~F = z(x2+ y2) ~k through the disk of radius 4 in the plane z = 2, centered on the z-axis, oriented upward.

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: 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 moment of inertia about the x-axis of a thin plate of constant density δ covering the…

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Q: Find the volume of the solid bounded by the plane 3x + 8y + 4z = 10 in the first octant. Leave your…

A: In the given problem the first octant denotes the region in the coordinated plane where x,y,z≥0 The…

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Q: Determine the centroid formed by revolving about the y-axis, the a bounded by the curve y = x*, the…

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Q: Find the centroid of the region that is enclosed between: y = x and y = 2 – 2?.

A: Let fx=2-x2, gx=x. Find the intersections. fx=gx2-x2 =x2-x2…

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Q: How do you locate the center of mass of a thin plate bounded by two curves y = ƒ(x) and y = g(x)…

A: Given:How do you locate the center of mass of a thin plate bounded by two curves y = ƒ(x) and y =…

Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

Q: Determine the centroid of the lamina bounded by y=sinx, y=cosx and x=0 in the interval 0,

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Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+6y+6z=24.…

A: Let's find.

Q: Calculate the moments of inertia of the triangle bounded by the straight lines x+y=1, x=0, y=0…

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Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

Q: A point moves along the intersection of the elliptic paraboloid z = 3x² + 5y² and the plane y = 4.…

A: We are given the curve Z=3x2+5y2 and y=4   Now we know that the rate of change is simply derivative…

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Q: A body of mass 6 kg moves in a (counterclockwise) circular path of radius 6 meters, making one…

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Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…

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Q: Find the center of mass of solid revolution if an area in Ist Quadrant (Kuadran Pertama) bounded by…

A: Given functions are Intersection points Area of region is Centre of mass revolution

Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+5y+6z=33.…

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Q: Find the volume of the solid bounded by the plane 3x + 6y + 3z = 4 in the first octant. Leave your…

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Q: Find the volume of the solid bounded by the plane 4x + 6y + 7z = 9 in the first octant. Leave your…

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Q: Find the area of the surface obtained by rotating the curve y = x², 0 < x< 1, about the y axis.

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Q: Use cylindrical coordinates to calculate the volume between the surfaces in the first octant if z =…

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Q: Find the area of the surface obtained by rotating the curve x = 3 (y + 2)3/2, 1 <y< 2, about the…

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Q: Let S be the surface obtained by revolving the plane curve 2x = /9 – y² about the y-axis.

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Q: Find the plane tangent to the surface z = x cos y - yex at (0, 0, 0).

A: Consider the following function: z=fx,y=xcosy-yex Differentiate function fx,y with respect to x:…

Q: Find the volume of the solid of revolution bounded by the cirde x+y = 16, and the lines z = 0 and 8,…

A: Given curve is x2+y2=16 and line x=0 and x=8 about x-axis We have to find the volume of the solid of…

Q: Find the maximum and minimum values of x^2 + y^2 − 2x − 2y on the disk of radius √ 8 centered at the…

A: Given function is  fx,y=x2+y2-2x-2y where bounded region is  x2+y2≤8.

Q: Find the moment of inertia of a right circular cone of base radius a and height h about its axis if…

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Q: A thin plate has mass 3. What is the x-moment of the plate if its center of mass has coordinates (2,…

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Q: Find the moment of inertia about the x-axis of a thin plate of constant density d covering the…

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Q: What is the volume of the body of rotation formed by rotating the region bounded by the function y =…

A: Let us consider the given curve y=f(x) The volume of the solid of revolution about x-axis is…

Q: Suppose that a thin metal plate of area A and constant density doccupies a region R in the xy-plane,…

A: A thin metal plate of area A and constant density δ occupies a region R in the xy-plane.

Q: Find the volume of the solid that lies under the plane 4x+6y-2z+15=0 and above the rectangle…

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Q: A point moves along the intersection of the elliptic paraboloid z = 2x? + 7y² and the planex = 4. At…

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Q: Find a parametrization of the circle of radius 7 with center (5, 3, 9) in a plane parallel to the…

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

A: Given Data The equation of the cylinder is z=12-3y². The equation of the plane is x+y=2.   Let, The…

Q: Find the volume of the solid bounded by the plane z = 3 - 5x - 9y and the coordinate planes in the…

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Q: Find the volume of the wedge cut from the first octant by the cylinder z=63-7y and the plane x+y=3

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Q: Find the moment of inertia of a right circular cone of base radius a and height h about its axis.…

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Q: A lamina is bounded by y-e and the lines y-0,r-0, and zI with density (r,y) - y. Find the moment of…

A: Calculate moment of inertia about y-axis:

Q: Find the surface area obtained by rotating y = V9 – x2 ,-2sxs-1 9– x² -2sxs-1

A: Given,             y=9-x2 , -2≤x≤-1

Q: Find the volume of the solid bounded by the plane 7x + 3y + 8z = 3 in the first octant. Leave your…

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Q: The center of mass of a lamina of total mass 5 has coordinates (2, 1). What are the lamina’s x- and…

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Q: Find the volume of the solid bounded by the plane 7x + 3y + 4z = 3 in the first octant. Leave your…

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Q: Find parametrization of the horizontal circle of radius 4 with center (5, -2, 6). r(t) = %3D

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Q: Find the volume of the solid D bounded from above by the surface z = 9 − 4x2 − 4y2 and below by the…

A: Consider the given surface z = 9 − 4x2 − 4y2 and below by the plane z = 0. ⇒ 0 = 9 − 4x2 − 4y2  ⇒…