Решебник по алгебре 9 класс Мерзляк Задание 796

\[\boxed{\mathbf{796\ (796).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[a_{1} = 4,9;\ \ \ d = 9,8;\ \ \ \ \ S_{n} = 490\]

\[S_{n} = \frac{2a_{1} + d(n - 1)}{2} \cdot n = 490\]

\[\frac{2 \cdot 4,9 + 9,8 \cdot (n - 1)}{2} \cdot n = 490\]

\[(9,8 + 9,8n - 9,8) \cdot n = 980\]

\[9,8n^{2} = 980\]

\[n^{2} = 100\]

\[n = \pm 10\]

\[n = 10\]

\[10\ с - время\ падения\ тела\]

\[\ с\ высоты\ 490\ м.\]

\[Ответ:10\ с.\ \]

\[\boxed{\mathbf{796.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x = - 3;\ ( - 3;0);\ \]

\[\ x_{0} = - \frac{b}{2a} = - 3,\ \ \]

\[- \frac{b}{2} = - 3,\ \ b = 6\]

\[D = ( - 3)^{2} + 6 \cdot ( - 3) + c\]

\[\ c = - 9 + 18 = 9\]

\[Ответ:b = 6;\ c = 9.\]

\[2)\ x = 0;\ \ (0;4);\]

\[x_{0} = - \frac{b}{2a} = 0;\ \ b = 0\]

\[4 = 0^{2} + 0 + c \Longrightarrow \ \ c = 4\]

\[Ответ:b = 0;\ \ c = 4.\]

\[3)\ x = - 2;\ x = 5\]

\[\left\{ \begin{matrix} 0 = ( - 2)^{2} + b \cdot ( - 2) + c \\ 0 = 5^{2} + b \cdot 5 + c\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 4 - 2b + c = 0\ \ \\ 25 + 5b + c = 0 \\ \end{matrix} \right.\ - \ \ \ \ \]

\[\ \left\{ \begin{matrix} - 21 - 7b = 0 \\ c = 2b - 4 \\ \end{matrix} \right.\ \text{\ \ \ }\left\{ \begin{matrix} b = - 3 \\ c = - 10 \\ \end{matrix} \right.\ \]

\[Ответ:b = - 3;\ c = - 10.\]