Решебник по алгебре 9 класс Мерзляк Задание 820

 

\[\boxed{\mathbf{820\ (820).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ b_{1} = 6;\ \ b_{2} = - 3\]

\[b_{2} = b_{1}\text{q\ \ }\]

\[q = \frac{b_{2}}{b_{1}} = - \frac{3}{6} = - \frac{1}{2}.\]

\[2)\ b_{7} = - 9;\ \ b_{8} = 15\]

\[b_{8} = b_{7}\text{q\ }\]

\[q = \frac{b_{8}}{b_{7}} = \frac{15}{- 9} = \frac{5}{- 3} = - 1\frac{2}{3}.\]

\[3)\ b_{10} = 3\sqrt{3};\ \ b_{11} = 9\]

\[b_{11} = b_{10}q\]

\[\ \ q = \frac{b_{11}}{b_{10}} = \frac{9}{3\sqrt{3}} = \frac{3}{\sqrt{3}} =\]

\[= \frac{3\sqrt{3}}{3} = \sqrt{3}.\]

\[\boxed{\mathbf{820.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[Пусть\ \text{x\ }\frac{км}{ч} - скорость\]

\[\ первого\ автомобиля,\ y\ \]

\[\frac{км}{ч} - скорость\]

\[второго\ автомобиля.\ Путь\ за\ 2\]

\[\ часа\ составил\ 240 + 40 =\]

\[= 280\ км,\ тогда\ \]

\[2 \cdot (x + y) = 280.\]

\[Составим\ систему:\]

\[\left\{ \begin{matrix} 2 \cdot (x + y) = 280\ \ \ |\ :2 \\ \frac{240}{x} - \frac{240}{y} = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\text{\ \ \ }\left\{ \begin{matrix} x + y = 140\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 240y - 240x - xy = 0 \\ \end{matrix} \right.\ ,\]

\[\ \ x = 140 - y\]

\[240y - 240 \cdot (140 - y) -\]

\[- y(140 - y) = 0\]

\[240y - 33\ 600 + 240y -\]

\[- 140y + y^{2} = 0\]

\[y^{2} + 340y - 33\ 600 = 0\]

\[y_{1} + y_{2} = - 340,\ \ \]

\[y_{1}y_{2} = - 33600\]

\[y = 80\ \ \ \ \ \ \ \ \ \ или\ \ \ \ \ \ \ \ y =\]

\[= - 420 \Longrightarrow не\ удовлетворяет.\]

\[\left\{ \begin{matrix} y = 80\ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = 140 - 80 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 80 \\ x = 60 \\ \end{matrix} \right.\ \]

\[Ответ:80\frac{км}{ч},\ 60\ \frac{км}{ч}\text{.\ }\]