z+i dz , where T is the circle Iz – 3i| = 1 traversed once (2) Compute counterclockwise.

Q: Find the values of a for which the point (a-1,a+1) lies in the larger segment of the circle…

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Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

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Q: Find the distance from the point (5,8) to the circle x2 + Y2 + 2x + 6y + 3 = 0

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Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: 2. Evaluateſ. a+ (z+30:) dz along C which is the circle |z + 3i| = 3, counterclockwise. %3D (z+3i)

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Q: What is the equation of the circle with centre (,0) and radius 2? (2a- 1)2 + y? = 2 4. (2x-1)2 + y?…

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Q: Find ∫C (2z + 9) / (z2 + 2z - 3) where C is the circle |z - 2| = 3.

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Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

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Q: Evaluate 12x-7 dz where (2213) (2-1)² Cis the circle Z = 2

A: Approach to solving the question:  Detailed explanation:

Q: rotate the point (2,8) by the (3/5,4/5) about the origin (0,0). (3/5,4/5) is on the unit circle.

A: Given data, Point A(2,8)

Q: (b) Evaluate 2 + 5z zdz, 22 — 2х — 3 - where C' is a circle |z + 2| = 2.

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Q: Evaluate (r2 + y?)ds, C is the left half of the circle with radius 4 centered at (0,0) and is…

A: We calculate this by using concepts of line Integrals !

Q: Find the distance between two points (1, 2) and (3, −1).

A: We want to find the distance between the given two points. We use formula for finding the distance…

Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

A: Use Cauchy Residue theorem to evaluate this integral.

Q: Evaluate (x² - y²) dx + (x² + y²) dy, where C is the circle x² + y² = 9 oriented counterclockwise.…

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Q: Find the distance between the plances 3x +y-4z = 2 and 3x+ y- 4z = 24

A: Find the distance between the planes   3x+y-4z=2    and    3x+y-4z=24

Q: Find the distance d between the points (1, 3) and (5, 6).

A: Our Aim is to find the distance between the points (1,3) and (5,6).

Q: A rectangular tank that is 7 feet long, 8 feet wide and 12 feet deep is filled with a heavy liquid…

A: Giveb atanl of lenght  feet, breadth  feet and a depth of  feet.The tank is filled with a heavy…

Q: Evaluate (x+ y)ds, where C is the top half of the circle x² + y² = 4, oriented counterclockwise.

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Q: ort er 2x² + 2y² + 4x + 8y + 8 = 0 is the equation of a circle with center (h, k) and radius r for:…

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Q: 3. Use the Secant method on the circle function (x + 1)²+(y – 2)²= 16 to %3D find the intersection…

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Q: calculate S S, y³ dA where Ris the vertex of the triangle (0, 2), ( 1,1) and (3, 2)|

A: In this question we have to calculate the following integral.

Q: What is the distance between the center of the two circles whose equation is r +y + 6x + 10y – 12 =…

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Q: Evaluate ſc zsin(2²) dz where C is the union of the lower-half of the unit circe in clockwise…

A: The complete solutions are given below