Given
where E <span>is the portion of the unit ball
that lies in the first octant.
This can be evaluated as follows:
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where E <span>is the portion of the unit ball
This can be evaluated as follows:
A number is 2/3 of another number. If the sum of the two numbers is 30, find the smaller number
2 answers:
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0.025 or 
The three vectors ,
, and
each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,
Then the cross product of these two results is normal to the plane:
Let be a point on the plane. Then the vector connecting
to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that
which reduces to the equation of the plane,
Let . Then the volume of the region above
and below the plane is