Evaluate the surface integral (2ayi – yzj + zk) · dS. Where S is the part of the paraboloid z = a2 - y? that lies above the square 0 < a < 5, 0

Q: Assume S is the surface x1000 + y8000 + z1000 = 1,000,000 and F = [9 + ee^(xyz), x8yz, 3x - 5y -…

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Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: Show G(r,0) = (rcose, rsine, 1-r^2) parametrizes the paraboloid z=1-x^2-y^2. Afterwhich, descrbie…

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Q: Parameterize (in 2 variables u, v) the paraboloid 4x2 +y2 -z=0

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Q: Let S be the paraboloid y = x^2 + z^2. Find a parametric representation for S and its tangent plane…

A: The given data is: Let S be the paraboloid y=x2+z2 Find a parametric representation for S and its…

Q: Sketch the following surfaces. 1) 4x^2+9z^2=9y^2 2)y^2-x^2=z Show all work.

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Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: 6) x² + (y – 4)² = 4 Center Radius

A: The given equation is x2+(y-4)2=4This is in the form of (x-h)2+(y-k)2=r2 which is a circle equation…

Q: Consider the following equation of a quadric surface 9x^2 - 81y^2 - (z^2/4)=0 (a) Find the…

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Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: Exercises 1-6 refer to the following systems of equations: (i) dz (i) dz = 10x (1-) - 20xy =0.3x -…

A: given system of differential equations case i dxdt=10x1-x10-20xydydt=-5y+xy20 case ii…

Q: d. P = 4x1 – 2x2, Q = 2x1 + 6x2; D is the interior of the ellipse: x1 = 2 cos 0, x2 = = sin 0, 0 E…

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Q: the sum of the distances from (x,y) to (-1,0) and from (x,y) to (1,0) is 4. show x and y is related…

A: Distance from (x,y) to (-1,0) is:  Distance from (x,y) to (1,0) is:

Q: Q3] (A) Verify Stokes' theorem where Ã= (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z =…

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Q: you know that a sphere has the equation of  x^2 + y^2 +z^2 -6x +4z =3 are the following points…

A: The equation of sphere is:-Now add 9 and 4 both side:-

Q: (x+ 4)² + (y – 4)² = 4 Center Radius

A: Compare given equation with (x-h)2 + (y-k)2 = r2

Q: Derive a cubic spline with natural boundary condition using the following points: (−2, 1), (0,0),…

A: Sol:-] To derive a cubic spline with natural boundary condition, we need to find the cubic…

Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

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Q: Consider the equation 4y^2 + z^2 − 4x − 8y + 4z + 8 = 0. Then classify the surface it represents…

A: Given equation of surfaces 4y2+z2-4x-8y+4z+8=0

Q: A space probe in the shape of the ellipsoid 16x² + y² +42² = 41 enters a planet's atmosphere and its…

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Q: Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2.…

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Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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