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

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

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 shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: Find the point at which the line f(z)= 5z + 21 intersects the line g(z) = - 2z -7 %3D -2 11 Submit…

A: To find the intersection point of the lines f(x)=5x+21 and g(x)=-2x-7.

Q: Find the points on the cone z² = x² + y² that are closest to the point (-5,4,0)

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Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

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

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Q: Find the minimum and maximum squared distance between the sphere x² + y² + z² = 9 and the point…

A: We have to find the minimum and maximum squared distances between the sphere x2+y2+z2=9 and the…

Q: Use calculus of variation to derive the shortest line (equation) that joining points (x,y,z) =…

A: Given plane -   7x + 2y + 3z = 7 Parametric equation will be =  (1 - t, 0- 2t, 0 - t) Hence,

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

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

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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Q: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

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

A: Use Lagrange multiplies we find heighest point on the curve ofintersection of the surface cone:…

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 minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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Q: Use Lagrange multipliers to find the minimum distance from the plane x+y+z=5  to the point (5,4,4) .…

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Q: Use the method of Lagrange multipliers to find the shortest distance from the point (-2, –3, 1) to…

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

A: Given:  The equation of cone is z2=x2+y2. To determine: The points on the given cone that are…

Q: Use the Lagrange multiplier method to find the point on the plane 4x +3y +2z = 0 with the smallest…

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Q: Use Lagrange multipliers to find the shortest distance, d, from the point  (1, 0, −2)  to the plane…

A: Lagrange Method:- The method of Lagrange multipliers is a strategy for finding the local maxima and…

Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e5", where the value ab is as…

A: We need to find the minimum value of ab So, let fx,y=xy We need to minimize this function and find…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: Given surface plane: x+y+z=1 Point (8,1,1).

Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e, the value ab is as small as…

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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: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: Find the points on the cone z2 = x² + y² that are closest to the point (-2,2,0)

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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 minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Use the Lagrange multiplier method to find the point of the plane 4x-5y+3z=1 with less distance to…

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Q: Use LaGrange multipliers to find the minimum distance between the origin and the plane x+2y+3z=28.

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

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

A: Let the point on the cone is P(x,y,z). The the distance of the point P from the given point…

Q: find the points on the curve x^2+xy+y^2=16 which one nearest and farthest from the origin using…

A: Let us consider the given function f(x,y) Subjected to g(x,y)=C Solving using Lagrange's multipliers…

Q: Use Lagrange multipliers to find all points on the cone z2 = x² + y² that are closest to the point…

A: The solution has been given below.

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: Use Lagrange multipliers to find the point on the circle x2 + y2 = 1 which is (a) closest to and (b)…

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Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

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: Use the method of Lagrange multipliers to maximize 2x + 3y – 4 on the circle x² + y? = 13

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Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

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

A: Given: Equation of cone is x2+y2-z2=0 and equation of plane is x+2z=4. To determine: The highest…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…