Answer:
what are you asking? Because I probably have the answer
Well idk what the numbers are, but the formula to find the are is 3.14(pi) x r^2
![cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}](https://tex.z-dn.net/?f=cos%5Cleft%20%28%20%5Cfrac%7B9%5Cpi%7D%7B12%7D%5Cright%20%29%3D%5Cfrac%7B%5Csqrt%7B2-%5Csqrt%7B3%7D%7D%7D%7B2%7D)
Step-by-step explanation:
We know that
cos 2x = 2cos²x - 1
So we have
![cosx=\sqrt{\frac{1+cos2x}{2}}](https://tex.z-dn.net/?f=cosx%3D%5Csqrt%7B%5Cfrac%7B1%2Bcos2x%7D%7B2%7D%7D)
Substituting ![x=\frac{19\pi}{12}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B19%5Cpi%7D%7B12%7D)
![cos\left ( \frac{19\pi}{12}\right )=\sqrt{\frac{1+cos2\left ( \frac{19\pi}{12}\right )}{2}}\\\\cos\left ( \frac{19\pi}{12}\right )=\sqrt{\frac{1+cos\left ( \frac{19\pi}{6}\right )}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{1+cos570}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{1-\frac{\sqrt{3}}{2}}{2}}\\\\cos\left ( \frac{9\pi}{12}\right )=\sqrt{\frac{2-\sqrt{3}}{4}}\\\\cos\left ( \frac{9\pi}{12}\right )=\frac{\sqrt{2-\sqrt{3}}}{2}](https://tex.z-dn.net/?f=cos%5Cleft%20%28%20%5Cfrac%7B19%5Cpi%7D%7B12%7D%5Cright%20%29%3D%5Csqrt%7B%5Cfrac%7B1%2Bcos2%5Cleft%20%28%20%5Cfrac%7B19%5Cpi%7D%7B12%7D%5Cright%20%29%7D%7B2%7D%7D%5C%5C%5C%5Ccos%5Cleft%20%28%20%5Cfrac%7B19%5Cpi%7D%7B12%7D%5Cright%20%29%3D%5Csqrt%7B%5Cfrac%7B1%2Bcos%5Cleft%20%28%20%5Cfrac%7B19%5Cpi%7D%7B6%7D%5Cright%20%29%7D%7B2%7D%7D%5C%5C%5C%5Ccos%5Cleft%20%28%20%5Cfrac%7B9%5Cpi%7D%7B12%7D%5Cright%20%29%3D%5Csqrt%7B%5Cfrac%7B1%2Bcos570%7D%7B2%7D%7D%5C%5C%5C%5Ccos%5Cleft%20%28%20%5Cfrac%7B9%5Cpi%7D%7B12%7D%5Cright%20%29%3D%5Csqrt%7B%5Cfrac%7B1-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%7B2%7D%7D%5C%5C%5C%5Ccos%5Cleft%20%28%20%5Cfrac%7B9%5Cpi%7D%7B12%7D%5Cright%20%29%3D%5Csqrt%7B%5Cfrac%7B2-%5Csqrt%7B3%7D%7D%7B4%7D%7D%5C%5C%5C%5Ccos%5Cleft%20%28%20%5Cfrac%7B9%5Cpi%7D%7B12%7D%5Cright%20%29%3D%5Cfrac%7B%5Csqrt%7B2-%5Csqrt%7B3%7D%7D%7D%7B2%7D)
Answer:
There can be at most
attendees in a corporate team-building event.
Step-by-step explanation:
Let
denotes number of attendees in a corporate team-building event.
Fixed cost = $19
Cost charged per attendee = $1
Budget for the corporate team-building event = $31
Therefore,
![19+1(x)\leq 31\\19+x\leq 31\\x\leq 31-19\\x\leq 12](https://tex.z-dn.net/?f=19%2B1%28x%29%5Cleq%2031%5C%5C19%2Bx%5Cleq%2031%5C%5Cx%5Cleq%2031-19%5C%5Cx%5Cleq%2012)
So, there can be at most
attendees in a corporate team-building event.