Sin(x-п/4) = 1
x-п/4 = п/2+2п*k
<span>x = 3*п/4+2п*k</span>
х - количество 50-рублёвых купюр, у - количество 10-рублёвых купюр.
![\left \{ {{50x+10y=500} \atop {x+y=22}} \right. \left \{ {{50x+10(22-x)=500} \atop {y=22-x}} \right. \; \left \{ {{50x+220-10x=500} \atop {y=22-x}} \right. \\\\\left \{ {{40x=280} \atop {y=22-x}} \right. \; \left \{ {{x=7} \atop {y=22-7}} \right. \; \left \{ {{x=7} \atop {y=15}} \right. \\\\x=7\; ,\; y=15](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B50x%2B10y%3D500%7D+%5Catop+%7Bx%2By%3D22%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7B50x%2B10%2822-x%29%3D500%7D+%5Catop+%7By%3D22-x%7D%7D+%5Cright.+%5C%3B+%5Cleft+%5C%7B+%7B%7B50x%2B220-10x%3D500%7D+%5Catop+%7By%3D22-x%7D%7D+%5Cright.+%5C%5C%5C%5C%5Cleft+%5C%7B+%7B%7B40x%3D280%7D+%5Catop+%7By%3D22-x%7D%7D+%5Cright.+%5C%3B+%5Cleft+%5C%7B+%7B%7Bx%3D7%7D+%5Catop+%7By%3D22-7%7D%7D+%5Cright.+%5C%3B+%5Cleft+%5C%7B+%7B%7Bx%3D7%7D+%5Catop+%7By%3D15%7D%7D+%5Cright.+%5C%5C%5C%5Cx%3D7%5C%3B+%2C%5C%3B+y%3D15+)
Пусть x - скорость теплохода в стоячей воде,
![t_{1}](https://tex.z-dn.net/?f=+t_%7B1%7D+)
время движения по течению,
![t_{2}](https://tex.z-dn.net/?f=+t_%7B2%7D+)
время движения против течения
. Тогда получаем следующую систему уравнений:
(x+4)*
![t_{1}](https://tex.z-dn.net/?f=+t_%7B1%7D+)
= 221
(x-4)*
![t_{2}](https://tex.z-dn.net/?f=+t_%7B2%7D+)
= 221
![t_{1}](https://tex.z-dn.net/?f=+t_%7B1%7D+)
+
![t_{2}](https://tex.z-dn.net/?f=+t_%7B2%7D+)
= 15
X^2-14x+49=x^2+20x+100
-34x=51
x=-1.5