Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

Q: calkulate the ) x+(y-)'=1 of the circle yo- area of the surface formed by rotating it around the…

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Q: Parametrize a path for the curve that is a circle in the x-y plane that has radius 2 (a) with center…

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Q: Calculate the distance between the points J (-7,0) and L= (-2,-4) in the coordinate plane. Give an…

A: Given,            Two points J(-7,0) and L(-2,-4) in coordinate plane we need to calculate distance…

Q: a. Find the area of the surface generated by revolving about the x-axis the loop of the

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Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 2 – 1 - lim R00 YR…

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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: Sketch the Surface z./4-x* and verify that fay -lyx.

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Q: Describe the transformation rules that map Circle F onto Circle F'. Translation rule: (x, y) -->…

A: We have to find dialtion

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: 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: You are given a y=sqrt(36-x^2) curve that rotates about the x-axis. What is the area of the…

A: To find the surface area of rotation of the below curve about the x-axis. y=36−x2

Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

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Q: Find the area of the resulting surface if an arc of a parabola y=x2 from (1,1) to (2,4) is rotated…

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Q: Write a parameterization for a circle of radius 4 centered at (1,0) starting at (5,0). Describe…

A: Parametric equation of circle

Q: Describe the transformation rules that map Circle A onto Circle B. Translation rule: (x, y) --> (x…

A: Dilation and transformation of circle

Q: Find the area of the ellipse x^2+14 x y+245 y^2=4 by using a suitable transformation that maps to…

A: Given equation is, x2+14xy+245y2=4 The equation can be written as,…

Q: The surface z - - = 1 is a hyperboloid of one sheet. Select one: True False

A: The general form of the equation of hyperboloid of one sheet is: x2a2+y2b2-z2c2=1

Q: ) I would need help wit

A: 22. Given,                4y2+z2-x-16y-4z+20=0

Q: Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by…

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Q: Find an arc length parameterization of the circle in the plane z = 9 with radius 4 and center (1, 4,…

A: The parametrization of the circle in the plane z=9 is:                                   r(t)=⟨1, 4,…

Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)ĵ where C is the circle x² + y² =…

A: In this we have to verify green theorem.

Q: Find a Möbius transformation which maps the region outside the unit circle onto the left- half…

A: a Möbius transformation of the complex plane is a rational function of the form {\displaystyle…

Q: Find a linear fractional transformation that maps the circle of radius 2 centred at z = 1 = 0. to…

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Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

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Q: Use cross products to find the area of the triangle in the xy-plane defined by (1,2), (3,4), and…

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Q: Screen. 28 Green's theorem is applicable to ans. yz-plane ху-plane All of these Zx-plane O Previous

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Q: Discribe the topology through diagrams of surface and curves

A: Describe topology through diagrams of surface and curves.

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: Does the product of inversion in the circle of radius 1 centered at the origin with inversion in the…

A: Does the product of inversion in the circle of radius 1 centered at the origin with inversion in the…

Q: (b) The circle of radius 2 centered at (0, 0, 0) and lying in the i. xy-plane ii. yz-plane iii.…

A: According to our company's guidelines I can only answer first question (b), since (c) is not…

Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: Incentre of the triangle formed by common tangents of the circles x2 + y2- 6x = 0 and %3D x2 + y2 +…

A: Draw the figure:

Q: Find a parameterization for a circle of radius 4 with center (-3,-1,2) in a plane parallel to the xz…

A: Aim: To find the parametric equation for the circle of radius with radius 4 and center -3, -1, 2…

Q: What is the path that traces the circle in the plane y = -3 with radius r = 4 and center (-2, –3,…

A: The solution is given below in the next step:

Q: Calculate the distance between the points M=(-9,8) and L=(-1, 1) in the coordinate plane. Give an…

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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: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

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Q: Let Ci be the line segment from the origin to (3, 2,0); C2 be the shorter circular arc of the circle…

A: The three curves given are as follows: C1: The line segment from 0,0,0 to 3,2,0. C2: The circular…

Q: Sketch the surface 1<z</9-x² - y² and x²+y² <1

A: To sketch the given surfaces.

Q: y = |x|, y = x² – 1, x = -1, x = 1 - г2 — 1,

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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: 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: 5. y-z =16

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 1 -dz = 0. lim z3 +…

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Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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Q: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: Find the area of the resulting surface if an arc of a parabola y=x2 from (1,1) to (2,4) is rotated…

A: The given curve is: y=x2        from   (1, 1)  to  (2, 4)

Q: Point W is the centroid of triangle TRV. VX = 204 and RW = 104. The length of VW = ____.

A: Triangle Question

Q: (1 point) Let C be the positively oriented circle z2 + y-1. Use Green's Theorem to evaluate the line…

A: The provided line integral is