X=180-110
x=70
Слишком легко
Составим функцию:
![F(t)=\frac{t}{t+\frac{1}{2}}- \frac{2}{49}t= \frac{2t}{2t+1} -\frac{2}{49}t](https://tex.z-dn.net/?f=F%28t%29%3D%5Cfrac%7Bt%7D%7Bt%2B%5Cfrac%7B1%7D%7B2%7D%7D-+%5Cfrac%7B2%7D%7B49%7Dt%3D+%5Cfrac%7B2t%7D%7B2t%2B1%7D+-%5Cfrac%7B2%7D%7B49%7Dt)
Найдём производную этой функции, используя формулы
![(\frac{u}{v})'=\frac{u'\cdot v - u \cdot v'}{v^2}; \ \ \ \ (x^n)'=n \cdot x^{n-1}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bu%7D%7Bv%7D%29%27%3D%5Cfrac%7Bu%27%5Ccdot+v+-+u+%5Ccdot+v%27%7D%7Bv%5E2%7D%3B+%5C+%5C+%5C+%5C+%28x%5En%29%27%3Dn+%5Ccdot+x%5E%7Bn-1%7D)
а также свойство:
![(u+v)'=u'+v'](https://tex.z-dn.net/?f=%28u%2Bv%29%27%3Du%27%2Bv%27)
![F'(t)= (\frac{2t}{2t+1} - \frac{2}{49}t)'=(\frac{2t}{2t+1})' - (\frac{2}{49}t)'=\frac{2\cdot(2t+1) - 2t \cdot 2}{(2t+1)^2}- \frac{2}{49}=\\ \\ =\frac{4t+2-4t}{(2t+1)^2}-\frac{2}{49}=\frac{2}{(2t+1)^2}-\frac{2}{49}](https://tex.z-dn.net/?f=F%27%28t%29%3D+%28%5Cfrac%7B2t%7D%7B2t%2B1%7D+-+%5Cfrac%7B2%7D%7B49%7Dt%29%27%3D%28%5Cfrac%7B2t%7D%7B2t%2B1%7D%29%27+-+%0A%28%5Cfrac%7B2%7D%7B49%7Dt%29%27%3D%5Cfrac%7B2%5Ccdot%282t%2B1%29+-+2t+%5Ccdot+2%7D%7B%282t%2B1%29%5E2%7D-+%0A%5Cfrac%7B2%7D%7B49%7D%3D%5C%5C+%5C%5C+%0A%3D%5Cfrac%7B4t%2B2-4t%7D%7B%282t%2B1%29%5E2%7D-%5Cfrac%7B2%7D%7B49%7D%3D%5Cfrac%7B2%7D%7B%282t%2B1%29%5E2%7D-%5Cfrac%7B2%7D%7B49%7D)
Приравняем производную функции к нулю:
![\frac{2}{(2t+1)^2}-\frac{2}{49}=0; \ \ \frac{2}{(2t+1)^2}=\frac{2}{49}; \\ \\ 2 \cdot (2t+1)^2 =98; \ \ 2 \cdot (4t^2 +4t+1)=98; \ \ \ 8t^2 +8t +2 -98=0; \\ \\ 8t^2 +8t -96=0; \ \ \ t^2 +t-12=0; \ \ t_{1,2}=\frac{-1 \pm \sqrt{1 +48}}{2}=\frac{-1 \pm 7}{2} \\ \\ t_1 =3; \ \ t_2=-4 \ \ (t\ \textgreater \ 0)](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B%282t%2B1%29%5E2%7D-%5Cfrac%7B2%7D%7B49%7D%3D0%3B+%5C+%5C+%0A%5Cfrac%7B2%7D%7B%282t%2B1%29%5E2%7D%3D%5Cfrac%7B2%7D%7B49%7D%3B+%5C%5C+%5C%5C+2+%5Ccdot+%282t%2B1%29%5E2+%3D98%3B+%5C+%5C+2+%5Ccdot%0A+%284t%5E2+%2B4t%2B1%29%3D98%3B+%5C+%5C+%5C+8t%5E2+%2B8t+%2B2+-98%3D0%3B+%5C%5C+%5C%5C+8t%5E2+%2B8t+-96%3D0%3B+%5C+%5C+%5C+%0At%5E2+%2Bt-12%3D0%3B+%5C+%5C+t_%7B1%2C2%7D%3D%5Cfrac%7B-1+%5Cpm+%5Csqrt%7B1+%2B48%7D%7D%7B2%7D%3D%5Cfrac%7B-1+%5Cpm+%0A7%7D%7B2%7D+%5C%5C+%5C%5C+t_1+%3D3%3B+%5C+%5C+t_2%3D-4+%5C+%5C+%28t%5C+%5Ctextgreater+%5C+0%29)
Ответ: 3 дня
9х²-4=0
9х²=4
х²=4/9
х=±2/3
2х²=3х
2х²-3х=0
х(2х-3)=0
х1=0
х2=1,5
2=7х²+2
-7х²=0
х=0
2х²-8х+х-4=х²-4
х²-7х=0
х(х-7)=0
х1=0
х2=7