Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x-2)²+(y-3)² = 4 Without using Green's Theorem.

Q: Q3: Evaluate z + 1 $c (z6 + 5z5 + 4z¹) (z + 4) dz where C is the circle |z1| = 5

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Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

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: Use Green's Theorem to find (8y + x) dx + (y + 2x) dy, where C: The circle (x - 4)2 + (y-3)2 9 541…

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

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Q: 2. Circle One. Are (x-3) and (x-2) factors of: f(x) = x'-3x -4x+12 YES or NO

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

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Q: What is the center of x² + y² – 6x = -4y + 68?

A: given equation of circle  x2 +y2-6x=-4y+68  x2+y2-6x+4y-68=0 Now compare with x2+y2+2gx+2fy+c=0…

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

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Q: Find the cоттоn points of the circles (x + 1)² + (y – 1)² = 5 and x² + y? = 1.

A: Common points of the circles simply means the point of intersection of the given circles.

Q: If the radical axis of the circles x² + y² + 2gx + 2 fy+c= 0 and 2x² + 2y² + 3x +8₂ touches the…

A: Given: Here the radical axis of the circles given x2+y2+2gx+2fy+c=02x2+2y2+3x+8y+2c=0 we have to…

Q: what

A: Please refer to the image below

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: The point (-1,0) lies on the circle x2+y2-4x+8y+k=0 . Find the radius of the circle.

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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: Prove that the line y = m(x-1) + 3√1+m² -2 touches the circle x² + y² - 2x + 4y-4-0 for all real…

A: We have to prove that the line y=mx-1+31+m2-2 touches the circle x2+y2-2x+4y-4=0 for all real values…