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:
7x+80
Step-by-step explanation:
7 times everything in the () and get
56+7x+24
combine like terms
7x+80
Answer:
Step-by-step explanation:
Let A = R−{0}, the set of all nonzero real numbers, and consider the following relations on A × A.
Given that (a,b) R (c,d) if
Or (a,b) R (c,d) if determinant
a) Reflexive:
We have (a,b) R (a,b) because ab-ab =0 Hence reflexive
b) Symmetric
(a,b) R (c,d) gives ad-bc =0
Or da-cb =0 or cb-da =0 Hence (c,d) R(a,b). Hence symmetric
Answer:
Point slope form:
The equation of line is given by: .....[1]
where m is the slope and a line contains a point .
As per the given statement:
Slope(m) = 3
. = (2, 1)
Substitute these in [1] we have;
therefore, the point slope form of a line with slope 3 that contains the point (2, 1) is;