(5 pts) Write an iterated integral for the volume of the tetrahedron cut from the first...
Use a triple integral to find the volume of the given solid.The tetrahedron enclosed by the coordinate planes and the plane 5x + y + z = 3Evaluate the triple integral.8z dV, where E is bounded by the cylinder y2 +z2 = 9 and the planes x = 0,y = 3x, and z = 0 in the first octantEUse a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane...
QUESTION 2 Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the tetrahedron cut from the first octant by the plane yz + 9(1 -y/10)3(1 -x/9-y/10) a dz dy dx 0 0 0 10(1 -x/9) ,3(1-x/9-y/10) 9 dz dy dx 0 0 1-x/9-y/10 C.9 1 -y/10 dz dy dx 0 0 0 d. 9 1 -x/9 1-x/9-y/10 dz dy dx 0 0 0
Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (5,0,0), (0,3,0), and (0,0,1) (0,3,0 5,0,0) The volume of the tetrahedron is. (Type an integer or a simplified fraction.) Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (5,0,0), (0,3,0), and (0,0,1) (0,3,0 5,0,0) The volume of the tetrahedron is. (Type an integer or a simplified fraction.)
Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (4,0,0), (0,3,0), and (0,0,5). (0.0.5) i (0,3,0) 4,0,0) The volume of the tetrahedron is . (Type an integer or a simplified fraction.)
5. (6) Consider the solid bound in the first octant by the surface 9x2 +4y 36 and the plane 9x+ 4y + 6z 36. a. Sketch the solid. b. Set-up the integral to find the volume of the solid by using a double integral. DO NOT INTEGRATE 5. (6) Consider the solid bound in the first octant by the surface 9x2 +4y 36 and the plane 9x+ 4y + 6z 36. a. Sketch the solid. b. Set-up the integral to...
Question 7 5 pts each Write iterated integrals for each of the given calu lations. Do not evaluate. (A) The integral of f(x, )212y over the domain D: 2 y 20. (B) The integral of f(x, y, z) = 12x + 3 over the volume contained in the first octant and below the graph z 8-y 2 (C) The mass of an object occupying the region bounded between the sur faces x2 + y2 + Z2 = 16 and z...
SET UP a triple integral to find the volume of the solid in the first octant (all coordinates positive) that is below the pla 10. (8 pts.) SET UP a triple integral to find the volume of the solid in the first octant (all coordinates positive) that is below the plane x+3y + 2z =12.
(7) Set up an iterated integral to compute the volume of the wedge of cheese cut W shown below. Use the cylindrical coordinates. - - ECO - - - - - - ---- -- ---- ----- -- -
7. Find the x-coordinate of the centroid of the tetrahedron in the first octant enclosed by coordinate planes and the plane x + y + z = 1. (6 pts)
N2 Use a triple integral to find the volume of the region in the first octant beneath the plane 40 pts 3x + y + 2z = 6