Find the sum of maximum and minimum values of the function f(x,y, z) = 5z + 10y + 15z on the elipse that is formed by the intersection of the cylinder z? + y? = 25 and the plane y + z= 5

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 variable density  d(x) = 4x2 covering the region bounded…

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

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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: 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 :…

Q: Find the plane x/a + y/b + z/c = 1 that pass-es through the point (2, 1, 2) and cuts off the least…

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Q: Find the center of mass of a thin plate of density δ = 3 bounded by the lines x = 0, y = x, and the…

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

A: We have to find volume.

Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x2 and…

A: Given:Find the center of mass of a thin plate covering the region bounded below by the parabola y =…

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 sum of maximum and minimum values of the function f(x, y, z) = 9x + 18y + 27z on the elipse…

A: Using Lagrange Multipliers with Two Constraints to find the maximum and minimum values of the given…

Q: A thin plate of constant density k, bounded by the parabola y=3x² and the line y=3 has a mass 4k.…

A: If mass of a region R bounded between y=f(x) and y=g(x) from x=a  to x=b  Then there two moments,…

Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

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: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x2 and…

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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: A _____ is the set of points (x, y) in a plane such that the difference in distances between (x, y)…

A: The standard form of the equation of the hyperbola is,

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: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: Find the center of mass of a thin plate covering the region between the x-axis and the curve y =…

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Q: The path C is a line segment of length 5 in the plane starting at (4, 1). For f(x, y) = 4x + 3y,…

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: The path C is a line segment of length 13 in the plane starting at (2, 2). For f(x, y) = 5x + 12y,…

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Q: find the center of mass of a thin triangular plate bounded by y-axis and the line y = x and y = 2-x…

A: The triangular plate is bounded by y-axis, y=x,y=2-x if ∂x,y=6x+3y+3. Thus, the region is…

Q: Suppose that the temperature in degrees Celsius at a point (x, y, z) of a solid E bounded by the…

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Q: Use the result of Exercise 37 in Section 6.1 (or the exercise above if your answer is correct) to…

A: Find the volume V of the solid obtained by revolving about the line y=-3 the region between the…

Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Given problem is :

Q: find the center of mass of a thin plate of constant density d covering the given region. 1. The…

A: Given information:

Q: The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of…

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

A: Volume of a solid is obtained using triple integration by the formulae =∫∫∫dx dy dz The solid is…

Q: Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y2 and…

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Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

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Q: Find the centroid of the region bounded by the given curves. y = 6 sin(5x), y = 6 cos(5x), x = 0, X…

A: In the question we have to find centroid of the region.

Q: How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2…

A: We will find out the limits first.

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

Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

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Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

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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: Calculate the volume under the elliptic paraboloid z=3x2+7y2 and over the rectangle R=[−2,2]×[−4,4

A: Explanation: We know that,  Volume =∬zdydx By using the double integral concept, the volume of the…

Q: Find the extreme values of the function f (x,y) = 2 - 4x - - y² on the closed region bounded by the…

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Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x 2…

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Q: Find the centroid of the region bounded by the graphs of the equations using any method y = √(1 −…

A: Consider the given equations y=fx=1-x2y=gx=0 First, find the point of intersection of the given…

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

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