Calculate the volume of the parallelepiped spanned by u = (2, 2, 1), v = (1,0, 3), w = (0, -4, 0)

Q: Use the new command from Example 3 above to find the volume of the parallelepiped formed by vectors…

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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: Find the centroid of masses of 3,5,7 units at (3,-2,3), (0,1,2) and (3,2,3) respectively

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Q: Find the volumes of the regions. The tetrahedron in the first octant bounded by the coordinate…

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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: what is the formula to find centroid of triangular prism

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

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 centroid of volume if the volum is equal to 7/15 π

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Q: Find the volume of the solid bounded by the planes z 0, 1%=1,1=2,y=-1,y-1 and the surface z=+.

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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 region under the surface z = 6x° and above the triangle in the xy-plane with…

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Q: how by integration that the centroid of a uniform semi-circular lamina of radius a from ne centre is…

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Q: Find the volume of the parallelepiped spanned by u, v, and w in the Figure below.

A: u=(1,0,4) v=(1,3,1) w=(-4,2,6)

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: Find the volume of the region under the surface z = corners (0, 0, 0), (6, 0, 0) and (0, 3, 0). 824…

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Q: Calculate the volume of the solid bounded by cone z2=x2+y2 and cylinder 4=x2+y2.

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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 an equation of the plane passing through the point (1,4,2) with a normal vector of the form n=…

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Q: Consider the lamina that occupies the triangular region with vertices (0, 0), (2, 2) and (2, –2),…

A: Given, the lamina that occupies the triangular region with vertices (0, 0), (2, 2) and (2, -2), with…

Q: Find the area of the portion of the plane in the first octant passing through the points (0,0,6),…

A: This question can be solved using the area of triangle in three dimensional geometry.

Q: Find the volume of the region under the surface z = 4x* and above the triangle in the xy-plane with…

A: The solution follows as

Q: Find the volume of the solid bounded by the surface z = 9 – x² and the planes z = 5, y = 0, and y =…

A: Given that z=9−x2, z=5, y=0 and y=4 Here, y varies from 0 to 4 z varies from 5 to 9-x2 Now, find the…

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: 9. The Theorem of Pappus will always be applicable to determine the volume of solid revolution for…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

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 of the solid in the first octant bounded by the coordinate planes and the passing…

A: Given- 1,0,00,2,0 and 0,0,3 To find- The volume of the solid in the first octant bounded by the…

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

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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 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 volumes of the solids generated by revolving the regionsbounded by the lines and curves…

A: y=x2, y=0 x=2 Volume V will be- V=π∫01x2dx

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

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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: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: We first sketch the region using a graphing calculator. The shaded region will rotate about the…

Q: 6) Find the volume of the solid enclosed by the paraboloid z = 2--y and the plane z = 2.

A: According to question given that z=2-x2-y2z=-2

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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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 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 that lies under the plane 4x+6y-2z+15=0 and above the rectangle…

A: Consider the given plane

Q: (Choose from: a. Disk Method, b.Washer Method, c. Shell Method, d. Disk and Washer, e. Disk and…

A: Given that, y = x2 ; x = 0; y = 15 3) Volume of the region bounded by the given curve rotated about…

Q: Find the volume of the solid bounded by surfaces z = /9-x2 - y2 , and z = /25 - x2 - y? and the…

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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 volumes OF the solids gewerated by revolving +he regions bounded by the graphs oF the…

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Q: 6) Find the volume of the solid in the first octant bounded by the plane 3x +4z=12, y=2 and the 3…

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Q: Find the volume of the region defined by the vectors. 7 -2

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Q: Find the volume of the region under the surface z = 9x and above the triangle in the xy-plane with…

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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 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 center of mass of the three particles having masses of 1, 2, and 3 kg located at the points…

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