Use Lagrange multipliers to find the point on the plane x 2y + 3z = 6 that is closest to the point (0, 2, 4). 5 9 71 14' 7 14 (x, y, z) = Additional Materials M eBook Submit Answer Submit Assignment Save Assignment Progress

Q: Using Lagrange Multipliers, find the points on the surface x(y^2)(z^3)=2 that are closest to the…

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Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

Q: M(3, 5) is the midpoint of PP2, where P has coordinates (0, 1). Find the coordinates of P2.

A: M (3,5) is the mid point of P1P2¯ , where P1 has coordinates (0,1).we have to find the coordinates…

Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A: We have given the equation of sphere: x2 + y2 + z2 = 36 and plane: 2x + y − z = 2 We have to find…

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. (Hint: Use Lagrange multipliers.)

A: Given plane is, 3x+2y+z=6, we need to find the point on this plane closest to the origin.

Q: Use Lagrange multipliers to find the distance from the point (3, 0, -1) to the plane 6x - 4y + 7z +…

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Q: Use Lagrange multipliers to find the point on the plane x-y+z=7 closest to the point (4,5,1).

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Q: Evaluate ff. yz do, where S is the part of the plane z = y + 3 that lies inside x? + y² = 1.

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Q: iewform?hr_submission. W Y 1 point ZX is the perpendicular bisector of WY, WZ = 4n – 13. and YZ = n…

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Q: Use Lagrange multipliers to find the points on the cone z2 = x2 + y2 that are closest to (8, 2, 0)…

A: Given: Equation of the cone: z2 = x2 + y2 Given point: (8, 2, 0)   To find: The points on the cone…

Q: 5. Find the coordinates of the points on the cross sectional curve of the intersection of the cone 2…

A: Given equation of cone and plane is  z=x2+y2⇒fx,y,z=z2-x2-y2…

Q: Use LaGrange multipliers to find the coordinates of the points on the surface z2 = z² +y² which are…

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Q: Find a plane through P0(2, 1, -1) and perpendicular to the line of intersection of the planes 2x + y…

A: The directional vectors of the planes are given by (2,1,-1) and (1,2,1)The directional vector of the…

Q: Use Lagrance Multipliers, and find the point P(r, Y, z) closest to the origin on the plane 2x + y –…

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Q: A. LIKE is an isosceles trapezoid. Given: mz1 = 32° and mz 2 = 35°. Find 1. m23 = 2. m25 3D 3. m26 =…

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Q: (a) Use the method of Lagrange multipliers to find all candidates of the point(s) on the surface x2…

A: Lagrange multiplier.

Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: • Find the area of the portion of the Sphere x² + y² + 2²² = 9 between the planes Z=1 and 2 = 0.…

A: The given equation of  plane is x2+y2+z2=9. The polar coordinates are x=rcosθ & y=rsinθ. The…

Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let (x,y,z) be the point which is closest to the point (2,4,0) .

Q: Find the average height of the paraboloid z = x + y over the square 0sxs2,0sys2. The average height…

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Q: Evaluate x² zdS, where S is the part of the plane z = 2 + 3x + y above the rectangle [0, 2] × [0, 5]

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Q: Using Lagrange multiplier, find the minimum value of f(x,y) = 3x +ly on the circle x2 + y2 = 1. Give…

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Q: Evaluate (y + Vx) dA, where R is the triangular region with vertices (0, 0), (1,0), and (0, 1). R

A: The solution starts from step 2. The information presented below will be helpful to understand the…

Q: Find the point on the plane 3x + 2y + z = 6 closest to the origin. Hint: Use Lagrange multipliers.

A: The given plane: 3x+2y+z=6 To find the point on the plane 3x+2y+z=6 closest to the origin. Solution:…

Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin…

A: To find the points on the given surface that are closest to the origin. We want to minimize the…

Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse 25 = 1…

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

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Q: e. The plane through Po(2, 4, 5) perpendicular to the line x = 5+ t, y = 1 + 31, z = 4t

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

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: Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).

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Q: Evaluate x2 zdS, where S is the part of the S plane z = 1+ 2x + 3y above the rectangle [0, 2] × [0,…

A: We have to evaluate ∬Sx2zdS, where S is the part of the plane z=1+2x+3y above the rectangle 0,2×0,3.…

Q: e find aplane through Po (2,,,-1) and Perpendicular to the line of Intersection of the planes…

A: Equation of plane

Q: // 2° zdS, where S is the part of the plane z = 4+ 2æ + y above the rectangle [0, 5] × [0, 3]…

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Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

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: Use Lagrance Multipliers, and find the point P(r, y, 2) closest to the origin n the plane 2r +y-z-5…

A: Given,

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: By using the Lagrange multiplier, find the point on the plane 2x + py – qz = r which is closest to…

A: We have to find point on the given plane which is closest to the origin by using the Langrages…

Q: Fit a least-squares parabola having the form y = a + bx + cx² to the given data. 1.8 3.1 4.9 5.9 7…

A: Calculate the necessary values in the following way:   x y x×y x2 y2   1.2 4.5 5.4 1.44 20.25…

Q: + + Find the area of the portion of Sphere x² + y² + 2 = 9 betw= the planes Z=1 and 2 = 0. Draw

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Q: nsider the parallelepiped with adjacent edges u = 6i + 7j +k v = i+j+5k w = i+ 7j + 9k d the volume.

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Q: Find the maximum and the minimum values of f(x,y,z) = 2x - 7y+7z on the sphere x² +y2 +z? = 102. ...…

A: Given f(x,y,z)=2x-7y+7z on the sphere x2+y2+z2=102

Q: quatin tov the tangrnt plane to Hhe surfece 2:x +y at point PCal,6). Find the

A: Given that, Plane of surface is following, z = x2 + 2y2 and Point is, (x0, y0, z0) = (2, 1, 6) We…

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: Use Lagrange multipliers to find the shortest distance from the point (7, 0, −9) to the plane x + y…

A: The square of distance function is given by fx,y,z=x-72+y2+z+92 and the constraint is…

Q: Maximize f(x, y, z) = 2x + 7y +9z on the sphere x + y+z = 67. Additional Materials eBook

A: f(x,y,z) = 2x + 7y + 9z and g(x,y,z) = x2 + y2 + z2 Approach:We will make use of the method of…

Q: Evaluate //R V2x(y – 2x)dA where R parallelogram on the xy-plane with vertices (0, 0), (0, 1), (2,…

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Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse x² 1² +…

A: The solution is given below

Q: Evaluate | x° zdS, where S is the part of the plane z = 2 + x + 4y above the rectangle S [0, 4] ×…

A: It is given that S is the part of the plane z = 2 + x + 4y above the rectangle [0, 4] * [0, 3]…