If F = V(4x² + 5y*), find ſ, F · di where C is the quarter of the circle a? + y² = 1 in the first quadrant, oriented counterclockwi SoF · dř =

Q: A circle has a diameter AB, and it's center is at (-3,3). Point A is at (1/2, 6). Where is point B…

A: Given AB is diameter of circle and center is at  ( -3 , 3 )     and point A is at   12 , 6Assume…

Q: What is the Length of the arc of the circle r = sin θ that remains outside of the cardioid r = 1 —…

A: Arc lenght in polar curves: The formula to find the arc length is, Arc length=∫θ1θ2dxdθ2+dydθ2dθ…

Q: 2x +3K Zx2 - 4x + 13

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Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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Q: Find the length of the arc formed by ² = 10y³ from point A to point B, where A = (0,0) and B = (100,…

A: We can find the length of arc by applying length of arc formula.

Q: 17. Concentric with the circle (x – 2)² + (y – 1)² = 4 and passes through (4, –1) %3D

A: Given, Concentric with (x-2)2+(y-1)2=4 and passes through (4,-1) General equation of circle is…

Q: A sphere in the first octant is tangent to the three coordinate planes. What is the radius of the…

A: Given:- A sphere in the first octant is tangent to the three coordinate planes To find:- Radius of…

Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

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Q: Find the length of arc of the curve 9y^2=4x^3 from the origin to the point (3,2 squareroot of 3)

A: The arc length of a curve y=f(x) from x=a to x=b is defined by the integral L=∫ab1+dydx2dx.

Q: as incorrect Based on the equation of the circle, what is its center and radius? 8x + 8y + 24x- 20y…

A: Given equation is: 8x2+8y2+24x-20y-39=0 We know that the standard equation of a circle with center…

Q: Q2 Calculate 8- z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: 2. Find points P and Q on the parabola y = 1 - x² so that the triangle ABC formed by the r-axis and…

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Q: The arc of the parabola y = 5x2 from (5, 125) to (15, 1125) is rotated about the y-axis. Find the…

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Q: Find the coordinates of a point on a circle with radius 25 corresponding to an angle of 165 (x,y) =…

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Q: Q2 Calculate 8- z dz, z(4- z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: A point starts at (x, y) = (6,0) and moves CCW along a circular path centered at (x, y) = (0, 0).…

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Q: Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

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Q: When is An angle in the xy-plane is said to be in standard position?

A: An angle is in standard position if its vertex is located at the origin and one ray is on the…

Q: Q2 Calculate 8 - z dz, (4- | where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Q2 Calculate 8-z dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Given a sphere in center-radius form, how will you get an equation tangent to only one of the…

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Q: The center of gravity of a quadrant of a circle lies along its central radius (r) at a distance of…

A: ANSWER: TRUE

Q: Find the coordinates of a point on a circle with radius 20 corresponding to an angle of 100° (x,y) =…

A: I have appended the formula used in the solution part of the question

Q: Find the coordinates of a point on a circle with radius 15 corresponding to an angle of 10° (x,y) =…

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Q: < sin!!), w5"1)? aiong.seni-circle. 4) Work done by o trom tJ5, 1) to' (-3,-1) t radius 2 · 个。 3+1…

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Q: If C is a circle of radius 3 centered at the point ( 3, -4 ), then evaluate £(3y – ein(=) ) dz +…

A: The integral is given by ∮C3y-esinxdx+10x-siny3+ydy Where, C is a circle of radius 3 centered at the…

Q: 6. In circle H, if mZDHG = (13x – 36)' and mEF = (x + 12)', find x. %3D %3D D G F

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Q: Find the arc length from (−3, 4) clockwise to (4, 3) along the circle x2+y2 = 25. Show that the…

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Q: 1. Line AB is tangent to circle O at A. If AB = 12 and OA = 5, find OB %3D B.

A: We have to find OB

Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

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

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Q: What is the relationship of two secants intersecting in the exterior of a circle to the measures of…

A: What is the relationship of two secants intersecting in the exterior of a circle to the measures of…

Q: In circle X, mZYXZ = 135° and the area of the shaded sector =T. Find the length of XY.

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Q: A lamp is placed three units to the right of the y-axis, and a shadow is cast by the elliptical…

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Q: What is the area of the largest triangle in the first quadrant with two sides on the axes and the…

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Q: C is the part of the circle of radius 3 in the first quadrant from (3,0) to (0,3) and F = (1, -y),…

A: Given, C is part of circle of radius 3 in the first quadrant from (3,0) to (0,3) and F=[1,-y] The…

Q: If 2x^4 + x^2y^2 - y^8 = 3x^2 + 4,what is the value of dyldx at point (4,1)? %3D

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Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

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Q: Tangents are drawn to the concentric circles x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=b^(2) at right angle…

A: We have to Show that locus of their point of intersection is a 3rd concentric circle and find its…

Q: Integrate counterclockwise dz, C' the circle with z² + 8z + 15 center -3 and radius 2. dz = La z2 +…

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Q: Find the equation of the osculating circle bent X=y^2-y at point (0,1) .

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Q: Find the coordinates of a point on a circle with radius 15 corresponding to an angle of 320° (x,y) =…

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Q: The DE for the family of circles of radius 9 is:

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Q: gments ST and SU are both tangent to circle V. If mZTVS = 74°, what is mzTSV? *

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Q: 2. Circles with fixed radius r and tangent to the y-axis.

A: Solution is given below:

Q: WHAT IS THE EQUATION OP A TAMILY OF CIRCLES WITH CENTER Czk) AND WITH RADIUC R THAT IS TANGENT TO…

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Q: Q2 Calculate 8- Z -dz, (4 – 2) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: $ ydx – xdy where C is the circle of radius 3 with center at (13, 28)

A: We use Green's theorem to evaluate the given line integral

Q: What is XY for triangle XYZ ?

A: Solution: