![\begin{cases}x(t)=5\sin2t\\y(t)=5\cos2t\end{cases}\implies\begin{cases}\frac{\mathrm dx}{\mathrm dt}=10\cos2t\\\frac{\mathrm dy}{\mathrm dt}=-10\sin2t\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%28t%29%3D5%5Csin2t%5C%5Cy%28t%29%3D5%5Ccos2t%5Cend%7Bcases%7D%5Cimplies%5Cbegin%7Bcases%7D%5Cfrac%7B%5Cmathrm%20dx%7D%7B%5Cmathrm%20dt%7D%3D10%5Ccos2t%5C%5C%5Cfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%3D-10%5Csin2t%5Cend%7Bcases%7D)
The distance traveled by the particle is given by the definite integral
![\displaystyle\int_C\mathrm dS=\int_0^{3\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_C%5Cmathrm%20dS%3D%5Cint_0%5E%7B3%5Cpi%7D%5Csqrt%7B%5Cleft%28%5Cfrac%7B%5Cmathrm%20dx%7D%7B%5Cmathrm%20dt%7D%5Cright%29%5E2%2B%5Cleft%28%5Cfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%5Cright%29%5E2%7D%5C%2C%5Cmathrm%20dt)
where
![C](https://tex.z-dn.net/?f=C)
is the path of the particle. The distance is then
Answer:
Option 2
Step-by-step explanation:
(12) - 2 = 10
(11) - 2 = 9
0 x 4 = 0
1 x 4 = 4
Answer: = (the third option)
Step-by-step explanation
Hi!
If they each got the same, then they each got 1/3 of the total $360. Therefore, we can divide 360 by 3. We can do this by dividing 36 by 3, 36/3, and that's 12. Then add the 0! 120.
Your sentence could be: "The amount of money each worker got can be represented by 360/3, which is $120."
Hope this helps! :D