Use Green's theorem to evaluate -y dx + x dy, where C is the unit circle r? + y? = 1

Q: Given line YZ tangent to OJ at point Y and mzWYZ = 119, what is the measure of arc WXY %3D Y W X.

A: Measurement of arc is the angle subtended by arc at the center of circle.

Q: B) Use Green's Theorem to evaluate /F-dr, where C is the circle r² + y? = 4 and F (r, y) = (y – 2…

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Q: dr Let A be the area of a circle with radius r. If dt 5, dA when r = 1. dt find

A: A is area of circle of radius r A = πr2 Differentiate the equation with respect to t

Q: Show that [(x- y) dx + (x – y)' dy] = 3ra" taken along the circle x +y =a° in C the counter…

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Q: dr Let A be the area of a circle with radiusr. If dt dA = 5, find when r = 5. dt %3D

A: Here we use the application of derivative.

Q: Use Green'sTheorem to evaluate O ydx – xdy where C is the circle with center at the origin and…

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Q: If C is a circle of radius 8 centered at the point ( 0, 5 ), then evaluate pain(2dr + (11æ sin(y*…

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Q: Jc z + 1 dz, where C is the right half of the circle |z|=1 from z = -i to z = i

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Q: BG and BH are tangents that intersect circle M at points G and H, then A. MZGMH = 120° B. BG = BH C.…

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Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

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Q: If C'is the circle of radius 3 centered at the origin, starting at the point (3,0) and moving around…

A: Answer and explanation is given below..

Q: Find the length of arc of the curve y = In r from r = 3 to r= 9. 8

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Q: Evaluate the line integral 3xy® ds, where C is the right half of the circle x? + y? = 36.

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Q: A- Using Simpson s Rule to estimate the area of the circle (r-4), c (1, 0) with (n=4). B- Prove…

A: The equation of a circle having center C(1,0) and radius r=4 is given by: x-12+(y-0)2=42…

Q: Evaluate (3y - esinz)da + (7x+ V +1)dy where C is the unit circle

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Q: Use Green's theorem to evaluate O -x²ydx + x°dy, where C is the circle x? + y? = 4 with a…

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Q: Evaluate the double integral 1+ 4x² + 43²&A where D is the bottom half of the circle x? + y? = 16.…

A: In polar coordinates,                                   and

Q: dz The value of the integral Jc 22+9 where c is the circle z - 3i| = 4 is %3D

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Q: 2.) What is line QP called? * U R. V S T Secant Tangent O Slicer Chord

A: In circle, all the point are at the same distance from the center.

Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: Evaluate O y°dx – x*dy, where C is the boundary of the region between the circles a? + y² = 4 %3D…

A: See below

Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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Q: e2z Evaluate a dz, where C is a circle with (z+1)* centre at origin, |z| = 3.

A: Given integral is ∮Ce2z(z+1)4dz Where C is  |Z| = 3

Q: dr dA Let A be the area of a circle with radius r. If dt 3, find when r = 5. dt

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Q: O Evaluate + z )ds where C is the circle F(E) = for 0EEE Zo

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Q: Using Green's theorem, evaluate f y°dx – x³dy, where C is the positively oriented circle of radius 4…

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Q: Please evaluate (3y – ein(e) dx + (7x + Vy* + 1) dy, where C is the circle a? + y = 9. Hint: use…

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Q: Ex: Fmd the lengthoftre arc af the Circle with P.R. ret)= [acest from Co,0 to asiut] o Ofa),- %3D

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Q: Please evaluate P (3y – esin(@)) dx + (7x + Vyª + 1) dy, - where C is the circle x2 + y? = 9. Hint:…

A: See the details solution in below

Q: Q2 Calculate 8-る dz, where C is the circle of radius 7, centre 0, negatively oriented.

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Q: 2 Green's theorem, evaluate ((+) dx + 3xy dy where C is the circle * +y = 4.

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Q: ſždz, y is the line segment from 0 to 1 + i §ždz, y is the unit circle with positive orientation

A: Line integral of function f(z) along a path C which given by parametric function γt from t=a to t=b…

Q: Compute . Z+1 dz, where C1 is a part of a circle with r = 3, and 0<0< %3D

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Q: Evaluate the line integral a ds where C is the unit circle, æ? + y² = 1, oriented in the…

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Q: Match the part of the circle with the term that best describes it. - 1. GH A. Center 2. М B. Chord…

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Q: Find the area of circle A given tangent CD = 4 and FD = 2. а. 36n b. 16л 12л C. d. е.

A: Given: CD is tangent to the given circle. CD = 4 DF = 2

Q: :aliul J Evaluate xy ds where Cis the first quadrant of the circle, x2 + y? = 16.

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Q: ⒸFind S (x- y²) dA, where I is bounded by the circle of D center (0,0) and radius 2.

A: As per as our guidelines i am supposed to answer

Q: True or false, AB is tangent to circle C. O True O False

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Q: Let F(x,y)=−yi+xj/x2 +y2 and let C be the circle r(t)=(cost)i+(sint)j, 0≤t≤2π. A. Compute ∂Q/∂x B.…

A: Given that F(x,y) = -yi + xix2 + y2=-yx2+y2i + xx2+y2 j Now P(x,y) = -yx2+y2i and Q(x,y) = xx2+y2.…

Q: 2. A CIRCLE IS TANGENT TO THE CINCLES x7 y? = 4 x*+ y? = 12Y+ 64 2 F IND THE LOcuS OF IT3 CENTEN AND…

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Q: e? dz, calculate give integral. When C is a circle z= 2 (z – 1)

A: Introduction :

Q: dr Let A be the area of a circle with radius r. If dt dA when dt 4, find %3D r = 3.

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Q: dr Let A be the area of a circle with radius r. If dt dA when r = dt 5, find = 4.

A: Given, drdt=5 and r=4

Q: Show that = sin t if t>0 and C is the circle z] = 3. 2mi Jz+1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: z2 dz, where c is a unit circle. 3) Evaluate C 4z-i

A: Given : ∫Cz24z-idz Here, C is a unit circle. we can write it as 14∫Cz2z-i4dz it has singularity at…

Q: ind the the exact length x = et – t, y = 4e/2, |

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Q: sin z 0 dz, where C is the positively oriented circle of radius 1, |z| = 1. %3D

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Q: Evaluate the contour integral and use appropriate graphs to illustr where is the circle with…

A: Given : ∮e2021zz2+1z2-1dz To Find : (a) z-i =1                                                     b…

Q: (i) Evaluate $.z'dz, where C is the positively oriented circle |z- 1| = 1.

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