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))
Related Questions
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]
Suppose a contract states that the designer should bear the responsibility if substantial differences were found between the design drawings and the reality. What type of disagreement may happen due to this statement? Select one:
a. Disagreement about the definition of concepts and terminology
b. Disagreement about irrelevant facts
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d. Disagreement about the definition of facts
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Answer:
C.) Disagreement about unknown facts
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Answer:
ABS makes it so that the wheels of a car do not lock and slide when the driver slams on the brakes for an emergency stop.
ABS system senses when the wheels have locked and then pumps brake fluid in bursts using a friction
What is the ABS system?An anti-lock braking system (ABS) is defined as an automobile safety system that allows the wheels on a motor vehicle to manage tractive contact with the road surface according to driver inputs by braking, preventing the wheels from closing up (ceasing rotation), and avoiding uncontrolled skidding.There are three basic types of anti-lock braking systems namely four-channel/four-sensor, three-channel/three-sensor, and one-channel/one-sensor.It has 4 components namely a speed sensor, valves, ECU, and Hydraulic Control Unit.To learn more about the ABS system refer to:
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What is Traction Control System?
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Answer:
A traction control system is a secondary function of electronic stability control on production motor vehicles, designed to prevent loss of traction of the driven road wheels.
uestion 10
0
On a day where the temperature is (25 C) and the pressure is
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explain the evolution of science in one sentence
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Answer:
the change in the characteristics of a species over several generations and relies on the process of natural selection.
Explanation:
I HOPE IT WILL HELP YOU
To calculate current you can use the following calculation
Answers
Answer:
It depends on the circuit. Many would answer with Ohm's law, but that is not accurate because Ohm's law is applicable only to a particular case:
Ohm's law I = U / R; where R is a constant linear resistance, U a voltage, I a current, and no other impedance is in the system.
Ohm's law allway applies to linear constant resistances, but there is much more to an electrical system than just plain resistances.
Besides linear constant resistances there are: inductances, couppled inductances, capacitances, non linear behaviour, voltage and current sources, radiation behaviour, etc.. They all play a role t
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Calculating electrical current in D C circuit : I (Intensity of current) =E (electromotive force) / R (Resistance of circuit).(ohm’s law)
Calculating electrical current in A C circuit : Ohm’s law for Capacitive circuit : The current in a capacitive circuit is directly proportional to applied voltage and inversely proportional to the capacitive reactance. I = E/Xc.
If there is a resistance in series with the capacitor,then I = E/Z , Z is the total impedance of, To find Z , square root of R square + Xc square.
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B. telling the oil levels remaining
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D. checking the engine's temperature
Answers
D. checking the engine's temperature
The thermostat is the gauge on your dashboard for checking the engine's temperature. The correct option is D.
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Your car's temperature gauge is made to gauge the coolant temperature in your engine. This gauge will indicate whether the coolant in your engine is cold, normal, or overheated. It is a crucial dial that may be found on your car's dashboard.
The same thermostat generates signals, typically electrical, combined in a system that includes relays, valves, controllers, and other components whenever the temperature rises or falls below the desired level.
Therefore, the correct option is D. checking the engine's temperature.
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Answers
Answer:
Maximum power is
P = V × I
P = 120 × 15
P = 1800 watt
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4.1.2 Rt (parallel)
Answers
Answer:
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Don't forget put heart ♥️
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Answer:
Explanation:
Generally speaking, flammable liquids will ignite (catch on fire) and burn easily at normal working temperatures. ... Fuels and many common products like solvents, thinners, cleaners, adhesives, paints, waxes and polishes may be flammable or combustible liquids.
The material which is considered flammable is: A. paint.
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In Science, some examples of the chemical properties of a material (substance) include the following;
TarnishingRustingReactivityFlammabilityFlammability refers to the ability of a material to support combustion or burn continuously in the presence of air. An example of a material which is considered to be flammable is paint because it contains a high level of solvents.
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Answer:
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Explanation:
hope it helps !!
Plssss mark as BRAINLIST
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Answer:
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Answer:
Recognize that there is a moral dilemma.
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A
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Answer:
a
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digital identity is the answer
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What is a Multi-party System?A multiparty system is a shared data infrastructure within the individual and the organizations that drive the efficiency nf new business and lead to the formation of the revenue models. They include the blockchain and distribution database and include a variety of technology and other capabilities.
Find out more information about the multi-party systems.
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Answer:
here
Explanation:
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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