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: 2. An is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two…

A: We know that, The sum of distances to any point on the ellipse x,y from the two foci c,0 and -c,0 is…

Q: in 4 method ТВС- тво-1 Example 1.8.6 Find the p sic equations of the plane that passes through the…

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Q: Use the Lagrange multiplier method to find the point on the surface z = Iy + 10 that is closest to…

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Q: A perpendicular line is drawn from point P(1,2,1) to the plane -2x + 4z = 4 and meets the plane at…

A: Given that a perpendicular line is drawn from point P(1,2,1) to the plane -2x+4z=4 and meete the…

Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: 6. Quadrilateral STUV with vertices S(-4, 2), T(-2, 6), U(1,7), and V(4, 1) in the x-axis. nioM S'L.…

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Q: Given that the system ry² + zu + v² = 3 z+ 2y uv zu + yu – ryz = 1 at (u, v) = (1, 1)? can be solved…

A: Solve

Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

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Q: Determine the Eq.  of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

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Q: Find the line of intersection of the planes 2x – y+ 3z = 1 and -r + 3y + z = 4. Lütfen birini seçin:…

A: Given planes are 2x−y+3z=1 and −x+3y+z=4. We have to find the line of intersecting of the plane…

Q: Soru 4 Find a plane through the points P(1,2,3), Q(3,4,1) and perpendicular to the plane x+3y+5z=7.…

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Q: 1. Find the area of the triangle in the R2 plane whose vertices are given by (0,0), (–1,4) and (7,…

A: 1. The Area of triangle with vertices (x1,y1),(x2,y2),(X3,y3) is given by formula : ∆…

Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

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Q: 3. Among all the points on the graph of z = 10 – x² – y² above the plane x + 2y + 3z = 0, find the…

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

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Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

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Q: (1,1, 1), ид points in the xyz-space, and S = {u1, u2, U3, U4}. 7. Let ui = (1,4, 2), и2 — (0, 3,…

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Q: Use the least squares method to fit a curve f(x)=ax² + b TO THE POINTS EMPIRICAL (0,1.1), (1,1.7),…

A: Given the points empirical  (0,1.1),  (1, 1.7),  (2, 5.2) We need to fit a curve fx=ax2+b using…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: 2.2 Find the maximum and the minimum values of f(x,y,z) = 5x – 3y +7z on the sphere x +y +z = 83. 2

A: Here we find the maximum and minimum value of f(x, y, z)

Q: Find the distance between the planes. 5x-2y+z-4 0, 5x-2y+z+6= 0

A: Given,  Equation of Plane 1: 5x - 2y + z - 4 = 0 Equation of Plane 2: 5x - 2y +z + 6 = 0 From the…

Q: 4- Derive the least square equations for fitting a curve of the type b y = a x² += To a set of n…

A: From the given information. The least squares equation is as follows. The x y data is as follows.

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: 5. Evaluate 2XZds where S is the part of the plane - 2x +4+Z =3 over the triangle with bounds…

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Q: 9. Find the equation of the plane through P(1,1,4) that is parallel to the plane x+ 5y – z + 8 = 0

A: The scalar equation of parallel planes differ only by a constant Therefore, equation of the required…

Q: Minimize c = s + t + u subject to 3s + 2t + u ≥ 48 2s + t + 3u ≥ 48 s + 3t + 2u ≥ 48 s ≥ 0, t ≥ 0, u…

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Q: 1. 2. The area bounded by y = = -(x - 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about…

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Q: Determine a direction vector of the line of intersection of the two planes 3x + 2y + 5z = 4 and 4x -…

A: The planes are given as- 3x+2y+5z=4........14x-3y+z=-1.........2 Solving both equations for x-…

Q: 4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest…

A: Given: The plane equation is x+y-z=5 and the point is -3, 5, 4.

Q: Z is a complex variable, z=x+iy

A: The z is complex variable with z = x + i y , and the given vertices are (0,0),(1,0),(1,1) and (0,1).

Q: 3. * Find f -6xydA over the triangular region D with vertices (0,0) (2,0), (0, 4) -16 -8 -68 16 68 8

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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: 5. Parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,-4) over the line y = x ty 6.…

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Q: 9 find the cqu. f Plane that Contains the two line Ś: X-1=3+ 6=そ X=リニで-4 and Passes through origin?…

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Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

Q: 4. y=4-x² , y=3x and the x-y plane is given by the fol expresions.

A: We have to choose the correct option according to the given information

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

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Q: 5. Quadrilateral WXYZ with vertices W(0, -4), X(13, 0), Y(9, -12), and 2(5, -12); scale factor: k -…

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Q: 5) An equation of the of the plane passing through the points P(0,2,1), Q(2,1,2), and R(3,3,1).

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Q: 8. Check if the two lines given below are coplanar or not: x = 1+t, y =1+2t, z = 3 +t and a = 3 + s,…

A: We have to check weather the given lines are coplaner are not.

Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

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Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

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Q: 12. Use Lagrange multipliers to find the point(s) on the intersection of the sphere r²+y²+z² = 16…

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Q: Minimize c = s + t + 2u subject to s + 4t + 2u ≥ 95 4s + t + 3u ≥ 95 s ≥ 0, t ≥ 0, u ≥ 0. c= (s, t,…

A: the given simplex problem is as follows  Minimize c=s+t+2u subject to…

Q: Find the shortest distance from the point (2,0,–3) to the plane x + y + z = 1. . Use Lagrange…

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Q: The line of intersection of the planes 2x +y - z= 4 and 4x – y+3z = 2 has equation %3D O a) (x, y,…

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Q: The pyramid is bounded below by the xy plane above by the plane x+y+z=3 and on the sides by the xz-…

A: According to the given information it is required to set the double integral to find the volume of…

Q: 8. Check if the two lines given below are coplanar or not: x = 1+t,y =1+ 2t, z = 3+t and x = 3+ s, y…

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