What is the following quotient?
2 answers:
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Answer:
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: