(∫ 2 dx) = e^(2x)

e^(2x)(dy/dx + 2y) = 6e^(2x)

e^(2x) dy + 2ye^(2x) dx = 6e^(2x) dx

Integrate both sides of the equation.

ye^(2x) = 3e^(2x) + C

Thus, the general solution is ye^(2x) - 3e^(2x) = C or (y - 3)e^(2x) = C.

Related Questions

Student tickets cost $6.25 each at a local movie theater. Which proportion could be used to find the number of student tickets, t, that could be purchased with a $25 gift card? need help now pls

Answers

Answer:a

Step-by-step explanation:all the other ones are not smart

if u think about it

U can’t dived t and I so just do the one that doesn’t do that

Tisha babysat for 5 hours and earned $32.50. At the same rate, how much would she earn in 8 hours?

$52.00
$14.50
$40.50
$48.50​

Answers

Answer: The answer is $48.50

Answer: The answer is $52.00.

Step-by-step explanation:

Step 1: Find the Unit Rate

$32.50 divided by 5 = $6.50

Step 2: Find the Price for Babysitting for 8 Hours

$6.50 x 8 (hours) = $52.00

I hope this helps!

Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 5 mi/h. How long (in hours) will it be before Amanda catches up to Ben?

Answers

Answer:

2 hours 15 minutes

Step-by-step explanation:

Given that :

Ben's speed = 3 mi/hr

One and half hours after Ben leaves = 1.5 hours

Ben's distance = 3 mi/hr * 1.5 = 4.5 miles

Amanda's speed = 5 mi/hr

Time taken before Amanda catches up:

Let time taken = x

Distance = speed * time

Ben's distance = Amanda's distance

4.5 mi + (3 * x) = 5 * x

4.5 + 3x = 5x

4.5 = 5x - 3x

4.5 = 2x

x = 4.5 / 2

x = 2.25 hours

Time taken = 2.25 * 60 = 135 minutes = 2 hours 15 minutes

It would take Amanda 2.25 hours to catch up with Ben

Speed is the ratio of distance to time. It is given by:

Speed = distance/time

Given that Ben covers a distance d at time t, hence:

3 = d/t

d = 3t

Since Amanda leaves One and a half hours (1.5) after Ben leaves, hence Time = t - 1.5

5 = d/(t - 1.5)

d = 5t - 7.5

Since they catch up, hence:

3t = 5t - 7.5

2t = 7.5

t = 3.75 hours

Time for Amanda = t - 1.5 = 3.75 - 1.5 = 2.25 hours

Hence it would take Amanda 2.25 hours to catch up with Ben.

Find out more at: https://brainly.com/question/22610586

A cylinder is 12 feet high and has a diameter of 10 feet. in cubic feet, what is the approximate volume of the cylinder

Answers

Answer:

300π or 942.477796077 cubic feet

Step-by-step explanation:

25π*12=300π

The approximate volume of the given cylinder is 942.48 ft³.

What is the volume of the cylinder?

The volume of the cylinder is the density which signifies the amount of substance it can hold.

Mathematically,

                        V = πr²h

where, r is the radius of the cylinder

and h is the height of the cylinder.

It is given that,

Height h of the cylinder = 12 ft

Diameter d of the cylinder = 10 ft

⇒ Radius r = d/2

⇒ r = 10/2

⇒ r = 5 ft

Now, Volume of the cylinder V = πr²h

Putting the values of r and h of given cylinder. We get,

⇒ V = 3.14 × (5 ft)² × 12ft

⇒ V = 3.14 × 25 ft² × 12 ft

⇒ V = 3.14 × 300 ft³

⇒ V ≈ 942.48 ft³

The approximate volume of the given cylinder is 942.48 ft³.

More about volume of cylinder :

https://brainly.com/question/49664655

#SPJ2

A +40 =0. What is the value of A?

Answers

Answer:

-40

Step-by-step explanation:

Answer:

hope you for the answer

Step-by-step explanation:

A+40=0

A=0-40

A=-40#

The length of a rectangle is 2x + 3. The width of the rectangle is x - 2. Which of the following represents the perimeter of the rectangle?

Answers

Answer:

6x+2

Step-by-step explanation:

The perimeter is the sum of all of the sides. A rectangle has four sides. You multiply each equation by two, and add the two equations together.

To get the perimeter, you have to add all sides. So you’ll have 2x+3+2x+3+x-2+x-2. So assuming I have done the math correctly, the answer should be 6x+2.

Jonathan put ice cream in the freezer, and the ice cream remained frozen.

Which of the following best describes this situation?

Based on the data, this is an example of correlation and causation.
Based on the data, this is an example of correlation.
Based on the data, this is an example of causation.
Based on the data, this is not an example of causation or correlation.

Answers

Answer:

C- Based on the data, this is an example of causation

Step-by-step explanation:

This is because by him putting the ice cream into a freezing area, the ice cream remained frozen. Imagine if he put in in a warm area, it would melt. Hope this helps!

The option best describes this situation is C; Based on this data, this is an example of causation.

What is correlation?

Correlation of two pairs of data values tells about the degree of movement that can occur in one of the data values when other data value is increased or decreased respectively.

Also, Causation refers to causing something. When one variable influences another variable.

The ice cream remained frozen caused by the fact that it was put in the freezer by Jonathan.

We can also say that, ice cream remained frozen is the result of the occurrence of the event that it was put in the freezer.

So, The option best describes this situation is C; Based on this data, this is an example of causation.

Learn more about causation here;

https://brainly.com/question/14063719

#SPJ2

Other Questions
Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australia. While booking her family's plane tickets, she notices on the itinerary that the airline is offering a sixteen hour straight flight from Los Angeles to Melbourne on a Boeing 747-8 Intercontinental Jet. In an effort to learn more about the capabilities of the Jet, Sheleah does a little research and stumbles upon the following graph and facts about the Jet's gasoline consumption.GRAPH IN SCREENSHOTThe Boeing 747-8 Intercontinental Jet can carry approximately 422,000 gallons of gasoline, making it possible for the jet to travel 14,430 kilometers before needing to refuel.Using the graph, approximate the Jet's average gas consumption, in gallons per hour, during the sixteen hour flight from Los Angeles, California to Melbourne, Australia. In your final answer, include all of your calculations. An object travels at 3.06 m distance with uniform acceleration in this interval it's velocity increases by 0.18 and it's average velocity over the interval was 0.34 m/s what is the acceleration? Your middle school has 900 students. 1/3 of students bring their lunch instead of buying lunch at school. How many students do and do not bring their lunch? I will give brainliest to whoever answers correctly and is first Help ASAP pls im being timed pls help (-2, 4) and (3, -1)Write equation in slope intercept form Redigez la quatrime etape de l'introduction,qui correspond a l'annonce du plan : 1:un personnage ambigu,qui suscite a la fois terreur et piti .2:une hrone tragique qui retrouve symboliquement une forme de libert How does the author of Passage 2 BEST conveythe point of view that personality development isextremely complex?by comparing personality to a spider webby describing a system to improve gradesby discussing the notion of placing people intopackagesby comparing personality to a field of flowers Find the slope of the line through the pair of points.C(3, 4), D(2, 2) Subtract -7x + 6 from -2x^2 + 9x - 2 State the equation of the straight line with:a - a gradient of 4 passing through the y-axis at (0,7)b - a gradient of 5 passing through the y-axis at (0,1)c - a gradient of 6 passing through the y-axis at (0,2)d - a gradient of 9 passing through the y-axis at (0,13). Jonathan put ice cream in the freezer, and the ice cream remained frozen.Which of the following best describes this situation? Based on the data, this is an example of correlation and causation. Based on the data, this is an example of correlation. Based on the data, this is an example of causation. Based on the data, this is not an example of causation or correlation. In which situation would it be more appropriate to use formal language The amount of kinetic energy an object has depends on which feature of the object?O its motionO its positionits gravityO its height The possible choices are ; production cost report, total manufacturing cost per unit, equivalent units of production, units transfered out, unit production costs, cost reconciliation schedule, total units accounted for, and physical units.Match the following statements to the appropriate terms. A summary of both production quantity and cost data for a production department. Shows that the total costs accounted for equal the total costs to be accounted for. Work done during a period expressed in fully completed units. Costs expressed in terms of equivalent units of production. Actual units to be accounted for during a period, irrespective of any work performed. Units transferred out during the period plus units in ending work in process. Unit materials costs plus unit conversion costs. Total units accounted for minus units in ending work in process. Why did scientists have to come up with a way of measuring distance in space? A cylinder is 12 feet high and has a diameter of 10 feet. in cubic feet, what is the approximate volume of the cylinder Using the sentence above for context, define the word integral in your own words How was the government of Sparta similar to the government of Athens? How was it different? What did Shi Huangdi do to ensure that no one knew the location of his tomb?