Answer:
(1 cm)cos3πt
Step-by-step explanation:
Since the piston starts at its maximal height and returns to its maximal height three times evert 2 seconds, it is modelled by a cosine functions, since a cosine function starts at its maximum point. So, its height h = Acos2πft
where A = amplitude of the oscillation and f = frequency of oscillation and t = time of propagation of oscillation.
Now, since the piston rises in such a way that it returns to the maximal height three times every two seconds, its frequency, f = number of oscillations/time taken for oscillation where number of oscillations = 3 and time taken for oscillations = 2 s
So, f = 3/2 s =1.5 /s = 1.5 Hz
Also, since the the piston moves between 3 cm and 5 cm, the distance between its maximum displacement(crest) of 5 cm and minimum displacement(trough) of 3 cm is H = 5 cm - 3 cm = 2 cm. So its amplitude, A = H/2 = 2 cm/2 = 1 cm
h = Acos2πft
= (1 cm)cos2π(1.5Hz)t
= (1 cm)cos3πt
Use trigonometry to solve for x.
The tangent function is defined to be opposite side divided by the adjacent side.
tan(78) = x/10
tan(78)(10) = x
47.0463010948 = x
We now round off to two decimal places. In other words, we round off to the nearest tenths.
47.05 = x
Done!
So, let's say the soft drink equals y and the sandwich equals x.
x + y = 9.9
The sandwich costs 3.5 times as much as the soft drink
x = 3.5y
Therefore, we can replace x with 3.5y since they're the same thing
3.5y + y = 9.9 <-- That's the equation :)
Answer:
42 ft
Step-by-step explanation:
2(L + W ) = P
2 (12 + 9) = P
2 (21) = P
42 = P
P = 42
Answer:
3.04
Step-by-step explanation:
