Jill took a photograph of a plane taking off. Her mother is an air-traffic controller and was able to estimate the measurements
shown. How far is the plane above the ground? Round to the nearest yard?
56 yards
75 yards
40 yards
60 yards
56 yards
75 yards
40 yards
60 yards
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: