The common difference is 11, you can see this because the number goes up by eleven each time.
Answer: (E) Not necessarily, because this wasn't an experiment
Step-by-step explanation:
As much as the results would suggest that the fast-paced music was responsible for the faster finishing time, this conclusion cannot be authoritatively made because this was not technically an experiment but rather a test to satisfy curiosity.
An experiment is planned and is scientific. It has more stringent requirements that ensure causation that Roshanda did not meet before she engaged in this trial so we cannot say for a fact that her findings are objective.
Answer:
φ ≈ 1.19029 radians (≈ 68.2°)
Step-by-step explanation:
There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.
We want to compare ...
y(t) = Asin(ωt +φ)
to
y(t) = Psin(ωt) +Qcos(ωt)
Using trig identities to expand the first equation, we have ...
y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Matching coefficients with the second equation, we have ...
P = Acos(φ)
Q = Asin(φ)
The ratio of these eliminates A and gives a relation for φ:
Q/P = sin(φ)/cos(φ)
Q/P = tan(φ)
φ = arctan(Q/P) . . . . taking quadrant into account
__
We can also use our equations for P and Q to find A:
P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²
A = √(P² +Q²)
_____
Here, we want φ.
φ = arctan(Q/P) = arctan(5/2)
φ ≈ 1.19029 . . . radians
Answer: (
x
,
−
x/
3
−
5
/3
)
Step-by-step explanation:
Answer:
4 - b
-1 - e
-4 - a
-5 - c
Step-by-step explanation:
