What is the percentage of lemons in this group of lemons and strawberries?
1 answer:
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The given plane, , has normal vector
. Any plane parallel to this one has the same normal vector.
Let be any point in the plane we want. The plane contains the point (1, 1, -1), so an arbitrary vector in this plane is
and this is perpendicular to .
So the equation of the plane is
or equivalently,
Find the percent of the circle
r=radius of circle
then r=1/2 of the diagonal of the square
use some pythagoran theorme
45,45,90 triangle
(r√2)/2=1/2 of a side
r√2 is one side
square it
2r²=square
area of circle is pir²
percent it is is
square/circle=
(2r²)/(pir²)=
2/pi= about
0.636
about 64% that it is in the square
r=radius of circle
then r=1/2 of the diagonal of the square
use some pythagoran theorme
45,45,90 triangle
(r√2)/2=1/2 of a side
r√2 is one side
square it
2r²=square
area of circle is pir²
percent it is is
square/circle=
(2r²)/(pir²)=
2/pi= about
0.636
about 64% that it is in the square