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:
99 square feet
Step-by-step explanation:
Because 8 times 9=72+27=99
Yes, as long as it's between the two numbers
51) -4 and 1
52) -1 and -3
53) -9 and -10
Eric took 20 hours to do the job alone.
<u>Step-by-step explanation</u>:
<u>Given </u>:
- Total work = 75 packages
- Joe took 5 hours to complete the total work.
The amount of work Joe alone can do per hour = 75/5 = 15 packages.
The amount of work Joe and Eric together do per hour = 75/4 = 18.75
The amount of work Eric alone can do per hour = 18.75 - 15 = 3.75
The time Eric took to complete the entire work = 75 / 3.75 = 20 hours.
Answer: $324
Step-by-step explanation:
i=prt
i=(6000)(.054)(1)
i=324