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
Answer:
Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x
Thus, option A) is true.
The solution to the system of equations be:

Step-by-step explanation:
It is important to remember that when we solve the system of equations, the first step we need to do is to solve one of the equations for one of the variables.
Given the system of equations


Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x

Add y to both sides


Thus, option A) is true.
<u>NOW LET US SOLVE THE REMAINING PORTION</u>
to solve for y



For x = -1 + y
substitute y = 5


Thus, the solution to the system of equations be:

The next number in the sequence should be 333.111
Answer:
11 + 16n
Step-by-step explanation:
Collect the like terms
2 + 9 = 11
10n + 6n = 16n
11 + 16n is the final answer, and cannot be simplified further
The current height of the bird is -16/3
The bird perched at a height of 15 feet
The bird dropped to a height of 61/3 feet when it saw a food
The current height can be calculated as follows
= 15 - 61/3
= 45-61/3
= -16/3
Hence the current height of the bird is -16/3
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