46. A least squares plane The plane z = Ax + By + C is to be "fitted" to the following points (xk, Yk, Zk): (0, 0, 0), Find the values of A, B, and C that minimize (0, 1, 1), (1, 1, 1), (1, 0, – 1). 2(Axx + Byk + C – z)², k=1 the sum of the squares of the deviations.

Q: Which of the following is the equation of the plane where x-2y + 32 = 3 and x+y+z=2 and passes from…

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Q: The plane z = Ax+By+C is to be "fitted" to the following points (XkYkZk): (1,-1,0), (-1,-1,1),…

A: Let Put the given points in f we have Now, we have minimize this function.

Q: Find the shortest distance between the lines i-(i+2j+k) + 2(i-j+â)and 7= 2i - j-k + 4(2i + j+ 2k)

A: The equation of the given lines are r→=i^+2j^+k^+λi^-j^+k^r→=2i^-j^-k^+μ2i^+j^+2k^ It is known that…

Q: Find the plane z = a + bx + cy that best fits the data points (0, -4, 0), (5, 0, 0), (3, -1, 1), (1,…

A: Data points 0,-4 , 0 ,5 , 0 ,0 ,3 , -1 , 1 ,1 , -2 ,1 ,1,-5 , -3. To Find: The plane z=a+bx+cy that…

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: b-h(x, y, z)=x+2y,x+y+z=1 and y² + z² = 4, use Lagrange multipliers."

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Q: 3. Find an equation for the plane in R³ containing the points P = (4, 1, 0) Q=(3, 2, 1) R = (5, 1,…

A: The given points are, P=(4,1,0)Q=(3,2,1)R=(5,1,1). Let an equation containing three points…

Q: Find the best quadratic approximation, Q(x, y) of V9 – 6x – 4y for (r, y) near (0,0).

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

Q: A triangular plate occupies the triangular region D with vertices (1,0), (5,0), and (1,4). The…

A: Given vertices of a triangular region are (1,0), (5,0), and (1,4) and the temperature at each point…

Q: 3) Evaluate elz+y)/(z-y) dA where Ris the quadrilateral with vertices (0,1), (0,-2), (1,0), and…

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Q: 3 find +he equation of Hhe plane perpendicul av bo the plane x+24+5z=|| and passing through the…

A: The given plane is,

Q: Valero's 5k Fun Run was held yesterday in the downtown district. The top runner 4 runners (one of…

A: Given 1. Ralph finished 1 minute after the competitor in the white shirt. 2. The competitor in the…

Q: 4. Derive the normal equations for finding the least-squares plane z = Ax+By+C for the N points (x1,…

A: The assumption is that the z component of the data is functionally dependent on the x and y…

Q: nt of intersectic -6 y + 8 = 3 O) カー

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Q: Determine which of the following points are in the plane 3(x − 2) + 2(y + 3) − 4(z − 4) = 0: (a) (0,…

A: To check whether the given points are in the plane or not, substitute given values in the equation…

Q: Find the best quadratic approximation, Q(r, y) of V9 – 6x – 4y for (r, y) (0,0). near

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Q: Use Lagrange Multiplier to find the Point P (x,y,z) closest to the origin on the plane containing…

A: The equation of the plane passing through the three points can be obtained using the matrices. The…

Q: x(t) Find a plane containing the point (6,-4,4) and the line y(t) z(t) 3 + 3t -3+ t 6 + 3t

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Q: The approximated value for e using the Maclaurin series expansion coasidering a true relative error…

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