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
His average rate is 120 meters per minute.
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Answer:
D. (-3, -2)
Step-by-step explanation:
The equations have different coefficients for x and y, so will have one solution. The solutions offered are easily tested in either equation.
Using (x, y) = (-2, -3):
x = y -1 ⇒ -2 = -3 -1 . . . . False
Using (x, y) = (-3, -2):
x = y -1 ⇒ -3 = -2 -1 . . . .True
2x = 3y ⇒ 2(-3) = 3(-2) . . . . True
The solution is (-3, -2).
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If you'd like to solve the set of equations, substitution for x works nicely.
2(y -1) = 3y
2y -2 = 3y . . eliminate parentheses
-2 = y . . . . . . subtract 2y
x = -2 -1 = -3
The solution is (x, y) = (-3, -2).
Answer:
In the given figure, line segment is constructed on the triangle parallel to line segment . ... This line can then be considered as a transversal of these parallel lines. Angle and angle are therefore corresponding angles. And as they're corresponding, this means that they're equal.
