(3п/2; 2п) - 4 четверть
cosa >0
sina <0
tga = sina/cosa
sin^2a+ cos^2a = 1
отсюда
sina= - корень квадратный из 1-cos^2a
sina = -3/√10
tga= -3√10 : 1/√10 = -3
1)400+200=600(м)-расстояние пройденной мамой и Вами.
2(x+y+z)=4
x+y+z=2
x+y=2-z
y+z=2-x
<span>z+x=2-y</span>
1) Из формулы n-го члена арифметической прогрессии имеем, что
![a_8=a_1+7d=a_1+2d+5d=a_3+5d=10+5\cdot3=25](https://tex.z-dn.net/?f=a_8%3Da_1%2B7d%3Da_1%2B2d%2B5d%3Da_3%2B5d%3D10%2B5%5Ccdot3%3D25)
2) Аналогично
![a_6=a_1+5d=a_1+2d+3d=a_3+3d=6+3\cdot1=9](https://tex.z-dn.net/?f=a_6%3Da_1%2B5d%3Da_1%2B2d%2B3d%3Da_3%2B3d%3D6%2B3%5Ccdot1%3D9)
3) По формуле n-го члена арифметической прогрессии найдем a11
![a_{11}=a_1+10d=12+10\cdot(-4)=12-40=-28](https://tex.z-dn.net/?f=a_%7B11%7D%3Da_1%2B10d%3D12%2B10%5Ccdot%28-4%29%3D12-40%3D-28)
4) Первый член арифметической прогрессии по формуле n-го члена этой же прогрессии:
![a_9=a_1+8d;~~\Rightarrow~~~a_1=a_9-8d=11-8\cdot2=-5](https://tex.z-dn.net/?f=a_9%3Da_1%2B8d%3B~~%5CRightarrow~~~a_1%3Da_9-8d%3D11-8%5Ccdot2%3D-5)
Сумма первых 12 членов арифметической прогрессии:
![S_{12}= \dfrac{2a_1+11d}{2}\cdot12=6(2a_1+11d)=6\cdot(2\cdot3+11\cdot2)= 168](https://tex.z-dn.net/?f=S_%7B12%7D%3D+%5Cdfrac%7B2a_1%2B11d%7D%7B2%7D%5Ccdot12%3D6%282a_1%2B11d%29%3D6%5Ccdot%282%5Ccdot3%2B11%5Ccdot2%29%3D+168)
5)
![a_1-a_2+a_3-a_4+...+a_{25}-a_{26}+a_{27}=](https://tex.z-dn.net/?f=a_1-a_2%2Ba_3-a_4%2B...%2Ba_%7B25%7D-a_%7B26%7D%2Ba_%7B27%7D%3D)
![=a_1+a_3+a_5+...+a_{25}+a_{27}-(a_2+a_4+...+a_{26})=\\ \\ =13a_1+2d+4d+...26d-(14a_1+d+3d+...+25d)=\\ \\ =-a_1+13d=-3+13\cdot2=23](https://tex.z-dn.net/?f=%3Da_1%2Ba_3%2Ba_5%2B...%2Ba_%7B25%7D%2Ba_%7B27%7D-%28a_2%2Ba_4%2B...%2Ba_%7B26%7D%29%3D%5C%5C+%5C%5C+%3D13a_1%2B2d%2B4d%2B...26d-%2814a_1%2Bd%2B3d%2B...%2B25d%29%3D%5C%5C+%5C%5C+%3D-a_1%2B13d%3D-3%2B13%5Ccdot2%3D23)
Х+у=77
х×2/3=0,8
х×2/3=4/5
находим х:
х=4/5÷2/3
х=4/5×3/2
х=12/10
х=1,2
у=77-1,2
у=75,8
ответ: (1,2; 75,8)