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

.
Jan. = -15
Feb. = +10
Mar. = -5
Apr. = +50
May = -25
June = -20
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
The equation of an ellipse is x²/a² + y²/b² =1
a being the distance between the center & x intercept =7
b being the distance between the center & y intercept =5
Hence the equation of this ellipse is:
x²/49 + y²/25 =1
Answer: (1a) 250° (1b) 70° (2) see below
<u>Step-by-step explanation:</u>
1a) -110 + 360 (one rotation clockwise) = 250°
1b) 430 - 360 (one rotation counterclockwise) = 70°
2) sec Ф = -8/5 in Quadrant III
Quadrant III identifies that both sin (y) and cos (x) are negative.
sec = r/x --> r = 8, x = -5, and y = -√39
(Use Pythagorean Theorem x² + y² = r² to solve for y)
rationalized = 
(GIVEN)
rationalized = 
NOTE THAT YOU ARE ALLOWED A MAXIMUM OF 3 QUESTIONS PER POST. Please repost #3 and #4 as a different question and I will answer them.
Answer:
4,720
Step-by-step explanation:
From my understanding, you just add the numbers together.
3310 + 1410=
4,720
I could be wrong. However, that's what I grasped out of your question. Hope this helped! Have a good day. :)