\[\boxed{\mathbf{770.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[Дано:\ \]
\[ABCD - параллелограмм;\]
\[\textbf{а)}\ \overrightarrow{a} = \overrightarrow{\text{AB}};\ \overrightarrow{b} = \overrightarrow{\text{BC}};\]
\[\textbf{б)}\ \overrightarrow{a} = \overrightarrow{\text{CB}};\ \overrightarrow{b} = \overrightarrow{\text{CD}};\]
\[\textbf{в)}\ \overrightarrow{a} = \overrightarrow{\text{AB}};\ \overrightarrow{b} = \overrightarrow{\text{DA}}.\]
\[Выразить:\ \]
\[\overrightarrow{\text{AC}}.\]
\[Решение.\]
\[\textbf{а)}\ \overrightarrow{\text{AC}} = \overrightarrow{\text{AB}} + \overrightarrow{\text{BC}} =\]
\[= \overrightarrow{a} + \overrightarrow{b}\ (по\ правилу\ треугольника).\]
\[\textbf{б)}\ \overrightarrow{\text{AC}} = \overrightarrow{\text{AD}} + \overrightarrow{\text{DC}} =\]
\[= \overrightarrow{\text{BC}} + \left( - \overrightarrow{\text{CD}} \right) =\]
\[= - \overrightarrow{\text{CB}} + \left( - \overrightarrow{\text{CD}} \right) =\]
\[= - \overrightarrow{a} + \left( - \overrightarrow{b} \right) = - \overrightarrow{a} - \overrightarrow{b}.\]
\[\textbf{в)}\ \overrightarrow{\text{AC}} = \overrightarrow{\text{AB}} + \overrightarrow{\text{AD}} =\]
\[= \overrightarrow{\text{AB}} + \left( - \overrightarrow{\text{DA}} \right) = \overrightarrow{a} + \left( - \overrightarrow{b} \right) =\]
\[= \overrightarrow{a} - \overrightarrow{b}\ (по\ правилу\ \]
\[треугольника).\]
\[\boxed{\mathbf{770.еуроки - ответы\ на\ пятёрку}}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[окружность\ (O,\ R);\ \]
\[\cup AB = 140{^\circ};\]
\(\cup AM\ :\ \cup BM = 6\ :5.\)
\[\mathbf{Найти:}\]
\[\angle BAM - ?\]
\[\mathbf{Решение.}\]
\[1)\ Пусть\ \cup AM = 6x;\ \]
\[\cup BM = 5x.\]
\[2)\ \cup AB = 360{^\circ} - 140{^\circ} = 220{^\circ}\]
\[\cup AM + \cup BM = 220{^\circ}\]
\[6x + 5x = 220{^\circ}\]
\[11x = 220{^\circ}\]
\[x = 20{^\circ}.\]
\[4)\ \cup BM = 5 \bullet 20{^\circ} = 100{^\circ}.\]
\[\angle BAM = \frac{1}{2} \cup BM = \frac{100{^\circ}}{2} = 50{^\circ}\ \]
\[(по\ теореме\ о\ вписанном\ угле).\]
\[Ответ:\angle BAM = 50{^\circ}.\]