Длина единичной окружности: с= 2·π·1 = 2π.
4.2
Дуга АМ =
![\frac{c}{8}=\frac{2 \pi }{8}=\frac{\pi }{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B8%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B8%7D%3D%5Cfrac%7B%5Cpi+%7D%7B4%7D)
Дуга BD =
![\frac{c}{2}=\frac{2 \pi }{2}=\pi](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B2%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B2%7D%3D%5Cpi)
Дуга CK =
![c*\frac{10}{12}=\frac{5c}{6}=\frac{5*2 \pi }{6}=\frac{5\pi }{3}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B10%7D%7B12%7D%3D%5Cfrac%7B5c%7D%7B6%7D%3D%5Cfrac%7B5%2A2+%5Cpi+%7D%7B6%7D%3D%5Cfrac%7B5%5Cpi+%7D%7B3%7D)
Дуга MP =
![c*(\frac{1}{8}+\frac{2}{12})=c*(\frac{1}{8}+\frac{1}{6})=\frac{7c}{24}=\frac{7*2 \pi }{24}=\frac{7\pi }{12}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B2%7D%7B12%7D%29%3Dc%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B6%7D%29%3D%5Cfrac%7B7c%7D%7B24%7D%3D%5Cfrac%7B7%2A2+%5Cpi+%7D%7B24%7D%3D%5Cfrac%7B7%5Cpi+%7D%7B12%7D)
Дуга DM =
![c*\frac{3}{8}=\frac{3*2 \pi }{8}=\frac{3\pi }{4}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B3%2A2+%5Cpi+%7D%7B8%7D%3D%5Cfrac%7B3%5Cpi+%7D%7B4%7D)
Дуга MK =
![c*(\frac{1}{8}+\frac{1}{12})=\frac{5c}{24}=\frac{5*2 \pi }{24}=\frac{5\pi }{12}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B12%7D%29%3D%5Cfrac%7B5c%7D%7B24%7D%3D%5Cfrac%7B5%2A2+%5Cpi+%7D%7B24%7D%3D%5Cfrac%7B5%5Cpi+%7D%7B12%7D)
Дуга CP =
![c*\frac{11}{12}=\frac{11*2 \pi }{12}=\frac{11\pi }{6}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B11%7D%7B12%7D%3D%5Cfrac%7B11%2A2+%5Cpi+%7D%7B12%7D%3D%5Cfrac%7B11%5Cpi+%7D%7B6%7D)
Дуга PC =
![\frac{c}{12}=\frac{2 \pi }{12}=\frac{\pi }{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B12%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B12%7D%3D%5Cfrac%7B%5Cpi+%7D%7B6%7D)
4.3
Дуга АМ =
![\frac{2}{5}*\frac{c}{4}=\frac{c}{10}=\frac{2 \pi }{10}=\frac{\pi }{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%2A%5Cfrac%7Bc%7D%7B4%7D%3D%5Cfrac%7Bc%7D%7B10%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B10%7D%3D%5Cfrac%7B%5Cpi+%7D%7B5%7D)
Дуга МB =
![\frac{3}{5}*\frac{c}{4}=\frac{3c}{20}=\frac{3*2\pi }{20}=\frac{3\pi }{10}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%2A%5Cfrac%7Bc%7D%7B4%7D%3D%5Cfrac%7B3c%7D%7B20%7D%3D%5Cfrac%7B3%2A2%5Cpi+%7D%7B20%7D%3D%5Cfrac%7B3%5Cpi+%7D%7B10%7D)
Дуга DМ =
![c*(\frac{1}{4}+\frac{2}{5}*\frac{1}{4})=c*(\frac{1}{4}+\frac{1}{10})=\frac{7c}{20}=\frac{7*2\pi }{20}=\frac{7\pi }{10}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B2%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B4%7D%29%3Dc%2A%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B10%7D%29%3D%5Cfrac%7B7c%7D%7B20%7D%3D%5Cfrac%7B7%2A2%5Cpi+%7D%7B20%7D%3D%5Cfrac%7B7%5Cpi+%7D%7B10%7D)
Дуга МC =
![c*(\frac{3}{5}*\frac{1}{4}+\frac{1}{4})=c*(\frac{3}{20}+\frac{1}{4})=\frac{8c}{20}=\frac{2c}{5}=\frac{2*2\pi }{5}=\frac{4\pi }{5}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B3%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B4%7D%29%3Dc%2A%28%5Cfrac%7B3%7D%7B20%7D%2B%5Cfrac%7B1%7D%7B4%7D%29%3D%5Cfrac%7B8c%7D%7B20%7D%3D%5Cfrac%7B2c%7D%7B5%7D%3D%5Cfrac%7B2%2A2%5Cpi+%7D%7B5%7D%3D%5Cfrac%7B4%5Cpi+%7D%7B5%7D)
Представим что в втором мешке Х яблок, тогда в первом мешке 2Х яблок. Следовательно в третьем мешке будет 2Х+12 яблок.
Составим уравнение:
X + 2X + (2X + 12) = 100
5X = 88
Х = 17.6 кг (яблок в втором мешке)
Тогда в первом будет:
17.6 × 2 = 35.2 кг
А в третьем:
35.2 + 12 = 47.2 кг
Ответ : 35.2кг, 17.6кг, 47.2кг.
Решим это уравнение как квадратное уравнение относительно cos x.
![D=b^2-4ac=(-3)^2-4\cdot2\cdot 1=1](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%3D%28-3%29%5E2-4%5Ccdot2%5Ccdot+1%3D1)
![\cos x= \dfrac{3+1}{2\cdot 2} =1;~~~~~~\Rightarrow~~~~~\boxed{x_1=2 \pi n,n \in \mathbb{Z}}\\ \\ \cos x= \dfrac{3-1}{2\cdot 2}=0.5;~~~~~\Rightarrow~~~~\boxed{x_2\pm \frac{\pi}{3}+2 \pi n,n \in \mathbb{Z} }](https://tex.z-dn.net/?f=%5Ccos+x%3D+%5Cdfrac%7B3%2B1%7D%7B2%5Ccdot+2%7D+%3D1%3B~~~~~~%5CRightarrow~~~~~%5Cboxed%7Bx_1%3D2+%5Cpi+n%2Cn+%5Cin+%5Cmathbb%7BZ%7D%7D%5C%5C+%5C%5C+%5Ccos+x%3D+%5Cdfrac%7B3-1%7D%7B2%5Ccdot+2%7D%3D0.5%3B~~~~~%5CRightarrow~~~~%5Cboxed%7Bx_2%5Cpm+%5Cfrac%7B%5Cpi%7D%7B3%7D%2B2+%5Cpi+n%2Cn+%5Cin+%5Cmathbb%7BZ%7D+%7D+)