Work the previous problem for the line integral f (x2+y2)dx + 3xy2 dy.

Answers

Answer 1

Feel free to consult the details in my answer to 24438105 if you wish to compute the line integral directly. I don't see any specification of which method to use, so I'll do it the faster way.

By Green's theorem,

[tex]\displaystyle \int_C (x^2+y^2)\,\mathrm dx + 3xy^2\,\mathrm dy = \iint_D \frac{\partial(3xy^2)}{\partial x} - \frac{\partial(x^2+y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \iint_D (3y^2-2y)\,\mathrm dx\,\mathrm dy[/tex]

Since D is a disk with radius 2 centered at the origin, consider converting to polar coordinates using x = r cos(t ) and y = r sin(t ). Then

[tex]D = \left\{(r,\theta) \mid 0\le r\le 2\text{ and }0\le t\le2\pi\right\}[/tex]

[tex]x^2+y^2 = r^2[/tex]

[tex]\mathrm dx\,\mathrm dy = r\,\mathrm dr\,\mathrm dt[/tex]

[tex]\implies \displaystyle \iint_D (3y^2-2y) \,\mathrm dx\,\mathrm dy = \int_0^{2\pi}\int_0^2 (3r^2\sin^2(t)-2r\sin(t))r\,\mathrm dr\,\mathrm dt \\\\ = \int_0^{2\pi} \int_0^2 (3r^3\sin^2(t)-2r^2\sin(t))\,\mathrm dr\,\mathrm dt \\\\ = \int_0^{2\pi} \left(12\sin^2(t)-\frac{16}3\sin(t)\right)\,\mathrm dt = \boxed{12\pi}[/tex]


Related Questions

B Urine
C Brass
D Sand
8. Separation of mixtures of solids with various sizes
include
A magnetic separation.
B coarsing
sublimation.
Air

Answers

Answer:

B

Explanation:

Calculate the engineering stress in SI units on a bar 25 cm long and having a cross section of 9.00 mm × 4.00 mm that is subjected to a load of 3500 kg.

Answers

Answer:

7500kg/mm

Explanation:

What are the factors that influence the power input to the compressor?

a) The mass flow of air

b) The pressure ratio of the compressor

c) The inlet temperature

d) Temperature difference between the inlet and outlet

e) The properties of the working medium

Answers

Answer:

option e is correct answer

the impact of engineering to socio economic development of the country​

Answers

Engineers help to develop the physical infrastructure we all rely on – transport networks, roads, bridges, water and energy supplies, and waste management. We also have them to thank for our digital infrastructure – communications and navigation networks that are part and parcel of urban life. Engineers play a huge role in healthcare and food, and in manufacturing and research.

And by building this infrastructure, engineering has had a much wider and more lasting impact – it has helped to fuel economic growth. Well-built housing and sanitation improves the quality of life of all residents. Good transport links make it easier for businesses to trade their goods, and enables the workforce to be more mobile. High-speed internet can boost productivity, improve efficiencies, and help an organization to look beyond its local or national borders… the list is endless.

a steel container expands in volume 1% when the pressure within it is increased by 70mpa at standard presssure​

Answers

Answer:

mooji udaanaamii!!!

Explanation:

Which of the following is the best analogy for the relationship between an equipment operator and the signal person?
The signal person is like the eyes and the equipment operator is like the hands.
The signal person is like the heart and the equipment operator is like the brain.
The signal person is like the arms and the equipment operator is like the legs.
The signal person is like the head and the equipment operator is like the tail.

Answers

Answer:

The signal person is like the eyes and the equipment operator is like the hands.

Explanation:

1. __________ is an example of an electrical device.

Answers

Answer:

1. Battery

2. Light bulb

3. Toaster

Explanation:

An electrical device is a device that produces or is powered by electricity.

Answer:

All of the above

Explanation:

Which of the following defines context?


the ability to find new ways of thinking about a problem

the condition in which a problem exists

the study of the theoretical nature of an event

the problem-solving technique of an engineer

Answers

Answer:

The condition in which a problem exists

Explanation:

Context is the situation surrounding information, e.g. if you don't understand a word in a passge you can look for "context clues" where you use surrounding words to infer the meaning of the unknown one

Radio capacity may be increased in cellular concept by​

Answers

Answer:

Answer is "Increasing the number of base stations & reusing the channels"

Explanation:

Answer:

radio capacity may be increased in cellular concept by increasing the number of base stations and reusing the channels.

Need help coding this i’m using python.

Answers

Answer:

ill help'

Explanation:

Which of the following policy actions could the federal reserve use to combat inflation

Answers

[tex] \huge{ \underbrace{ \overbrace{OPTIONS}}}[/tex]

[tex] \huge{ \underbrace{ \overbrace{PlEASE}}}[/tex]

1. An ideal gas undergoes a process according to PV" = k. Initially, the temperature and volume are 2 bar and 0.1m?, respectively. After the process, the volume doubles. Determine the work done during the process. Take n = 1.4 ​

Answers

Tryna boost my score for college stuff could you give me the brainiest and a thanks? Hope you find your answer your looking for!

Cho động cơ có Z=24 rãnh, 2p=4 cực. Vẽ sơ đồ khai triển dây quấn động cơ kiểu đồng tâm hai mặt phẳng, q tập trung, đầu vào các pha liên tiếp lệch 1200 điện.

Answers

Answer:

can u write it in English

Explanation:

can't understand it

what is geometrical shape? list them and describe any two of them with sketch

Answers

Explanation:

Geometric Shapes can be defined as figure or area closed by a boundary which is created by combining the specific amount of curves, points, and lines.

In a pipe of diameter 350mm and length 75mm, water is flowing at a velocity of 2.8m/s. If the Kinematic viscosity of water is 0.012 Stokes, calculate the Reynolds number,Evaluate the coefficient of friction​

Answers

Explanation:

the answer is in picture

Tech A says that open loop is when the PCM pretty much ignores the oxygen sensor signals. Tech B says that closed loop is when the PCM shuts off the fuel injectors during a collision. Who is correct

Answers

Answer:

Tech A

Explanation:

A double-threaded Acme stub screw of known major diameter is used in ajack having a plain thrust collar of known mean diameter. Coefficients of running friction are estimated as 0.10 for the collar and 0.11 for the screw. Assume (1) the starting friction is about 1/3 higher than running friction and (2) the screw is not exposed to vibration.

Required:
a. Determine the pitch, lead, thread depth, mean pitch diameter, and helix angle of the screw.
b. Estimate the starting torque for raising and for lowering a 5000 lb load.
c. If the screw is lifting a 5000 lb load at the rate of 4 ft/min, what is the screw rpm? What is the efficiency of the jack under this steady-state condition?
d. Would the screw overhaul if a ball thrust bearing (of negligible friction) were used in place of the plain thrust collar.

Answers

Answer:

I'm pretty sure it's c but i may be wrong

tìm phản lực gối tựa

Answers

Answer:

jwjehevrvbdbejd HB dbnwjsishrb t bxjwbkozkwnwn shxvbebhgvevhehjhr. jebn

Match the term to the best description scientific method

Answers

Answer:

a method of research in which a problem is identified, relevant data are gathered, a hypothesis is formulated from these data, and the hypothesis is empirically tested.

The electrical contractor association is typical example of a

Answers

Answer:

Trade association.

Explanation:

I'm thinking it is as it represents contractors who design, install, inspect and maintain amongst other activities electrical and electronic equipments or service.

Two question here please answer it correctly
40. Evaluate f (x2-2xy)dx +(x2y+3)dy around the boundary of the region defined by y2 = 8x and x = 2
(a) directly, (b) by using Green's theorem. Ans. 128/5
(TT.2)
41. Evaluate f (6xy - y2) dx + (3x2 --- 2xy) dy along the cycloid x = 6 - sin 6, y = 1 - cos 6.

Answers

(40) It looks like the line integral is

[tex]\displaystyle \int_C (x^2-2xy)\,\mathrm dx + (x^2y+3)\,\mathrm dy[/tex]

where C is the boundary of the region D,

[tex]D = \left\{(x,y) \mid \dfrac{y^2}8\le x\le2\text{ and }-4\le y\le4\right\}[/tex]

(a) To evaluate the line integral directly, split up C into two paths C₁ and C₂, parameterized by

C₁ : x = t ²/8 and y = -t, where -4 ≤ t ≤ 4

(the y component is negative to make this path have a positive/counterclockwise orientation)

• C₂ : x = 2 and y = t, where -4 ≤ t ≤ 4

Then the line integral over C is the sum of the line integrals over C₁ and C₂ :

[tex]\displaystyle \int_C = \int_C \left(\left(x(t)^2-2x(t)y(t)\right)\dfrac{\mathrm dx}{\mathrm dt} + \left(x(t)^2y(t)-3\right)\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt \\\\ = \int_{-4}^4 \left(\left(\frac{t^3}4+\frac{t^4}{64}\right)\frac t4 - \left(3-\frac{t^5}{64}\right)\right)\,\mathrm dt + \int_{-4}^4 (4t+3)\,\mathrm dt \\\\ = \int_{-4}^4 \left(4t+\dfrac{t^4}{16}+\dfrac{5t^5}{256}\right)\,\mathrm dt = \boxed{\frac{128}5}[/tex]

(b) Using Green's theorem, we have

[tex]\displaystyle \int_C (x^2-2xy)\,\mathrm dx + (x^2+3)\,\mathrm dy = \iint_D \frac{\partial(x^2y+3)}{\partial x} - \frac{\partial(x^2-2xy)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_{-4}^4 \int_{y^2/8}^2 (2xy+2x)\,\mathrm dx\,\mathrm dy = \boxed{\frac{128}5}[/tex]

# # #

(41) I assume you meant to use θ in the parameterization, and not 6, so that C is parameterized by x = θ - sin(θ) and y = 1 - cos(θ). There's no range given for θ, so I'll just assume 0 ≤ θ ≤ π.

Then ... (for some reason, the math text won't render properly. I've attached the computation as an image)

(where s = sin(θ) and c = cos(θ))

How does Brake system work

Answers

Answer:

To stop a car, the brakes have to get rid of that kinetic energy. They do so by using the force of friction to convert that kinetic energy into heat. This hydraulic system multiplies the force of your foot on the brake pedal into enough force to apply the brakes and make the car stop.

A chemical rocket is used for launch into earth orbit. The combustion stagnation temperature is 3000K. The molecular weight of the combustion products is 26. The gases expand isentropically as an ideal gas mixture with specific-heat ratio of 1.2. The area ratio Ae/A* of the nozzle is 20, and the throat diameter is 0.1m. Determine:

a. The stagnation pressure if the expansion is correct at sea level
b. The rocket thrust at sea level, 15- km, 30km, and 60km altitude.

Answers

The answer would be a. The stagnation pressure of the expansion is correct at see level

A pin B and D are each of 8mm diameter and act as single shape pin C is 6mm diameter and act as double shape for the laoding shaw determine averege shear stress in each​

Answers

Answer:

what's the question?...........

Propose any improvements if there are any in brake system

Answers

Improvements to brake systems are

Increase in disc radiusIncrease in caliper piston areaLine pressureThe friction coefficient between the pad and the rotorWhat is a brake system?Converts the thermal energy through friction, and the brake system takes the kinetic energy of your moving vehicle.Larger discs will permit for more brake torque as the brake pad will apply pressure at a larger radius, permitting for a higher moment.Increasing the size of the pistons means you have more area to put in a specific pressure. If the pressure remains the same and the area increases, the force applied will be increased.Push your foot harder, and the car brakes harder due to this the line pressure increases. Self-explanatory, but if you can increase the friction between the pad and the rotor, you can increase the braking torque.

To learn more about the brake system refer to:

https://brainly.com/question/24408495

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Where does Astro Teller work? What do they do there?

Answers

Answer:

Astro Teller oversees X, Alphabet's moonshot factory for building magical, audacious ideas that can solve concrete problems for millions of people through science and technology. As X's head, Teller has an unmatched vantage point from which to watch possible futures unfold.

Explanation:

hope it helps !!

ss mark me as BRAINLIST

in the metric system what is the prefix for 1000

Answers

Yes dialogue since the corresponding peragular colum is negative to prefix

Which statement most thoroughly describes the profession of an engineer?


Engineers work in teams to design and implement various products using specific processes.

Engineers should never complete a project without collaborating with experts in other fields.

Engineers strive to complete a project in the most cost-conscious and timely manner possible.

Engineers are being increasingly constrained by governmental regulations, limiting their creativity and effectiveness.

Answers

Answer:

Engineers work in teams to design and implement various products using specific processes.

Engineers work in teams to design and implement various products using specific processes. The correct option is A.

Who is an engineers?

An engineer is a person who designs, builds, and maintains machinery and structures like bridges, railroads, and highways using scientific knowledge.

The word engineer, from which the term engineering is derived, was first used in 1390 to refer to "a constructor of military engines." The term engine'er literally means "one who operates an engine."

In this now-outdated meaning, the term "engine" refers to a military machine, or a mechanical device employed in battle.

An engineer is someone who practices engineering, and those who are qualified to do so may hold more official titles like "Designated Engineering Representative," "Professional Engineer," "Chartered Engineer," "Incorporated Engineer," "Ingenieur," or "European Engineer."

Teams of engineers design and deploy various goods utilizing predetermined procedures.

Thus, the correct option is A.

For more details regarding engineer, visit:

#SPJ2

Express the following numbers in decimal:
(a) (11001.1011)
2

(b) (A3.C)
16

(c) (75.16)
8

(d) (ABCD)
16

Answers

(a)

11001.1011₂ = 1×2⁴ + 1×2³ + 1×2⁰ + 1×2 ⁻¹ + 1×2 ⁻³ + 1×2 ⁻⁴

… = 16 + 8 + 1 + 1/2 + 1/8 + 1/16

… = 411/16

(b) In base 16, we have A₁₆ = 10 and C₁₆ = 12, so

A3.C₁₆ = 10×16¹ + 3×16⁰ + 12×16 ⁻¹

… = 160 + 3 + 12/16

… = 2620/16 = 655/4

(c)

75.16₈ = 7×8¹ + 5×8⁰ + 1×8 ⁻¹ + 6×8 ⁻²

… = 56 + 5 + 1/8 + 6/64

… = 3918/64 = 1959/32

(d) B₁₆ = 11 and D₁₆ = 13, so

ABCD₁₆ = 10×16³ + 11×16² + 12×16¹ + 13×16⁰

… = 40960 + 2816 + 192 + 13

… = 43981

WILL GIVE BRAINLEY PLZZZZZZZ

how is a electrical resistance similar to the diameter of a pipe of water

Answers

Answer:

The resistance of the flow of charges in an electric circuit (electrical resistance) is analogous to the frictional effect between water flow through a pipe and the pipe's surface

Explanation:

In comparison to its similarity to the diameter of the pipe affects the flow of water and acts a a factor affecting resistance so are there factors affecting electrical resistance.

in an electrical circuit:

the total length of the wire is to the length of a pipe of water

the cross-sectional area of the wire is to the diameter of a pipe of water.

Thus, the cross sectional are affects the amount of electrical resistance. Wider wires have wider cross-sectional area and vice versa. Also, water will flow (i.e. current) through a wider pipe (i.e. large diameter) at a faster rate than a narrow pipe (i.e. small diameter). This is due to the lower amount of resistance offered by the wider pipe.

in the same manner, the wider the wire, the lesser the electrical resistance to the flow of elsctric charge and vice versa for thiner wires.

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