Find the polar of the pyramid in R3 which is the convex hull of the points: {(0, 1, −1),(0, −1, −1),(1, 0, −1),(−1, 0, −1),(0, 0, 1)}. (NOT about polar coordinates, this is convex analysis)

Q: quation of the hyperb

A: Given,      z=-16

Q: (a) Find and identify the traces of the quadric surface x2 + y2 - z2 = 36 given the plane.

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

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

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Q: On a plane equipped with a polar coordinate system, what is the area of ​​the triangle with vertices…

A: In polar coordinate system x=rcosθy=rsinθ

Q: Let T be the tetrahedron with vertices (2, 0, 0), (0, 3, 0), (0, 0, 5) and the origin. Write (a, y,…

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Q: Find a parametrization of the hyperboloid of two sheets (z2/c2) - (x2/a2) - (y2/b2) = 1.

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Q: Find the centroid (ã, §) of the triangle with vertices at (0, 0), (2, 0), and (0, 8). || 18

A: Recall: Centroid of a Triangle with vertices are (x1,y1) , (x2,y2) and (x3,y3) is…

Q: Find the centroid (ĩ, g) of the triangle with vertices at (0, 0), (10, 0), and (0, 9).

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Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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A: Consider the equation of the surface, z = 8 - x2 - y2

Q: C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0,…

A: Given : Vertices : (5,-5) , (5,5), (0,10), (-5,5), (-5,-5) and (0,-10) Integral given :…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: EXAMPLE 2 Find the area of the part of the paraboloid z = x + y' that lies under the plane

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Q: Find the centroid (x, y) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 18 15 X=

A: Consider a triangle with vertices at (0,0),(10,0) and (0,2)

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<0.…

Q: Prove that the centroid of a parallelogram is the point of intersection of the diagonals of the…

A: The vertices of the parallelogram are (0, 0), (0, a), (b, c), and (b, a + c)

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: Find the centroid of the region in the polar coordinate plane defined by the inequalities 0<=…

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Q: Find the area of the portion of the surface z = 8x+4y that lies above the triangular region with…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 1. Find the area of the part of the surface z = a? + 2y that lies above the triangle with vertices…

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Q: Compute the orthogonal projection of point A H coordinates (2,0) onto the Set M (the closed unit…

A: Hint: The formula of orthogonal projection of a point w on a set Aa1,a2,a3,... is…

Q: 3. Evaluate ff(+2y- )dS where S is the portion of z = 5= 2y + that lies over the triangle in the…

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Q: This exercise refers to the hyperbolic paraboloid z = y² - x². (a) Find an equation of the…

A: Note: Hi! Thank you for your question. As per the guideline we can solve three subparts at a time in…

Q: Find parametrizations The portion of the paraboloid z =-(x2 + y2)/2 above the plane z =-2

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Q: G' are centroids of the two triangles ABC änd A' B'C! Show that AA' + BB' t CC =3GG' %3D

A: If G and G` be the centroids of the triangle ABC and triangle A`B`C` respectively then show that,…

Q: C is counterclockwise around the rectangle with vertices (0, 0), (5, 0), (5, 3), (0, 3) (a) directly…

A: The given integral is: ∮xy dx+x2 dy C is the counterclockwise around the rectangle with vertices…

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: The part of the plane 2x 5y + z = 10 that lies above the triangle with vertices (0, 0), (0, 6), and…

A: Double integration need to be done.

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A: Note that r ≥ 3 Hence, the area of interest will be area outside the circle r = 3. Also π ≤ θ ≤ 2π…

Q: 5. What are the coordinates of the centroid of triangle FGH: F(6,-1), G(12,4), H(15,-2)?

A: follow next step

Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

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A: Given points are         0,0,4,0,&0,6      And centriod G ?      centriod G= x1+x2+x33…

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A: As we know that for a figure or object that has rotational symmetry, the angle of turning during…

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A: Explained below

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Q: Find the centroid of the parabolic spandrel shown in the figure.

A: We have given a diagram of parabolic spandrel;

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A: We can find the vertices as below

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Q: Find the area of the surface. The part of the paraboloid z = 1 - x² – y2 that lies above the plane z…

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Q: Sketch the surfaces HYPERBOLOIDS z2 - x2 - y2 = 1

A: Sketch the surfaces HYPERBOLOIDS z2 - x2 - y2 = 1

Q: A plane meets the coordinate axes in A, B, C. If the centroid of aAl Show that the equation of the…

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Q: Find the centroid (ã, g) of the triangle with vertices at (0, 0), (5, 0), and (0, 9). y=

A: In the question it is asked to find centroid of the triangle with coordinates (0,0), (5,0) and…