Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein model, solve: to When X2+Y2<=1, find the point F(x,y) that is the intersection lxy with the sphere E

Q: 5. Find a parametric representation for the part of the sphere x + y + z2 = 4 that lies between the…

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Q: Find the area of the portion, for which z > T9, of the sphere in R° with radius /3 centered 2 at the…

A: Here we find the area.

Q: Find the center C and the radius a for the spheres in Exercises 51–52. 51. (x + 2)2 + y2 + (z - 2)2…

A: To determine the centre and radius of the sphere.

Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

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Q: The distance between the centers-of the following two spheres: x²-22x+y2-58y+z?=-961,…

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Q: (4) Find the points Po = (xo, Yo, 2o) on the sphere x? + y? + z² = 9 so that the tangent plane to…

A: Topic- equation of tangent in 3D

Q: Find the extreme values of ƒ(x, y, z) = x - y + z on the unit sphere x2 + y2 + z2 = 1.

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Q: 2. Find the equation of the sphere with the given conditions: (a) center at (1, – 2, – 4) and its…

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Q: Given a sphere with center (9, 2, – 4) and radius 5. Find an equation of the intersection of this…

A: To find the equation of the intersection of the sphere with the xz plane.

Q: rove that the surface area of a sphere of radius a is 4πa2 by revolving the curve y=√(a2−x2) where…

A: Given that

Q: hoose the correct equation for a sphere centered at (1, –2, 1) with radius 7. O (x + 1)² + (y + 2)²…

A: Given that centre is (1,-2,1) and redius (r)=7 . And we find equations of sphere.     Here i…

Q: The surface S formed by the point P(x,y,z) such that the distance from P to the point A(1.0,-1) is…

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Q: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

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Q: Find equations for all the planes that intersect the y-axis at y =1 and the z-axis at z =2, and are…

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Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: 1. Find the area of the surface the part of the plane 3x + 2y + z = 6 that lies on the first octant

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Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2…

A: Biref answer is given below.

Q: PICTURE

A: We are given that the cone ax2+by2+z2 = 0 and the ellipsoid 2x2+4y2+z2 = 42 intersect and are…

Q: Given a sphere with center (6, 4, – 3) and radius 5. Find an equation of the intersection of this…

A: First write the equation of sphere then satisfy the condition for xz-plane.

Q: 6. Consider the sphere a2 + y? + (z-3)2 = 1. Find the point P (a, b, c) on the sphere such that the…

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Q: Given a sphere with center (7,3, – 4) and radius 5. Find an equation of the intersection of this…

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Q: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

Q: Write the equation x +z* - (y- 1) = 0 in cylindrical sy stem. W hich surface does it represent? Give…

A: Given :            The equation x2 + z2 - (y - 1)2 = 0   To write the given equation in…

Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: he cone z^2= x^2+ y^2, for z ≥0, cuts the sphere x^2+ y^2+ z^2= 16 along a curve C. That is, C is…

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Q: Given a sphere with center (10, 3, – 1) and radius 5. Find an equation of the intersection of this…

A: Given. The ceter of sphere is located at  (10,3,-1) Radius is 5. Equation of XZ plane is Y = 0.

Q: For the surface a?+ - z = 1, a curve in a form of a parabola can be formed bi passing through a…

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Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

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Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z2 = 9 and x2 +…

A: Given equations of spheres: x2+y2+z2=9 x2+y2+z2=36 For spherical coordinates: x=ρ cosθ sinϕy=p sinθ…

Q: Please help.

A: Note: The tangent plane to the surface given by f(x, y, z) = 0 at (x0, y0, z0) has the equation,…

Q: Use spheri\cal coordinatcs Evaluate y'zdV, where E lies above the cone 4 = /3 and below the Sphere…

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Q: 28 Describe the surface withe cylindrical equabion p?+z?=9. [ Oraw it and Solve it] .

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Q: Using Stoke's Theorem Evaluate [(2x- y)dx – yz²dy – y° zdz) where is the circlex + y = 9…

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Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: Using Newton- Raphson method, Determine the points of intersection between the circle x +y = 3 and…

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Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein…

A: Determine the parametric equation by first determining the equation of the line and then…

Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

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Q: A tangent plane to the ellipsoid x². y? a b2 meets the axes in A, B, C. Show that the envelope of…

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Q: a. Find a parametrization for the hyperboloid of one sheet x2 + y2 - z2 = 1 in terms of the angle u…

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Q: The equation of the sphere with radius r = V75 and center C(2,1, – 1) is (a) x² + y² + z² + 4x + 2y…

A: The general equation of a sphere with radius r and center a,b,c is x-a2 + y-b2 + z-c2 = r2

Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given the surface r(u,v) =  (0 ≤ u ≤ 5, 0 ≤ v ≤ 4pi) Explain clearly what gridlines are found when…

A: Given surface is ru,v=ucosv,usinv,v To find the equation of tangent plane for u=3, v=8π3…

Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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Q: In cylindrical coordinates, the set {(r, 0, z): 0<r< 1, 0<0 <T, -1 <z < 1} is (a) a full right…

A: In the given cylindrical coordinates, r,θ,z Radius of the cylinder lies between 0 to 1. r=0≤r≤1r=1…