Use a computer as a computational ald. Use 0+1+0+1+44-2, +4-1-4-0 to approximate the solution of Leplece's equation at the interior points of the given region. Use symmetry when possible. (Assume ce(0, 0)) 011- eBook N(D, 2-0, 0(2,y)-0, 0
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- Part A: IG=27, Find CI Part B: In △RST,X△RST,X is the centroid. If SX=14,SX=14, find XWXW and SW.A median of a triangle is a segment connecting a vertex of a triangle to the midpoint of the opposite side. Let T be the triangle with vertices (0, 0), (a, 0), and (c, d). Prove that the centroid of triangle T is two-thirds of the way from each vertex to the opposite side.Consider the model with a single regressor. This model also can be written as Yit =β0 +β1Xit +δ2B2t +...+δTBTt +γ2D2i +...+γnDni +ui,where B2t=1if t=2 and 0 otherwise, and D2i = 1 if i = 2 and 0 otherwise, and so forth. How are the coefficients (β0, δ2,..., δT, γ2,..., γn) related to the coefficients (α1,..., αn, λ1,..., λT)?
- Gauss’s law says that the electric flux through any closed surface is equal to the total chargecontained in the closed surface divided by the permittivity of free space, E0Find the charge contained inside a cube with vertices at (±1, ±1, ±1) when E =< x, y,z >Four particles are located at points (1,1), (2,4), (3,1), (4,1). Find the moments Mx and My and the center of mass of the system, assuming that the particles have equal mass m. Mx= My= xcm= ycm= Find the center of mass of the system, assuming the particles have mass 3, 2, 5, and 7, respectively. xcm= ycm=hilber space hermitian part 2 b c d e
- using laplace transformation the solution of the following D.E y''+y=3 with y(0)=0 , y'(0)=2 is:14 - Find the center of gravity M of the three dimensional homogeneous wire ABCD by using the coordinate set (x, y, z) in the figure. The dimensions of the wire are a = 24 cm, b = 36 cm. The coordinates of the AB part of the homogeneous wire in the x, y and z axes are given in the following:A) (36; 24; 12)B) (18; 12; 0)C) (36; 24; 0)D) (36; 12; 24)E) (36; 12; 0)Explain why fitting a conic through the points P1(x1, y1), . . . , Pm(xm, ym) amounts to finding the kernel of an m × 6 matrix A. Give the entries of the ith row of A. Note that a one-dimensional subspace of the kernel of A defines a unique conic, since the equations f (x, y) = 0 and k f (x, y) = 0 describe the same conic.
- a. Find a parametrization for the hyperboloid of one sheet x2 + y2 - z2 = 1 in terms of the angle u associated with the circle x2 + y2 = r2 and the hyperbolic parameter u associated with the hyperbolic function r2 - z2 = 1. (Hint: cosh2 u - sinh2 u = 1.) b. Generalize the result in part (a) to the hyperboloid (x2/a2 ) + (y2/b2 ) - (z2/c2 ) = 1.3. Find the coordinates of the centroid of the triangle enclosed by x = 1, y = 0,and y = 4x.MTH 261 SECTION 2.4 220 alt DELTA COLLEGE Consider the points A(3, −1, 10), B(−1, 4, 1), C(5, −2, −1), and D(1, 1, 1) (a) Determine the volume of the parallelepiped P with adjacent sides−→ DA,−→ DB, and−→ DC. (b) To the nearest tenth of a unit, calculate the distance from D to the plane determined by A, B, and C. (c) To the nearest tenth of a unit, calculate the distance from A to the plane determined by D, B, and C. (d) To the nearest tenth of a degree, calculate the measures of the three acute angles between each pair of parallel faces of P. Solution: