\[\boxed{\mathbf{1032.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\overrightarrow{F_{1}} = \overrightarrow{F_{2}};\]
\[\angle F_{1}AF_{2} = 72{^\circ};\]
\[\left| \overrightarrow{F} \right| = 120\ кг.\]
\[\mathbf{Найти:}\]
\[\left| \overrightarrow{F_{1}} \right|;\left| \overrightarrow{F_{2}} \right| - ?\]
\[\mathbf{Решение.}\]
\[1)\ В\ \mathrm{\Delta}AA_{1}F_{2}:\]
\[\angle A_{1} = 90{^\circ};\ \angle AF_{2}A_{1} = 72{^\circ} \Longrightarrow\]
\[\Longrightarrow AA_{1} = AF_{2} \bullet \sin{72{^\circ}}.\]
\[2)\ AF_{1}FF_{2} - ромб\ \]
\[(по\ построению).\]
\[3)\ В\ \mathrm{\Delta}AA_{1}F:\]
\[\angle A_{1} = 90{^\circ};\ \]
\[\angle AFA_{1} = 36{^\circ} \Longrightarrow\]
\[\Longrightarrow \ AA_{1} = AF \bullet \sin{36{^\circ}}.\]
\[4)\ AF_{2} \bullet \sin{72{^\circ}} = AF \bullet \sin{36{^\circ}}\]
\[AF_{2} \bullet \sin{72{^\circ}} = 120 \bullet \sin{36{^\circ}}\]
\[AF_{2} = \frac{120 \bullet 0,5878}{0,9511} = 74,2\ кг.\]
\[5)\ AF_{2} = AF_{1} = 74,2\ кг.\]
\[\mathbf{Ответ:}\left| \overrightarrow{F_{1}} \right| = \left| \overrightarrow{F_{2}} \right| = 74,2\ к\mathbf{г}\mathbf{.}\]
\[\boxed{\mathbf{1032.еуроки - ответы\ на\ пятёрку}}\]
\[\mathbf{Дано:}\]
\[\textbf{а)}\ AB = 2;A(2;3);\]
\[B(x;1).\]
\[\textbf{б)}\ M_{1}M_{2} = 7;\]
\[M_{1}( - 1;x);M_{2}(2x;3).\]
\[\mathbf{Найти:}\]
\[x - ?\]
\[\mathbf{Решение.}\]
\[\textbf{а)}\ AB = \sqrt{(x - 2)^{2} + (1 - 3)^{2}} =\]
\[= 2:\]
\[\sqrt{(x - 2)^{2} + 4} = 2\ \]
\[(x - 2)^{2} + 4 = 4\]
\[(x - 2)^{2} = 0\]
\[x = 2.\]
\[\textbf{б)}\ M_{1}M_{2} =\]
\[= \sqrt{(2x + 1)^{2} + (3 - x)^{2}} = 7\]
\[(2x + 1)^{2} + (3 - x)^{2} = 49\]
\[4x^{2} + 4x + 1 + 9 - 6x + x^{2} =\]
\[= 49\]
\[5x^{2} - 2x - 39 = 0\]
\[D = b^{2} - 4ac =\]
\[= ( - 2)^{2} - 4 \bullet 5 \bullet ( - 39) =\]
\[= 4 + 7801 = 784\]
\[= 4 + 780 = 784\]
\[x_{1} = \frac{2 + 28}{10} = \frac{30}{3} = 3;\ \]
\[x_{2} = \frac{2 - 28}{10} = - \frac{26}{10} = - 2,6.\]
\[\mathbf{Ответ:}\mathbf{\ }а)\ 2;\ \ \ б)\ 3;\ - 2,6.\]