Prove that the centroid of any triangle is located at the pointof intersection of the medians. [Hints: Place the axes so thatthe vertices are (a,0) ,(0 ,b )  and (c,0). Recall that a medianis a line segment from a vertex to the midpoint of the oppositeside. Recall also that the medians intersect at a pointtwo-thirds of the way from each vertex (along the median)to the opposite side.]

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: HW Find the valume af theSelid beunded abave the Planc 2= x+2y+2,belw the X-y plane and Taterally…

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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…

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Q: Every triangle has a balancing point, called the centroid. O True O False

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Q: The half-space consisting of the points on and below the xy-plane

A: Concept:

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Q: EXERCISE 4.3. Let S be a connected regular surface such that the image of the Gauss map is a great…

A: The answer is given below thank you for the question upvote is really appreciable

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Q: A. Use the figure on the right to name each of the following: 1. three collinear points 2. three…

A: A) 1) Collinear points are the points which are on the same line. Hence 3 collinear points are A , P…

Q: Let z E C. Draw the following regions on the xy-plane. Justify your work. (a) {z E C : 4 < |z| < 6}…

A: Given: a) z∈ℂ: 4&lt;z&lt;6 b) z∈ℂ: z-22=4

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Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

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Q: Find the coordinates of the centroid (to the nearest 0.01 in.) of the uniform flat-plate machine…

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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,…

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Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

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Q: m

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A: Let's find.

Q: A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that…

A: A rectangle ℛ with sides a and b is divided into two parts ℛ1 and ℛ2 by an arc of a parabola that…

Q: Consider the figure below, point D is the centroid of △ABC with DF = 4x − 1 and BD = 6x + 4. Use the…

A: Figure of triangle is given, where point D is centroid with DF=4x-1 and BD=6x+4.

Q: The tangent planes to the ellipsoid =1 meets %3D 62 the coordinate axes in points A, B and C. Prove…

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Q: Let E be the region in the plane between the two ellipses 4x² +9y? = 1 and 4x2 + 9y2 = 4. Evaluate…

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Q: Let S be the triangular prism with the triangular face in the plane y-3 removed. Let C be the…

A: Given curl F→=xi^-yj^ and the given plane is y=3 So, ϕx,y,z=3j^ Therefore, calculate curl F→·n^ curl…

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Q: find the centroids of the triangleswhose vertices appear . Assume a, b &gt; 0. (0, 0), (1, 0), (0,…

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Q: Find the points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

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Q: Which of the following represents a plane surfac whose x-, y-, and z-intercepts are a, b, and c…

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Q: Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, –…

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

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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: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians,…

A: We can find the centroid as below using the required formula.

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A: and point (1,0,0)

Q: 6. Find the centroid of each of the given plane region bounded by the following curves: y? = x³, y =…

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Q: •Consider the graph of z = f(x, y) = 2x2 + y? which is a paraboloid. The equation of the plane…

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Q: Consider AB in the coordinate plane below. 10 7 5 4 3. 2 A B 6 7 89 10 10-9 -8 -7 -6 -5 -4 -3 -2 -1…

A: i am going to solve the given problem by using some simple geometry to get the required result.

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

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A: Definition used:

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A: We will use basic knowledge of vector calculus.

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Q: 2 Let w = z². Find the image of the first quadrant in z-plane

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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…