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

Answer 1

(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))


Related Questions

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

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

a television set having apower rating of 120w and electric lawnmower of power rating 1kw are both connected to a 250v supply if 3A 5A and 10A fuses are available state which is the most appropriate for each appliance​

Answers

Answer:

Television

Power = 120 w

p.d = 240 v

I = p / v

I = 120 / 240 = 0.5

Fuse can be used 3A

lawnmower

Power = 1000w

p.d = 240 v

I = 1000/ 240 = 4.16

Fuse can be used = 5A

Do you think that the country that has the right to force vaccinations on the community?

Answers

Answer:

no

Explanation:

we all have the freedom to choose whether we want to have something injected in our bodies that we aren't sure about. This would be a violation of our constitutional right to force us to take the vaccine.

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

Answers

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]

 Observe how the components of the brake system is connected together using Motor Tricycle
 Open the Rear Axle provided to you and observe how drum brake system operate
 Using the Caravan Van, Observe how does the Disk Brake System works
 Prepare a diagram how does the brake system work
 Observe How does the “Brake Booster” works
 Observe how does the ABS system interfere with the Braking using the ABS training Module

Answers

Answer:

The term drum brake usually means a brake in which shoes press on the inner surface of the drum. When shoes press on the outside of the drum, it is usually called a clasp brake. Where the drum is pinched between two shoes, similar to a conventional disc brake, it is sometimes called a pinch drum brake, though such brakes are relatively rare. A related type called a band brake uses a flexible belt or "band" wrapping around the outside of a drum.

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

Rt = R1 + R2 + R3

[tex] \frac{1}{rt} = \frac{1}{r1} + \frac{1}{r2} + \frac{1}{r3} [/tex]

If R1 = 4Ω , R2 = 6Ω and R3 = 8Ω (Ω= ohm)


Calculate: 4.1.1 Rt (series)
4.1.2 Rt (parallel)





Answers

Answer:

In series:

[tex] \frac{1}{r} = \frac{1}{r_{1} } + \frac{1}{r _{2} } + \frac{1}{r_{3} } [/tex]

[tex] \frac{1}{r} = \frac{1}{4} + \frac{1}{6} + \frac{1}{8} \\ \\ \frac{1}{r} = \frac{13}{24} \\ \\ r = \frac{24}{13} \\ { \underline{r = 1.85 \: Ω}}[/tex]

In parallel:

[tex]r = r _{1} + r _{2} + r _{3} \\ r = 4 + 6 + 8 \\ r = 18Ω[/tex]

Q2

a) Prove that the rotor copper loss of 3-phase induction motor is.

Pr = sP2

where Pr = rotor copper loss

S = slip

P2 = rotor input power

Pm = mechanical power developed by the roto

Answers

Answer:

Pr=sP2

Pr=rotor copper loss.

in the metric system what is the prefix for 1000

Answers

Yes dialogue since the corresponding peragular colum is negative to prefix

On a typical 120 volt circuit in your home, you may have a 15 ampere fuse or circuit breaker. What is the maximum power (watts) that this circuit can handle? How many 10 Watt light bulbs could you turn on without blowing the fuse?

Answers

Answer:

Maximum power is

P = V × I

P = 120 × 15

P = 1800 watt

What is the measurement

Answers

Bahaiajkabaiiakqbqhja

Many vehicles use halogen light bulbs. What must you avoid when handling halogen bulbs?

Answers

Answer:

here

Explanation:

try not to touch the Glass on Halogen Light Bulbs, even when changing the bulb. This is because when you touch a Halogen Light Bulb, you leave behind a residue on the Light Bulb which can in time cause the bulb to heat up unevenly, and even cause the bulb to shatter as a result.

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.

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

20 pts!
Calculate or write the formula please

A) the value of “dd”
B) the angle theta1
C) angle of transmission (μ)

Answers

Answer:

A the value of dd because you can see how the value is to the dd

Need help coding this i’m using python.

Answers

Answer:

ill help'

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:

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