Avariable star is one whose brightness alternately increases and decreases. for one such star, the time between periods of maximum brightness is 5.7 days, the average brightness (or magnitude) of the star is 4.2, and its brightness varies by ±0.25 magnitude. find a function that models the brightness of the star as a function of time (in days), t. (assume that at t = 0 the brightness of the star is 4.2 and that it is increasing.)

The equation is:
f(t) = 0.25 sin((2pi / 5.7) t) + 4.2
f(t) = 0.25 sin((pi / 2.85) t) + 4.2 

This is because the general form of the equation is f(x) = A sin((2pi/T)x) + C 

where
A = amplitude 
T = period 
C = mean value

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

there are no correct statementd on the list of choices you provided.