Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces. Cone: x2 + y2 - z2 = 0, Plane: x + 2z = 1

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

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Q: Find the maximum value of f(x,y,z)=15x+y+6z on the sphere x²+y²+z²=441

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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: 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: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: Use the method of Lagrange multiplier to determine the maximum and minimum values of f(x, y) = x* +…

A: Local Maximum and Minimum by using lagranges Multiplayer.

Q: Find the surface are generated when y= (x^3)/5 is revolved about the x axis on the interval…

A: Explanation of the solution is given below...

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

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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: lo.find a pount in the plane x+24+3z =13 neerest to the point (r.1,1) usung the methed of Lagrange's…

A: To find a point on the plane x+2y+3z=13 nearest to the point (1,1,1).

Q: Find the points on the cone z = x+y' that are closest to the point (-2,3,0) 22

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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: Find the surface area of the portion of the bowl z = 8+x² + y that lies below the plane z = 14.

A: Given, z=8+x2+y2 ,z=14 Now substitute z=14 into the given surface for finding the intersection of…

Q: Find minimum distance from the surface x² – y? – z² = 1 (Lagrange Multipliers) to the origin.

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Q: Find the points on the cone z = x² + y that are closest to the point (-3,-2,0) %3D

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Q: Find the maximum value of f(x, y) = x2y9 for x, y ≥ 0 on the unit circle.

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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: Find the area of the vertical wall whose base is the semicircle {(x, y) | x² + y² = 1 and y>0} and…

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Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: Find the area of the surface. The surface cut from the bottom of the paraboloid z = x2 + y2 by the…

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Q: Determine the convexity/concavity property of the following: (ii) f (x, y) = 2x² – y?

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Q: Find the area of the surface cut from the paraboloid x2 + y + z2 = 2 by the plane y = 0.

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Q: Find the area of the surfaces The surface cut from the bottom of the paraboloid z = x2 + y2 bythe…

A: The formula for the surfaces area of the paraboloid above the region R is: A=∬Rzx2+zy2+1dxdy Where,…

Q: Find the point closest to the origin on the curve of intersection of the plane x + y + z = 1 and the…

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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: 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: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = √(x2 + y2).

A: to find the area

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: Find for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if the…

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

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Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

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Q: to find the use lagrange Multiplier Point p (x1s,Z) Closest to the origion on the Plane 2x +y - 2=5…

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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: Find the area of the surface cut from the paraboloid x2 + y2 - z = 0 by the plane z = 2.

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Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

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Q: Find the maximum value of  f(x,y,z)=27x+7y+3z on the sphere x2+y2+z2=81

A: For this question we will use Lagrange multipliers where f(x,y,z)=given function and…

Q: Use Lagrange multipliers to find the maximum and minimum of f(r, y, z) = -r + 2y + 2z on the ellipse…

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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: 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 cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

Q: )الكــره the Sphere OThe Portion of planes z=l x +y+Z² = \6 between the %3D and z=2.

A: Volume of the sphere x2+y2+z2=16 or x2+y2=16-z2 is: V=∫z=12∬x2+y2≤16-z2dxdydz   =∫z=12π16-z2dz…

Q: Q6) (Lagrange Multipliers) to the origin Find minimum distance from the surface r? – y – 2? =1

A: The solution is given below in the next step:

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: Find the point closest to the origin on the curve of intersection of the plane 2y + 4z = 5 and the…

A: We have to find the point closest to the origin on the curve of the intersection of the plane…

Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Sketch the section of the surface at y = 0. z = V4 +x² + y? 6 6 -8 -6 -4 -2 -2 -5-4-3--1, -8 -6 -4…

A: Given query is to the graph of the given expression.

Q: Sketch the surfaces 1. z = y2 - 1 2. 4x2 + y2 = 36

A: Using graphing calculator to sketch themz=y^2-1

Q: Find the minimum distance from the surface to the given point. (Hint: Start by minimizing the square…

A: The minimizing function is, d2=(x-8)2+y2+z2

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…