Download photo math and it will let you take a picture of the equation and answer it for you
D. It Is The Most Fitting Answer. The Other 3 Equal More Than Needed.
Answer: true
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
Many ways...
x+x-3
2x-6+3
5x-3x-3
(4x-6)/2
And the list goes on...
ANSWER
4 ft
EXPLANATION
The velocity equation of the oscillating spring is given by the function.
![v(t)=2 \sin(t) \: \: {ms}^{ - 1}](https://tex.z-dn.net/?f=v%28t%29%3D2%20%20%5Csin%28t%29%20%20%20%5C%3A%20%20%5C%3A%20%20%7Bms%7D%5E%7B%20-%201%7D%20)
To find the displacement function, we need to to Integrate the velocity function.
![s(t) = \int \: 2 \sin(t) dt](https://tex.z-dn.net/?f=%20s%28t%29%20%3D%20%5Cint%20%5C%3A%202%20%5Csin%28t%29%20dt)
![s(t) = - 2 \cos(t) + k](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%20-%20%202%20%5Ccos%28t%29%20%20%2B%20k)
At time t=0, there was no displacement.
This implies that,
![s(0) = 0](https://tex.z-dn.net/?f=s%280%29%20%3D%200)
![0= - 2 \cos(0) + k](https://tex.z-dn.net/?f=0%3D%20%20-%20%202%20%5Ccos%280%29%20%20%2B%20k)
![0= - 2 + k](https://tex.z-dn.net/?f=0%3D%20%20-%20%202%20%2B%20k)
![k = 2](https://tex.z-dn.net/?f=k%20%3D%202)
The displacement function then becomes,
![s(t) = - 2 \cos(t) + 2](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%20-%20%202%20%5Ccos%28t%29%20%20%2B%202)
To find the displacement over the first π seconds, we put
![t = \pi](https://tex.z-dn.net/?f=t%20%3D%20%5Cpi)
into the equation for the displacement to get,
![s(\pi) = - 2 \cos(\pi) + 2](https://tex.z-dn.net/?f=s%28%5Cpi%29%20%3D%20%20-%20%202%20%5Ccos%28%5Cpi%29%20%20%2B%202)
![s(\pi) = - 2 ( - 1) + 2](https://tex.z-dn.net/?f=s%28%5Cpi%29%20%3D%20%20-%20%202%20%28%20-%201%29%20%20%2B%202)
![s(\pi) = 2 + 2 =4 ft](https://tex.z-dn.net/?f=s%28%5Cpi%29%20%3D%20%202%20%20%2B%202%20%3D4%20ft)