(a) Fermat's little theorem states that for any prime , we have
for any integer . Then
so 7 does indeed divide 999,999.
(b) Generalizing, we have
for positive integer . Now, since 1 = 1001 - 1000 and
, it follows that
is its own inverse modulo 1001, i.e.
This means
which is what we wanted to show.
Answer:
Central angle of θ
Step-by-step explanation:
Suppose a sector of a circle with radius r has a central angle of θ.
Since a sector is a fraction of a full circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the central angle of θ to the measure of a full rotation of the circle.
A full rotation of a circle is 2π radians.
This proportion can be written as:
Multiply both sides by
Simplify to get:
Where θ is the measure of the central angle of the sector and r is the radius of the circle.