120*2-1=240-1=239.....................
производительность время работа
1 тр 1/25 басс/мин 25 мин 1
2 тр 1/15 басс/мин 15 мин 1
1+2 тр ? ? 1
1) 1/25+1/15 = 3/75 + 5/75 = 8/75 (басс/мин) общая производительность обеих труб
2) 1 : 8/75 = 75/8 = 9_3/8 (мин) требуется для заполнения данного бассейна обеими трудами при работе вместе
3) 9_3/8 < 10 (мин) бассейн успеет наполниться за 10 мин при данных условиях
-7+×=13
×= 13+7
×= 20
Проверка: -7+20=13. 13=13
×+ -15=10
×=10+15
×=25
Проверка: 25+ -15=10. 10=10
-6+×=5
×=6+5
×=11
Проверка: -6+11=5. 5=5
340+мкм во 2 день
340+340+м=680+мкм весь путь
Формулы для арифметической прогрессии:
![a_n=a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29d)
составим систему:
![\left \{ {{a_3+a_4+a_5+a_6=64} \atop {a_3a_6=252}} \right. \left \{ {{a_3+a_3+d+a_6-d+a_6=64} \atop {a_3a_6=252}} \left \{ {{a_3+a_6=32} \atop {a_3a_6=252}} \right.\right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Ba_3%2Ba_4%2Ba_5%2Ba_6%3D64%7D+%5Catop+%7Ba_3a_6%3D252%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7Ba_3%2Ba_3%2Bd%2Ba_6-d%2Ba_6%3D64%7D+%5Catop+%7Ba_3a_6%3D252%7D%7D+%5Cleft+%5C%7B+%7B%7Ba_3%2Ba_6%3D32%7D+%5Catop+%7Ba_3a_6%3D252%7D%7D+%5Cright.%5Cright.+)
в принципе...
![a_3](https://tex.z-dn.net/?f=a_3)
и
![a_6](https://tex.z-dn.net/?f=a_6)
можно найти по теореме Виета, но лучше мы найдем по старинке...
![\left \{ {{a_3=32-a_6} \atop {(32-a_6)a_6=252}} \right.\left \{ {{a_3=32-a_6} \atop {32a_6-a_6^2-252=0}} \right.\left \{ {{a_3=32-a_6} \atop {a_6^2-32a_6+252=0}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Ba_3%3D32-a_6%7D+%5Catop+%7B%2832-a_6%29a_6%3D252%7D%7D+%5Cright.%5Cleft+%5C%7B+%7B%7Ba_3%3D32-a_6%7D+%5Catop+%7B32a_6-a_6%5E2-252%3D0%7D%7D+%5Cright.%5Cleft+%5C%7B+%7B%7Ba_3%3D32-a_6%7D+%5Catop+%7Ba_6%5E2-32a_6%2B252%3D0%7D%7D+%5Cright.)
найдем корни для
![a_6^2-32a_6+252=0](https://tex.z-dn.net/?f=a_6%5E2-32a_6%2B252%3D0)
:
![D/2=(\frac{32}{2})^2-252=256-252=4](https://tex.z-dn.net/?f=D%2F2%3D%28%5Cfrac%7B32%7D%7B2%7D%29%5E2-252%3D256-252%3D4)
![a_6=\frac{32}{2}-\sqrt{4}=14](https://tex.z-dn.net/?f=a_6%3D%5Cfrac%7B32%7D%7B2%7D-%5Csqrt%7B4%7D%3D14)
или
![a_6=\frac{32}{2}+\sqrt{4}=18](https://tex.z-dn.net/?f=a_6%3D%5Cfrac%7B32%7D%7B2%7D%2B%5Csqrt%7B4%7D%3D18)
![\left \{ {{a_3=32-a_6} \atop {\left[\begin{array}{c}a_6=14\\a_6=18\end{array}\right}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Ba_3%3D32-a_6%7D+%5Catop+%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da_6%3D14%5C%5Ca_6%3D18%5Cend%7Barray%7D%5Cright%7D%7D+%5Cright.+)
![\left[\begin{array}{c} \left \{ {{a_3=14} \atop {a_6=18}} \right. \\ \left \{ {{a_3=18} \atop {a_6=14}} \right. \end{array}\right](https://tex.z-dn.net/?f=+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D+%5Cleft+%5C%7B+%7B%7Ba_3%3D14%7D+%5Catop+%7Ba_6%3D18%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7Ba_3%3D18%7D+%5Catop+%7Ba_6%3D14%7D%7D+%5Cright.+%5Cend%7Barray%7D%5Cright)
теперь найдем
![a_{1}](https://tex.z-dn.net/?f=a_%7B1%7D)
и
![d](https://tex.z-dn.net/?f=+d)
для каждой системы
![\left[\begin{array}{c} \left \{ {{14=a_1+2d} \atop {18=a_1+5d}} \right. \\ \left \{ {{18=a_1+2d} \atop {14=a_1+5d}} \right. \end{array}\right \left[\begin{array}{c} \left \{ {{a_1=14-2d} \atop {5d=18-14+2d}} \right. \\ \left \{ {{a_1=18-2d} \atop {5d=14-18+2d}} \right. \end{array}\right \left[\begin{array}{c} \left \{ {{a_1=\frac{34}{3}} \atop {d=\frac{4}{3}}} \right. \\ \left \{ {{a_1=\frac{62}{3}} \atop {d=-\frac{4}{3}}} \right. \end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D+%5Cleft+%5C%7B+%7B%7B14%3Da_1%2B2d%7D+%5Catop+%7B18%3Da_1%2B5d%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7B18%3Da_1%2B2d%7D+%5Catop+%7B14%3Da_1%2B5d%7D%7D+%5Cright.+%5Cend%7Barray%7D%5Cright+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D+%5Cleft+%5C%7B+%7B%7Ba_1%3D14-2d%7D+%5Catop+%7B5d%3D18-14%2B2d%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7Ba_1%3D18-2d%7D+%5Catop+%7B5d%3D14-18%2B2d%7D%7D+%5Cright.+%5Cend%7Barray%7D%5Cright+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D+%5Cleft+%5C%7B+%7B%7Ba_1%3D%5Cfrac%7B34%7D%7B3%7D%7D+%5Catop+%7Bd%3D%5Cfrac%7B4%7D%7B3%7D%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7Ba_1%3D%5Cfrac%7B62%7D%7B3%7D%7D+%5Catop+%7Bd%3D-%5Cfrac%7B4%7D%7B3%7D%7D%7D+%5Cright.+%5Cend%7Barray%7D%5Cright+)
теперь найдем
![a_{10}](https://tex.z-dn.net/?f=a_%7B10%7D)
для каждой системы
![\left[\begin{array}{c}a_{10}=\frac{34}{3}+9\frac{4}{3}=\frac{58}{3}\\a_{10}=\frac{62}{3}-9\frac{4}{3}=\frac{38}{3}\end{array}\right](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da_%7B10%7D%3D%5Cfrac%7B34%7D%7B3%7D%2B9%5Cfrac%7B4%7D%7B3%7D%3D%5Cfrac%7B58%7D%7B3%7D%5C%5Ca_%7B10%7D%3D%5Cfrac%7B62%7D%7B3%7D-9%5Cfrac%7B4%7D%7B3%7D%3D%5Cfrac%7B38%7D%7B3%7D%5Cend%7Barray%7D%5Cright)
Ответ:
![\frac{58}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B58%7D%7B3%7D)
и
![\frac{38}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B38%7D%7B3%7D)