Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (2 comma 0 comma 0 ), (0 comma 5 comma 0 ), and (0 comma 0 comma 4 ).

The volume of the tetrahedron is:

Step-by-step explanation:

The volume of the tetrahedron is given by the intersection of the planes x = 0, y = 0, z = 0 and the plane formed by the three points given.

The equation of the plane formed by the three points is:

Points: (2,0,0);(0,5,0);(0,0,4)

It can also be expressed as:

We have to calculate the triple integral, therefore we must define the domain:

The values of x are given by:

0≤x≤2

We will integrate the values of y between the y = 0 axis and the line formed when z = 0:

z=0 ⇒ 10x + 4y=2 ⇒

We will integrate the values of z between the plane z = 0 and the plane 10x + 4y+5z=20

10x + 4y+5z=20 ⇒

The volume of the tetrahedron is:

step-by-step explanation: