Answer:
-9a^2+14
Step-by-step explanation:
Following are the responses to the given points:
For point a:
![Diameter\ (d)= 16\ m\\\\](https://tex.z-dn.net/?f=Diameter%5C%20%28d%29%3D%2016%5C%20m%5C%5C%5C%5C)
Calculating the 3 rotations for every minute:
Calculating time for completing 1 rotation:
The standard form of the equation of the sine and cosine function is:
Calculating the Amplitue:
![A=\frac{max-min}{2}=\frac{17-1}{2}=\frac{16}{2}=8\\\\Period=\frac{2\pi}{B}\\\\20=\frac{2\pi}{B}\\\\B=\frac{2\pi}{20}\\\\B=\frac{\pi}{10}\\\\](https://tex.z-dn.net/?f=A%3D%5Cfrac%7Bmax-min%7D%7B2%7D%3D%5Cfrac%7B17-1%7D%7B2%7D%3D%5Cfrac%7B16%7D%7B2%7D%3D8%5C%5C%5C%5CPeriod%3D%5Cfrac%7B2%5Cpi%7D%7BB%7D%5C%5C%5C%5C20%3D%5Cfrac%7B2%5Cpi%7D%7BB%7D%5C%5C%5C%5CB%3D%5Cfrac%7B2%5Cpi%7D%7B20%7D%5C%5C%5C%5CB%3D%5Cfrac%7B%5Cpi%7D%7B10%7D%5C%5C%5C%5C)
Calculating the phase shift:
for
function:
for
function:
Calculating the vertical shift:
![\to D=\frac{max+ min }{2}=\frac{17+ 1}{2}=\frac{18}{2}=9\\\\y=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\y=8 \cos \{ \frac{\pi}{10}(t-10)\} +9\\\\](https://tex.z-dn.net/?f=%5Cto%20D%3D%5Cfrac%7Bmax%2B%20min%20%7D%7B2%7D%3D%5Cfrac%7B17%2B%201%7D%7B2%7D%3D%5Cfrac%7B18%7D%7B2%7D%3D9%5C%5C%5C%5Cy%3D8%20%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%2B9%5C%5C%5C%5Cy%3D8%20%5Ccos%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-10%29%5C%7D%20%2B9%5C%5C%5C%5C)
For point b:
![y> 12\ m\\\\12=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\12-9=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\3=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\\frac{3}{8}=\sin \{ \frac{\pi}{10}(t-5)\} \\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (0.38439677)=(t-5) \\\\1.22357+5=t \\\\t=6.22357\ second\\\\t=6.22\ second\\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (2.7571961)=(t-5) \\\\t=8.7764+5\\\\t=13.78\ second\\\\t_2-t_1=13.7764-6.22357= 7.55283\approx 7.55\ second \\\\](https://tex.z-dn.net/?f=y%3E%2012%5C%20m%5C%5C%5C%5C12%3D8%20%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%2B9%5C%5C%5C%5C12-9%3D8%20%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%5C%5C%5C%5C3%3D8%20%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%5C%5C%5C%5C%5Cfrac%7B3%7D%7B8%7D%3D%5Csin%20%5C%7B%20%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%5C%7D%20%5C%5C%5C%5C%5Csin%5E%7B-1%7D%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%20%5C%5C%5C%5C%5Cfrac%7B%5Cpi%7D%7B10%7D%20%280.38439677%29%3D%28t-5%29%20%5C%5C%5C%5C1.22357%2B5%3Dt%20%5C%5C%5C%5Ct%3D6.22357%5C%20second%5C%5C%5C%5Ct%3D6.22%5C%20second%5C%5C%5C%5C%5Csin%5E%7B-1%7D%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B%5Cpi%7D%7B10%7D%28t-5%29%20%5C%5C%5C%5C%5Cfrac%7B%5Cpi%7D%7B10%7D%20%282.7571961%29%3D%28t-5%29%20%5C%5C%5C%5Ct%3D8.7764%2B5%5C%5C%5C%5Ct%3D13.78%5C%20second%5C%5C%5C%5Ct_2-t_1%3D13.7764-6.22357%3D%207.55283%5Capprox%207.55%5C%20second%20%5C%5C%5C%5C)
Learn more:
Rotation: brainly.in/question/39626227
Answer:
$4.00
Step-by-step explanation:
expected value - -$1.00
cost of play - $5.00
5-1 = $4.00