Question

Determine the volume of the tetrahedron cut from the first octant by the plane 6x +...

  1. Determine the volume of the tetrahedron cut from the first octant by the plane 6x + 2y + z = 6. Sketch the solid.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find 6 different iterated triple integrals for the volume of the tetrahedron cut from the first...
Find 6 different iterated triple integrals for the volume of the tetrahedron cut from the first octant (when x > 0, y > 0, and z > 0) by the plane 6x + 2y + 3z = 6. Dont evaluate the integrals.
The tetrahedron is the first octant bounded by the coordinate planes and the plane passing through...
The tetrahedron is the first octant bounded by the coordinate planes and the plane passing through (1,0,0), (0,2,0), and (0,0,3). I need to calculate the volume of this region, how should this be done?
6. Let R be the tetrahedron in the first octant bounded by the coordinate planes and...
6. Let R be the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1, 0, 0), (0, 1, 0), and (0, 0, 2) with equation 2x + 2y + z = 2, as shown below. Using rectangular coordinates, set up the triple integral to find the volume of R in each of the two following variable orders, but DO NOT EVALUATE. (a) triple integral 1 dxdydz (b) triple integral of 1 dzdydx
a)   Sketch the solid in the first octant bounded by: z = x^2 + y^2 and...
a)   Sketch the solid in the first octant bounded by: z = x^2 + y^2 and x^2 + y^2 = 1, b)   Given the volume density which is proportional to the distance from the xz-plane, set up integrals               for finding the mass of the solid using cylindrical coordinates, and spherical coordinates. c)   Evaluate one of these to find the mass.
1) Use calculus to find the volume of the solid pyramid in the first octant that...
1) Use calculus to find the volume of the solid pyramid in the first octant that is below the planes x/ 3 + z/ 2 = 1 and y /5 + z /2 = 1. Include a sketch of the pyramid. 2)Find three positive numbers whose sum is 12, and whose sum of squares is as small as possible, (a) using Lagrange multipliers (b )using critical numbers and the second derivative test.
Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by...
Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane 11x + y + z = 2
B is the solid occupying the region of the space in the first octant and bounded...
B is the solid occupying the region of the space in the first octant and bounded by the paraboloid z = x2 + y2- 1 and the planes z = 0, z = 1, x = 0 and y = 0. The density of B is proportional to the distance at the plane of (x, y). Determine the coordinates of the mass centre of solid B.
Find the surface area of the portion of the plane 3x+2y+z=6 that lies in the first...
Find the surface area of the portion of the plane 3x+2y+z=6 that lies in the first octant
1- Set up the triple integral for the volume of the sphere Q=8 in rectangular coordinates....
1- Set up the triple integral for the volume of the sphere Q=8 in rectangular coordinates. 2- Find the volume of the indicated region. the solid cut from the first octant by the surface z= 64 - x^2 -y 3- Write an iterated triple integral in the order dz dy dx for the volume of the region in the first octant enclosed by the cylinder x^2+y^2=16 and the plane z=10
A solid Tetrahedron has vertices (0, 0, 0), (2, 0, 0), (0, 4, 0), and (0,...
A solid Tetrahedron has vertices (0, 0, 0), (2, 0, 0), (0, 4, 0), and (0, 0, 6). (a) i. Sketch the tetrahedron in the xyz-space. ii. Sketch (and shade) the region of integration in the xy-plane. (b) Setup one double integral that expresses the volume of the tetrahedron. Define the proper limits of integration and the order of integration. DO NOT EVALUATE.