8+150Х-450=608
150Х=608+450-8
150Х=1050
Х=1050/150
Х=7
1,53х+0,47х=15
2х=15
х=15:2
х=7.5
3.28х+4.72х=17
8х=17
х=17:8
х=2.125
84х-44.6х=35
40х=35
х=35:40=0.875
39.49х+10.51х=18
50х=18
х=18:50=0.36
Пусть
![arctg \frac{1}{6} =t](https://tex.z-dn.net/?f=arctg+%5Cfrac%7B1%7D%7B6%7D+%3Dt)
, тогда
![tg\ t= \frac{1}{6},\ 0\ \textless \ t\ \textless \ \frac{ \pi }{2}](https://tex.z-dn.net/?f=tg%5C+t%3D+%5Cfrac%7B1%7D%7B6%7D%2C%5C+0%5C+%5Ctextless+%5C+t%5C+%5Ctextless+%5C++%5Cfrac%7B+%5Cpi+%7D%7B2%7D+)
Теперь задача сводится к вычислению значения выражения cos 2t.
![1+tg^2t= \frac{1}{cos^2t} \\ cos^2t= \frac{1}{1+tg^2t} } =\frac{1}{1+( \frac{1}{6}) ^2} }= \frac{36}{37}\\ cos2t=2cos^2t-1=2*\frac{36}{37}-1=\frac{72-37}{37}=\frac{35}{37}](https://tex.z-dn.net/?f=1%2Btg%5E2t%3D+%5Cfrac%7B1%7D%7Bcos%5E2t%7D+%5C%5C+cos%5E2t%3D+%5Cfrac%7B1%7D%7B1%2Btg%5E2t%7D+%7D+%3D%5Cfrac%7B1%7D%7B1%2B%28+%5Cfrac%7B1%7D%7B6%7D%29+%5E2%7D+%7D%3D+%5Cfrac%7B36%7D%7B37%7D%5C%5C%0Acos2t%3D2cos%5E2t-1%3D2%2A%5Cfrac%7B36%7D%7B37%7D-1%3D%5Cfrac%7B72-37%7D%7B37%7D%3D%5Cfrac%7B35%7D%7B37%7D)
Значит,
![cos(2arctg \frac{1}{6} )=\frac{35}{37}](https://tex.z-dn.net/?f=cos%282arctg+%5Cfrac%7B1%7D%7B6%7D+%29%3D%5Cfrac%7B35%7D%7B37%7D)
Ответ:
![\frac{35}{37}](https://tex.z-dn.net/?f=%5Cfrac%7B35%7D%7B37%7D)
(х - 1 15/16) + 7 3/16 = 8 1/16 + 4 9/16
(х - 31/16) + 115/16 = 129/16 + 73/16
(х - 31/16) + 115/16 = 202/16
х - 31/16 = 202/16 - 115/16
х - 31/16 = 87/16
х = 87/16 + 31/16
х = 118/16 = 7 6/16
(118/16 - 31/16) + 115/16 = 202/16
87/16 + 115/16 = 202/16
202/16 = 202/16