{[]-0=y<{u{[;} In R², let S = Describe (or sketch) the convex hull of S.

Q: In AMNP, T is the centroid. If MR=30 find MT. N R T M S

A: We are given that T is the centroid and MR=30. We know that the centroid divides each median in a…

Q: Determine a scalar s such that A2x = sx when Ax = rx.

A: To determine a scalar s such that A2x=sx when Ax=rx Given Ax=rx On multiplying both the sides by…

Q: Let f(z) = E-oo Qn (2 – zo)" in the annulus 0 < |z – z0| < R. Give the definition of zo being a…

A: Consider the given information.

Q: In AABC, X is the centroid. If CW = 15 , find XW. %3D

A: Given,           In △ABC, X is the centroid and CW¯=15

Q: find the projection of v onto u.

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Q: Consider AABC with its centroid at point G and median at BH. What is the length of GH if BG = 3x + 4…

A: Given Data: The length of BG is: BG=3x+4 The length of GH is: GH=x+10 The ∆ABC with its centroid at…

Q: 6. For any closed surface S, prove that || CurlF.N dS=0.

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Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.

A: We have to find the distance d from y to the plane in R^3.

Q: 1 : : Evaluate F dS whereF = (r",y",) and S is the solid bounded by the ry plane and the elliptic…

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Q: Describe the convex hull of the set S of points in R² that satisfy the given conditions. Justify…

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Q: If point N is the centroid of AHIJ, IM = 18, KN = 4, and HL = 15, find JN. %3D %3D %3D K /N/

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Q: 10. Find all the planar and hyperbolic points on the surface o(u, v) = u-3uv².

A: A point on a surface is said to be a hyperbolic point if the Gaussian curvature at p,i.e., κp&lt;0.…

Q: Let M be an elliptic paraboloid z = y² + 2?. (A) "Compute the Gauss map and the shape operator. (B)…

A: Answer for sub question a: Given x=y2+z2 A parametrization is given by: Xu,v=u2+v2,u,v Then,…

Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

Q: The parametric form of the solutions of the PDES Uy + u u z = 0 , u(x,0) = -x is

A:

Q: 6. Use Stoke's Theorem to evaluate fF dr, where F =, and C is the part of the paraboloid z = 4 - x2-…

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Q: Show that, in the triangular region with vertices (0,0), (1,0) and (1,1) the following double…

A: Double integral

Q: . Solve the following Dirichlet problem on a disk V²U(r,0) = 0, 0<r<1, -asosa U(1,0) = 0, - <o< T.

A: This question based on Dirichlet problem on a disk from partial differential equation.

Q: In ANPQ, U is the centroid. If NS=15 find US. R S U

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Q: | Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2). (0, 2). Use Green's…

A: greens theorem

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

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Q: Show the following results used in the class: S =(z1 - E1)² = (zn - n)In = %3D %3D S (-)3D %3D iml…

A: Given that Sxx = ∑xi-x12       = ∑i=1nxi12 + x12 - 2xi1·x1= ∑i=1nxi12 + nx12 - 2xi1·x1 ∑i=1nxi12=…

Q: 3. Consider the ra greater across z =1-r² - y² plane and the s and a paramet

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Q: Find a conformal map that takes {z|0<argz <} onto the unit disk.

A: Given that a conformal map that takes z | 0&lt;argz&lt;π8 onto the unit disk.

Q: Let M be an elliptic paraboloid a = y? + z². Compute the Gauss map and the shape operator. Find k…

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Q: 3) . Find the centroid of the upper half of a sphere of radius 1, that is, of the set of points in…

A: Given the upper half of the sphere with radius 1, that is x2+y2+z2=1,z≥0. Find the centroid x¯,y¯,z¯…

Q: Which of the centroid(s) are trivial

A: Note that : A region if is symmetric about y-axis then x-coordinate of the centroid of the region is…

Q: Let E be the solid parallekepiped with vertices Co,0,o).(LLO).co,l,3),(1,0,). C1,2,3),Cし,4).(2,1,1)…

A: Here, vertices are given in 3D. So, for taking limits of X and Y, we'll look for the projection of…

Q: The inverse image of the disk | z |< under T(z)=is z+1

A: Given: Disk z&lt;12. To find: Inverse image of disk under Tz=zz+1.

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,3,0), and (0,0,5)

A:

Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: 2. Show that the xy plane W = (x, y, 0) in R³ is generated by: (i)u = 2 and v= |1| (ii)u and v = 3…

A: Given the plane: W=(x,y,0) in ℝ3.Let (x,y,0) be any element from W. For a and b in ℝ, we…

Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 5, 0), (0, 0, 5) and the origin. Write f(x, y,…

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Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

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Q: In space coordinates, the xy plane consists of all the points of the form O (0, y, z) O (X, y, z) O…

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Q: ) For the vector space C[0,1], define the inner product (f,g) = , f(x)g(x)dx. Let f = x + 1 and g =…

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Q: Suppose {u, v, w} is an orthonormal set in R". Prove that u +v is not orthogonal to v + w.

A: The set {u, v, w} is an orthonormal set. Therefore, the modulus of each vector is 1. The vectors u,…

Q: Let H be the set of all points in the second quadrant in the plane V=R^2. That is, H={(x,y) | x ≤ 0,…

A: Here in the question H be the set of all points in the second quadrant in the plane V=R2. That is,…

Q: Find the area of the portion of the paraboloid x = 4 - y2 - z2 that lies above the ring 1&lt;=y2 +…

A: Given surface is  The required surface area is given by where

Q: In R, let S be the piece of the plane 3x + 3y + 3z = 3 that lies in the first octant, oriented…

A: Given S is the piece of the plane 3x+3y+3z=3 that lies in the first octant oriented upward. The…

Q: Let D be the solid region bounded above by z = -3/x² + y² and below by z = -3. Then the projection…

A: Given Region D is bounded  above by cone  Z=-x2+y2and bounded the  below by  plane z=-3

Q: 3) Let D be the region enclosed by the two paraboloids z = 4 + x² + y² and z = 10-x² - y². Then the…

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Q: Find %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

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Q: Given: AB = BN; NU = UT ; AG GT Prove: M is the centroid of AANT U B %23 A G

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Q: 6. If S is the surface of the sphere x + y² + z? = 9. Prove that curl F- ds = 0. %3D

A: Solution:-

Q: Find the average haight of the Paraboloid z- xry* over the square osx <2, osd<2

A: We need to find the average height of paraboloid

Q: Q1- Determine the coordinates of the centroid of the area.: (1, 1)

A: We need to find the x coordinate and y coordinate of the shaded region which is bounded by two…

Q: Find the centroid (, j) of the triangle with vertices at (0, 0), (8, 0), and (0, 9). x=

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Q: 2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2),…

A: The double integral is an integral with respect to two different variables the integral of a…