Find the volume of the parallelepiped spanned by u = (1, 0, 4), v = (1, 2, 1) and w = (-4, 2, 9) in the figure below.

Q: Find the volume of the solid region bounded in the first octant by the plane. z = 1- 8x - 2y

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Q: Find the volume of tetrahedron with vertices (0,0,0),(1,0,0),(0,1,0)and (0,0,2) by triple integral?…

A: We have to find the volume of the tetrahedrane with vertices 0,0,0, 1,0,0, 0,1,0 and 0,0,2 by triple…

Q: Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

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Q: By using the double integral, find the volume of the tetrahedron bounded by the 3x ordinate planes…

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Q: Find the volume of the solid generated by revolving the region enclosed by the triangle with…

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Q: Question included in image

A: Find the volume of the wedge cut from the first octane by the cylinder and the plane

Q: what is the formula to find centroid of triangular prism

A: Centroid of triangular prism is determined as shown below.

Q: Find the volume under the surface z = 3x³ + 3x²y and over the rectangle R = {(x,y):1 < x < 3,0 < y <…

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Q: Calculate the volume of the wedge cut from the cylinder x2+y2=25 and from the z=3y and z=0 planes,…

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Q: Find the centroid (ã, j) of the region bounded by у — 9х? + 5а, у — 0, х — 0, and æ = 7. x =

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Q: . Sketch and compute the volume of the parallelepiped spanned by u = (1, 0, 0), v= (0, 2, 0), w =…

A: u={1,0,0} , v={0,2,0},  and w={1,1,2}

Q: Find the volume of the solid generated by revolving the triangularregion bounded by the lines y =…

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Q: Find the volume of the solid cut from the square column |x|+ |y|&lt;=1 by the planes z = 0 and 3x +…

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Q: Find the volume under the plane z= 2x + y and over the rectangle R = {(x, y) : 3<x< 5,1< y< 2

A: Given Rectangle  R=x,y:3≤x≤5,1≤y≤2

Q: verify that (u * v) . w = (v * w) . u =(w * u) . v and find the volume of the parallelepiped (box)…

A: Concept:…

Q: Use the Theorem of Pappus to find the volume of thegiven solid. The solid obtained by rotating the…

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Q: Determine the volume of the solid lying under the elliptic paraboloid z = 6y² – 2x² + 3 and above…

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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: Find the volume of the parallelepiped (box) determined by u, v, and w. u V i+ 3j 4i - j+4k 2i + 4k

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Q: Find the centroid of the area of a trapezoid that has two equal slanting sides, a 6 cm base and a 3…

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Q: Find the volume of the solid that is bounded by the cylinder z = 4x2, on the sides by the cylinder…

A: Let's find volume of solid.

Q: integrate ƒ over the given region.Quadrilateral ƒ(x, y) = x&gt;y over the region in the first…

A: Given,

Q: Find the volumes of the solids whose bases are bounded by the circle x^2+y^2=4, with the indicated…

A: Given, x2+y2=4 Part a: We have, x2+y2=4⇒y2=-x2+4⇒y=±4-x2 Now we find the area to use in finding the…

Q: Find the volume of the solid bounded by the ellipic paraboloid z = 3 + 4x2 + 2y², the planes x = 2…

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Q: Find the volume in the first octant bounded by the cone z2 = x2 − y2 and the plane x = 4.

A: The given conic curve is, z2=x2-y2 Boundary limits are as follows, Limit of x: 0 to 4Limit of y: 0…

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 generated by revolving the region enclosed by the triangle whose…

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Q: Find the volume of the solid bounded from up by surface f (x,y) = 2x + y2 and from below by the…

A: According to question, surface :f(x, y) = 2x+ y2,Traingle vertices : 0, 2, 0, 0 and 3, 2

Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4-x2-y2, y= 2-2x2,…

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Q: Find the centroid (a, j) of the region bounded by: 7а? + 5a, у — 0, г %3D 0, and x = 9

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Q: Compute the volume of the column with a square base R= {(x,y): |x|< 3, |y| <3} cut by the plane z =…

A: We have to find volume whose base is square-

Q: Find the volume of the tetrahedron in the first octant that is bounded by the three coordinate…

A: The objective is to find the volume of the tetrahedron in the first octant that is bounded by the…

Q: Find the volume of the solid in the first octant bounded bythe cylinder z=16 -x2 and the plane y=5

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Q: Find the area of the surface obtained by rotating the region formed by 1 In x, 1<x < 2, - 2

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Q: Find the volume of the solid in the first octant by bounded by the plane 3x +42 = 12, y = 2 and the…

A: Volume bounded by thefirst octent

Q: Find the centroid (¤, y) of the region bounded by: 52? + 6х, у — 0, х —D 0, and x = 9

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Q: Find the volume of the solid bounded by the ellipic 4 + 5x² + 3y², the planes x paraboloid z = = 2…

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Q: Find the volume of the region under the surface z = and above the triangle in the xy-plane with 1+x2…

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Q: Find the volume of the solid generated by revolving the pentagon with vertices (1, 0), (2, 2), (0,…

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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 volumes OF the solids gewerated by revolving +he regions bounded by the graphs oF 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 volume of the region defined by the vectors. 7 -2

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Q: 3. Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

A: Given

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: he volume bounded by y = x², y = 0 and x = 2 rotated about the specified = specified orientation of…

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Q: Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z…

A: Volume of box = xyz Surface area = 2xy+ 2yz+2zx

Q: Find My for a triangle whose vertices are located at (0,0), (1,0), (1,1) if the density of the…

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Q: find the are of the plane region bounded by the urves y=3x2 and y=16-x2

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Q: Find the volume of the solid enclosed by the paraboloids z=16(x^2+y^2) and z=8−16(x^2+y^2)

A: To calculate the volume of the region contained between the two given surfaces