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

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Q: find a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

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Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

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A: To find the Midpoint of the line.

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

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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: Find parametric equations for the line segment joining the points (6, 2) and (9, 10). x=t, y 2+8t,…

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Q: Sketch the section of the surface at y = 0. 9x^2+4z^2=36

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Q: The intersection between the surface x + y + z = - 1 and the circle x2 + y2 = 1,z = 0 is

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Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: Find the center of the circle tangent to x^2 + y^2 + 2x - 6y + 5 = 0 at (1,2) passing through point…

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Q: Find the center of the circle tangent to x^2 + y^2 + 2x - 6y + 5 = 0 at (1,2) passing through the…

A: First find the equation of the tangent. The point (1,2) is tangent to the given circle. The general…

Q: Find the distance from the point (-4, 5, 1) to the plane – kr – ly – 2 = 5.

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Q: Verify Green's Theorem where F1=y^2-7y , F2=2xy+2x and the curve C is a circle x^2+y^2=1

A: Given: F1=y2-7y , F2=2xy+2x and C is a circle i.e., x2+y2=1 As, we have:…

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

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Q: · What is the shortest distance from the surface xy + 6x + z = 41 to the origin? distance =

A: The surface is given as , xy+6x+z2=41 find the shortest distance from the surface to the origin.

Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = <t, t2>That implies,

Q: Find a path that traces the circle in the plane y = 3 with radiusr = 5 and center (0, –3, 2) with…

A: the plane y = -3 with radius r = 5 and center (0, -3,2) with constant speed 20 To determine a path…

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

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Q: Find the point on the line y = 3x + 5 that is closest to the origim %3D (x, y) = %3D

A: We have to solve

Q: Find the area and centroidal distances of the curve that lies between the equations y=4-x^2 and…

A: Consider the region bounded between the curves is as shown in the figure below: Here, the objective…

Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: Find the DE of a family of circles with center at (1,-2). Hint: Equation of circle with center (h,…

A: We know that equation of circle with center h, k and radius r is given by, x-h2 + y-k2 = r2 We have…

Q: 5 – 4z Show that the reactiob w= transformation the circle z =1 4z -2 in to a circle of a radius…

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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: Find a parametrization for the line segment beginning at P, (-5, - 2,3) and ending at P2 0, 5/4

A: We have to use parameterization of the line.

Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

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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)…

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

Q: F = (y + 2x, 2x + 5z, 1y + 8x), C is the circle with radius 5, center at (2, 0, 0), in the plane x =…

A: F=y+2x, 2x+52, 7y+8xCircle centered at (2, 0, 0) and radius is 5In x=2 planeOrientation- counter…

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

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Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: Identify the center and radius of the circle passing through the points P(1, 3) and is tangent to…

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Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

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Q: Find the curvature k of the circle C : (x – 2)² + (y+ 3)² 16 at the point (2, 1).

A: Use the formula of curvature to solve this problem.

Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

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Q: Let C be a circle with |z - i| = 3 travelled once in counterclockwise direction. Evaluate: 5z3 + 3z2…

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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 a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

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

A: In this question we have to find the Integration.

Q: Find the curvature K of the circle C: (x - 2) + (y+3)² = 16 %3D at the point (2, 1).

A: Given: Equation of circle C: (x-2)2+(y+3)2=16 ⇒ (x-2)2+(y-(-3))2=42 We know that circle equation is…

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

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Q: Find the sphere’s center and radius. x2 + y2 + z2 + 10z = 0

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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: 8. centered at Which of the following equations represents the circle with radius F 16x2 + 16y2- 16x…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.