The centroid of any triangle is located at the point of intersection of the medians. Recall that a median is a line segment from a vertex to the midpoint of the opposite side. Recall also that the media ntersect at a point two-thirds of the way from each vertex (along the median) to the opposite side. Find the centroid of the region shown, not by integration, but by locating the centroids of the rectangles and triangles (from the above information) and using additivity of moments. (x₁) = ([ x ) -3 -2 -1 3 2

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: 8. Evaluate the double integral S Sp y³dA where A is the triangular region with vertices (0, 2),…

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Q: Q3: Find the centroid of the next shaded area. 4m

A: Solution :-

Q: Find the centroid of masses of 3,5,7 units at (3,-2,3), (0,1,2) and (3,2,3) respectively

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Q: Describe and sketch the region of following: Im (z²) = 4 %3D

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Q: Find a primitive root of 29 Solve x6 = 4 (mod 29)

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Q: Find the orthogonal projection y of y = -{-----} = նշ W = Span ŷ Ex: 1.23 2 6 onto the subspace

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Q: Determine where D is the region enclosed (5, 0, 0), (0,3,0), (0, 0, 3), by the tetrahedron with…

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Q: 2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1,…

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Q: b.) show that IR³ - W₁ + W₂. t C.) Find a subspace V such that IR³ =W₁ U.

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Q: find the area betwen two curve-(red)  PLAR CORDINATE SYSTEM

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Q: 3. Fit a curve of the type y bx™ to the following data: (2, 27.8), (3, 62.1), (4, 110), and (5,…

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Q: d positive Z* such that   -Z* and Z* enclose the central 34% of the area under the Z curve. State…

A: P(X<a) = 0.33 the z value when p value is 0.33 is  - 0.44

Q: 3. This problem is about set addition and subspaces. Let d = and dz = and V = span{d}, %3D U =…

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Q: Let P = (1, 0, -1) and Q = (1, 1, 1) and R = (2, 2, 1). Choose S so that PQRS is a parallelogram and…

A: The given vertices of the parallelogram PQRS is P=(1,0,-1) , Q=(1,1,1) and R=(2,2,1)  One of the…

Q: Compute the dot product (7, 6, 8) - (4, 10, 8).

A: To find - Compute the dot product 7, 6, 8·4, 10, 8

Q: Q)Determine the centroid of the shaded portion as shown in the Fig the area with the lines is the…

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Q: In R, let S be the set of all vectors with third component 0. { a S = ER Show that S is a subspace…

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Q: Given points P = (2,1,5), Q = (-1,3,4), R = (3,0,6), %3D

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Q: The net of a cone consists of three different two-dimensional areas. O True O False

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