Решебник по алгебре 9 класс Мерзляк Задание 801

 

\[\boxed{\mathbf{801\ (801).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[a_{1} = 100;\ \ S_{6} = 5 \cdot S_{7 - 12}\]

\[S_{6} = \frac{2cc + 5d}{2} \cdot 6 =\]

\[= (2 \cdot 100 + 5d) \cdot 3 =\]

\[= (200 + 5d) \cdot 3\]

\[(200 + 5d) \cdot 3 = 5 \cdot S_{7 - 12}\]

\[S_{7 - 12} = \frac{2a_{7} + 5d}{2} \cdot 6 =\]

\[= \left( 2 \cdot \left( a_{1} + 6d \right) + 5d \right) \cdot 3 =\]

\[= \left( 2a_{1} + 12d + 5d \right) \cdot 3 =\]

\[= \left( 2a_{1} + 17d \right) \cdot 3 =\]

\[= (200 + 17d) \cdot 3\]

\[(200 + 5d) \cdot 3 =\]

\[= 5 \cdot (200 + 17d) \cdot 3\ \ \ \ \ |\ :3\]

\[200 + 5d = 1000 + 85d\]

\[80d = - 800,\ \ d = - 10\]

\[Ответ:\ d = - 10.\]

\[\boxed{\mathbf{801.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[y = ax^{2} + bx + c;\ \ (0;10);\ \]

\[\text{\ \ }\left( x_{0};y_{0} \right) = (6;\ - 2)\]

\[10 = 0 + 0 + c \Longrightarrow \ \ c = 10\]

\[- \frac{b}{2a} = 6 \Longrightarrow \ \ b = - 12a\]

\[- 2 = 36a + 6b + 10\]

\[- 2 = 36a + 6 \cdot ( - 12a) + 10\]

\[- 2 = 36a - 72a + 10\]

\[36a = 12\]

\[a = \frac{1}{3} \Longrightarrow \ \ b = - 12 \cdot \frac{1}{3} = - 4\]

\[Ответ:a = \frac{1}{3};\ \ b = - 4;\ \ c = 10.\]