Answer:

Step-by-step explanation:
Write the terms of numerator and denominator using a common denominator.

A function

is periodic if there is some constant

such that

for all

in the domain of

. Then

is the "period" of

.
Example:
If

, then we have

, and so

is periodic with period

.
It gets a bit more complicated for a function like yours. We're looking for

such that

Expanding on the left, you have

and

It follows that the following must be satisfied:

The first two equations are satisfied whenever

, or more generally, when

and

(i.e. any multiple of 4).
The second two are satisfied whenever

, and more generally when

with

(any multiple of 10/7).
It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when

is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.
Let's verify:


More generally, it can be shown that

is periodic with period

.
Answer:
$675.00
Step-by-step explanation:
4500 x 0.05 x 3 = 675
Answer:
Circumference = 10π
Step-by-step explanation:
First identify the circumference formula as such:
2πr (where r ⇒ radius, π ⇒ pi)
Knowing 2 times the radius (2r) in the formula can be rewritten as the diameter, the formula itself can be rewritten as:
πd (where d ⇒ diameter, π ⇒ pi)
If we know the diameter = 10 inches, substitute in the circumference formula πd to get:
π * 10 inches = 10 * π inches = 10π inches
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