Answer:
Answer is D: (5,4,-11), 9 sqrt2
Step-by-step explanation:
B. If square-foot is on the x-axis then we can substitute for x in the equation and solve, and when we do, we get 2473.302 which is is B when rounded.
21 x 3.14 = 65.94 inches basically multiply by 3.14 there is another way to do it but I don’t know it. Hope this helps!
We have the function d, representing the distance from the ground of a person riding on a Ferris wheel:
![d(t)=20\sin (\frac{\pi}{30}t)+10](https://tex.z-dn.net/?f=d%28t%29%3D20%5Csin%20%28%5Cfrac%7B%5Cpi%7D%7B30%7Dt%29%2B10)
If we consider the position of the person at t = 0, which is:
![d(0)=20\sin (\frac{\pi}{30}\cdot0)+10=20\cdot0+10=10](https://tex.z-dn.net/?f=d%280%29%3D20%5Csin%20%28%5Cfrac%7B%5Cpi%7D%7B30%7D%5Ccdot0%29%2B10%3D20%5Ccdot0%2B10%3D10)
This position, for t = 0, will be the same position as when the argument of the sine function is equal to 2π, which is equivalent to one cycle of the wheel. Then, we can find the value of t:
![\begin{gathered} \sin (\frac{\pi}{30}t)=\sin (2\pi) \\ \frac{\pi}{30}\cdot t=2\pi \\ t=2\pi\cdot\frac{30}{\pi} \\ t=60 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csin%20%28%5Cfrac%7B%5Cpi%7D%7B30%7Dt%29%3D%5Csin%20%282%5Cpi%29%20%5C%5C%20%5Cfrac%7B%5Cpi%7D%7B30%7D%5Ccdot%20t%3D2%5Cpi%20%5C%5C%20t%3D2%5Cpi%5Ccdot%5Cfrac%7B30%7D%7B%5Cpi%7D%20%5C%5C%20t%3D60%20%5Cend%7Bgathered%7D)
Then, the wheel will repeat its position after t = 60 seconds.
Answer: 60 seconds.