Find an inner product on R such that the unit sphere is the ellipsoid z? = 1, a, b, c > 0. c? y? a b? + +

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: Compote the volume of a reoion inside the Sphere x" +Y? +z² =4 ond between two sheets of the…

A: We have to find V0, V0 = Volume of sphere - V1-V2And from Symmetry we know that V1 = V2⇒V0 = Volume…

Q: Using spherical coordinates, the volume of the solid inside the sphere x+y+z -9 and above the plane…

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Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

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Q: Let E be the solid enclosed by the sphere æ² + y² + (z – 3)² = 9 above the plane z = 2. The %3D…

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Q: 9. Use spherical coordinates to find the volume of the part of the ballps 4 that lies between the…

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Q: Find the surface area of the tetrahedron bounded by the coordinate planes and the plane 8x + 12y +…

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Q: 1. Consider the parallelepiped with adjacent edges u = 6i + 4j + 2k; v= 2i + 2j + 4k; w = 2i + 6k +…

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Q: Find the area of the part of the sphere x² + y? + 2? = 12z that lies inside the paraboloid 2 % = x²…

A: Topic = Application of integration

Q: Oose the correct net for each solid shape. b) c) al b) al b) c) b) b) a) bi C)

A: We open these 3D figure and check the answer.

Q: The surface r(u,v)=(u,2v,3u – 4v) is a (a) cone. (b) plane. (c) sphere.

A: Given :The given surface is r(u,v)=<u,2v,3u-4v>To find:we have to check the given…

Q: In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 8, YX = 10, and WX = 20. Find height h (the…

A: Given  The  WXYZ  is isosceles trapezoid  with bases ZY and WX .  Here ZY =8  , YX =10  and WX =20

Q: 1. Consider the parallelepiped with adjacent edges u = 6i + 4j + 2k; v= 2i+ 2j + 4k; w = 2i + 6k +…

A: Let's find.

Q: Verify Stoke's Theorem. F=, C'is the boundary of the paraboloid z = x² + y² lying pelow z = 1 plane.…

A: To verify Stoke's theorem for the below function. F=y,−xz,xz2

Q: The solid enclosed by the sphere x² +y² +z? = 4a* and the planes z = O and z = a.

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Q: 1. Consider the parallelepiped with adjacent edges u = 6i + 4j + 2k; v= 2i + 2j + 4k; w = 2i + 6k +…

A: To answer the given questions using the given details.

Q: A hole is drilled through the center of a sphere x?+y² + z² = R,?, leaving a ring-shape solid. If…

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Q: In the (yz) plane consider the polygon A of vertices (3,0) (4, 2) (5, 0) and (4,-2) The volume of…

A: The volume of the solid of the revolution can be calculated using Pappu's theorem. The formula for…

Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? = 32 and the coordinate…

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Q: Draw the solid of revolution obtained by rotating the given plane region about line L. Which figure…

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Q: Let E be the solid ellipsoid bounded by the surface y? = 1, a2 62 c2

A: Given that, the solid ellipsoid bounded by the surface x2a2+y2b2+z2c2=1 The volume of the unit…

Q: b) let R be the disk in the xx-plane centered at the point (0.2) and with radius 2. Calculate JJ₁…

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Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

Q: Let G be the solid in the first octant bounded by the sphere 2x? + 2y? + 2z? and the coordinate…

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Q: Find the area of the part of the sphere r? + y + z² = 4 that lies within the first octant and inside…

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Q: 29. Using Pappus' theorem, the value of the y-coordinate of the centroid of a uniform semi-circular…

A: Pappus centroid theorem states that the volume V of a solid of revolution generated by revolving a…

Q: From the stereographic projection of the Lobachevsky plane from the north pole (0, 0, -R) on disk D…

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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: When the shaded region is rotated around the y-axis, a horizontal strip of vertical span Ay creates…

A: We have to find the volume V of the solid obtained by rotating the region bounded by the given…

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: The set E is part of the third octant which is enclosed by the sphere r+y +z = 3. In spherical…

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Q: (a) Evaluate (x? + y?)" dA where R is the unit disk r2+ y? < 1.

A: The solution is given as

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: Pr. #1) || zdA, Dis the triangular region with vertices (0,0), (4, 2), and (0,6) (aketch D on the…

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Q: rclockwise, that encloses disk R in the plane. neck Answer. 71

A: Given : F = &lt;5x^6y, 8xy^2 + 4x^7&gt;

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y? – x² + 4 and above…

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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: SSx x dA; R is the portion of the disk x + ys 16 in the second quadrart

A: I use polar conversion method

Q: Express the area of the given surface as an iterated double inegral in polar coordiantes, and then…

A: We need to find the surface area in the portion of the sphere x^2+y^2+z^2=16 between the planes z=1…

Q: 3. If D is the centroid of APQR, PA = 17, BD = 9. and DQ = 14, find each missing measure. %3D P a)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the surface area of the portion of the sphere x² + y? + z² = 8 that is cut out by the cone z =…

A: The objective is to find the surface area of the portion of the sphere x2+y2+z2=8 that is cut out by…

Q: A hole is drilled through the center of a sphere x² + y² + z? = R,², leaving a ring-shape solid. If…

A: given sphere x2+y2+z2=R2s and a drill of cylinderical shape x2+y2=R2d use polar coordinate to…

Q: 1 2 n- 1 n 1 lim en+en+e n +en n 0o n

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Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

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Q: Evaluate the surface integral s F. dS where F (-x, -4z, 4y) and S is the part of the sphere x? + y?…

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Q: Find the area of the part of Sphere x? + y? + z? = 16 that is outside the paraboloid z=16 – x² – y?.…

A: The part of the object outside another object can be obtained by first calculating the intersection…

Q: Let E be the solid enclosed by the sphere a? + y? + (z – 3)2 = 9 above the plane z = 2. The volume…

A: Given, Sphere : x2+y2+z-32=9Plane , z=2∫∫∫dV=∫02π∫0a∫bcρ2 sinϕ dρ dϕ dθ To find : Value of a,b,c

Q: 1 %3D 12 27

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