Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse that is formed by the intersection of the cylinder x? +y² = 16 and the plane y + z = 4

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

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Q: find the center of mass of a thin plate of constant density d covering the given region. The region…

A: Given: y=2x2-4x and y=2x-x2 Graph:

Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y-2)² = 2x -2, S4: x = 0, S5: y =…

A: To find- The Solid bounded by the surfaces S1 : 2x + 3z = 6, S2 : y = 2, S3 : y - 22 = 2x - 2, S4 :…

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Q: A point moves along the intersection of the elliptic paraboloid z = x² + 3y² and the plane y = 1. At…

A: Point moves along the intersection of the elliptic paraboloid z=x2+3y2 and the plane y = 1. We have…

Q: 1. Under the paraboloid = 3z2 + y? and above the region bounded by y = x and r= y² – y

A: Find point of intersection of:  y=xx=y2-y y=y2-yy2-2y=0y=0,2

Q: d. .2 The solid bounded by the cylinder x+y = 9 and the planes z = 0 and z = 3- x. %3D

A: The solution of the problem is given in the next steps.

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y + 18z on the elipse…

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Q: 39.) The solid bounded by the cylinder x+y² = 9 and the planes z= 0 and z = 3 - x. 40

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Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

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Q: The surface area of the solid generated by revolving the straight line 2y = x+1 bounded by x-1, x 3…

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Q: 1. Find the minimum distance from the point (0, 0, 0) to the plane x- y+z = 3.

A: perpendicular distance

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A: Here is the solution of the given problem

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y+ 18z on the elipse…

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Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

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Q: 3 Find the abscissa of the centroid of the region between the parabola y = 9 − x2 and the line y…

A: Given :The parabola y=9-x2 and the line y=2-2x from x=0 to x=2.To find :The abscissa of the centroid…

Q: The path C is a line segment of length 13 in the plane starting at (4,5). For f(x,y)=5x+12y,…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A: Using Lagrange Multipliers with Two Constraints

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A: Given that, A solid is bound by the surfaces, S1: -2(z-2)=y2S2: x=5-2zS3: x=0S4: y=0S5: z=0

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Q: The value of the integral (inage 1). where C is the closed curve 4x2 + 5y2= 7, 3x + 2y − 9z = 5.

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Q: Evaluate the solid bounded by 2x+z=2 and (x-1)2+y2=z.

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Q: The solid bounded by z = x, z = 2 – x², z + y = 3, and y = 0

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Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y − 2) 2 = 2x − 2, S4: x = 0, S5:…

A: Consider the surfaces  S1: 2x + 3z = 6, S2: y = 2S3: (y − 2)2=2x − 2, S4: x = 0S5: y = 0S6: z = 0

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Q: Find the abscissa of the centroid of the region between the parabola y = 6 − x2 and the line y = 1 −…

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Q: 2 : Use Lagrange multipliers method to show that the maximum value of f(x, y, z) = x²y²z² on the…

A: In lagrange method, the Critical points are the points that cancel the first order partial…

Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

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Q: The solid bounded by the surfaces S : -2(: – 2) = y² S2 : 1 = 5– 2y S3: r=0 S4 : y = 0 Ss : z = 0…

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Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

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