\[\boxed{\mathbf{1124.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[r_{1} = 1;r_{2} = 2;\]
\[r_{3} = 3;r_{4} = 4.\]
\[\mathbf{Найти:}\]
\[S_{1};S_{2кольца};\]
\[S_{3к};S_{4к}.\]
\[\mathbf{Решение.}\]
\[1)\ S_{1} = \pi \bullet \left( r_{1} \right)^{2} = \pi \bullet 1^{2} = \pi;\]
\[2)\ S_{2} = \pi \bullet \left( r_{2} \right)^{2} = \pi \bullet 2^{2} = 4\pi;\]
\[3)\ S_{3} = \pi \bullet \left( r_{3} \right)^{2} = \pi \bullet 3^{2} = 9\pi;\]
\[4)\ S_{4} = \pi \bullet \left( r_{4} \right)^{2} = \pi \bullet 4^{2} = 16\pi;\]
\[5)\ S_{2к} = S_{2} - S_{1} = 4\pi - \pi = 3\pi;\]
\[6)\ S_{3к} = S_{3} - S_{2} = 9\pi - 4\pi =\]
\[= 5\pi;\]
\[7)\ S_{4к} = S_{4} - S_{3} = 16\pi - 9\pi =\]
\[= 7\pi.\]
\[Ответ:S_{1} = \pi;\ S_{2к} = 3\pi;\ \]
\[S_{3к} = 5\pi;\ S_{4к} = 7\pi.\]
\[\boxed{\mathbf{1124.еуроки - ответы\ на\ пятёрку}}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[Окружность\ (O;r);\]
\[AB,CD - хорды;\]
\[AB \cap CD = E;\]
\[AB = 13\ см;\]
\[CE = 9\ см;\]
\[ED = 4\ см;\]
\[BD = 4\sqrt{3}\ см.\]
\[\mathbf{Найти:}\]
\[\angle BED - ?\]
\[\mathbf{Решение.}\]
\[1)\ Пусть\ AE = x;\ EB = 13 - x.\]
\[x(13 - x) = 9 \bullet 4\]
\[- x^{2} + 13x = 36\]
\[x^{2} - 13x + 36 = 0.\]
\[3)\ EB = 4 \Longrightarrow \mathrm{\Delta}DEB -\]
\[равнобедренный.\]
\[По\ теоремме\ косинусов:\]
\[\left( 4\sqrt{3} \right)^{2} = 32 - 32\cos{\angle DEB}\]
\[32\cos{\angle DEB} = - 16\]
\[\cos{\angle DEB} = - 0,5\]
\[\angle DEB = 120{^\circ}.\]
\[3)\ EB = 9.\]
\[По\ теореме\ косинусов:\]
\[\left( 4\sqrt{3} \right)^{2} =\]
\[= 4^{2} + 9^{2} - 72\cos{\angle DEB}\]
\[72\cos{\angle DEB} = 49\]
\[\cos{\angle DEB} \approx 0,6806\]
\[\angle DEB \approx 47{^\circ}7^{'}.\]
\[Ответ:120{^\circ}\ или\ 47{^\circ}7'.\]