Answer: The costs are 8.4% of the total revenue.
The stadium is going to make $750,000 for the naming rights of the stadium. The cost to the stadium is on $63,000.
To find the percent, we have to divide the two values and multiply by 100.
63000 / 750000 x 100 = 8.4%
Answer:
This is actually a reduction, and the scale factor of this dilation is 0.5.
If he spent half his savings on supplies and the other half on lunch he shouldn't have money left over. It's a trick question.
![\bf \textit{Double Angle Identities} \\\\ sin(2\theta)=2sin(\theta)cos(\theta) \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ 2cos^2(\theta)-1 \end{cases}\quad \begin{array}{llll} \\ \leftarrow \textit{we'll use}\\ \leftarrow \textit{these two} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{double-angle identity}}{2cos^2(3x)-1}=-sin(3x)\implies cos[2(3x)]=-sin(3x)](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BDouble%20Angle%20Identities%7D%20%5C%5C%5C%5C%20sin%282%5Ctheta%29%3D2sin%28%5Ctheta%29cos%28%5Ctheta%29%20%5C%5C%5C%5C%20cos%282%5Ctheta%29%3D%20%5Cbegin%7Bcases%7D%20cos%5E2%28%5Ctheta%29-sin%5E2%28%5Ctheta%29%5C%5C%201-2sin%5E2%28%5Ctheta%29%5C%5C%202cos%5E2%28%5Ctheta%29-1%20%5Cend%7Bcases%7D%5Cquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5C%5C%20%5Cleftarrow%20%5Ctextit%7Bwe%27ll%20use%7D%5C%5C%20%5Cleftarrow%20%5Ctextit%7Bthese%20two%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bdouble-angle%20identity%7D%7D%7B2cos%5E2%283x%29-1%7D%3D-sin%283x%29%5Cimplies%20cos%5B2%283x%29%5D%3D-sin%283x%29)
![\bf 1-2sin^2(3x)=-sin(3x)\implies 0=\stackrel{\stackrel{ax^2+bx+c}{\downarrow }}{2sin^2(3x)-sin(3x)-1} \\\\\\ 0=[2sin(3x)+1][sin(3x)-1] \\\\[-0.35em] ~\dotfill\\\\ 0=2sin(3x)+1\implies -1=2sin(3x)\implies -\cfrac{1}{2}=sin(3x) \\\\\\ \cfrac{7\pi }{6}~,~\cfrac{11\pi }{6}=3x\implies \boxed{\cfrac{7\pi }{18}~,~\cfrac{11\pi }{18}=x} \\\\[-0.35em] ~\dotfill\\\\ 0=sin(3x)-1\implies 1=sin(3x)\implies \cfrac{\pi }{2}=3x\implies \boxed{\cfrac{\pi }{6}=x}](https://tex.z-dn.net/?f=%5Cbf%201-2sin%5E2%283x%29%3D-sin%283x%29%5Cimplies%200%3D%5Cstackrel%7B%5Cstackrel%7Bax%5E2%2Bbx%2Bc%7D%7B%5Cdownarrow%20%7D%7D%7B2sin%5E2%283x%29-sin%283x%29-1%7D%20%5C%5C%5C%5C%5C%5C%200%3D%5B2sin%283x%29%2B1%5D%5Bsin%283x%29-1%5D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%200%3D2sin%283x%29%2B1%5Cimplies%20-1%3D2sin%283x%29%5Cimplies%20-%5Ccfrac%7B1%7D%7B2%7D%3Dsin%283x%29%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B7%5Cpi%20%7D%7B6%7D~%2C~%5Ccfrac%7B11%5Cpi%20%7D%7B6%7D%3D3x%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B7%5Cpi%20%7D%7B18%7D~%2C~%5Ccfrac%7B11%5Cpi%20%7D%7B18%7D%3Dx%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%200%3Dsin%283x%29-1%5Cimplies%201%3Dsin%283x%29%5Cimplies%20%5Ccfrac%7B%5Cpi%20%7D%7B2%7D%3D3x%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B%5Cpi%20%7D%7B6%7D%3Dx%7D)
now, those angles are the angles in the range of [0, 2π] only.
a general solution angles will be
