\[\boxed{\mathbf{1047.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[\mathbf{Дано:}\ \]
\[\overrightarrow{a}\ и\ \overrightarrow{b}.\]
\[Найти:\]
\[x,\ при\ котором\ \overrightarrow{a}\bot\overrightarrow{b}.\]
\[Решение:\]
\[Если\ \overrightarrow{a}\bot\overrightarrow{b},\ то\ должно\ \]
\[выполнять\ условие:\]
\[\overrightarrow{a} \bullet \overrightarrow{b} = 0.\]
\[\textbf{а)}\ \overrightarrow{a}\left\{ 4;5 \right\};\ \overrightarrow{b}\left\{ x; - 6 \right\}:\]
\[\overrightarrow{a} \bullet \overrightarrow{b} = 4x + 5 \bullet ( - 6) = 0\]
\[4x - 30 = 0\]
\[x = 7,5.\]
\[\textbf{б)}\ \overrightarrow{a}\left\{ x; - 1 \right\};\ \overrightarrow{b}\left\{ 3;2 \right\}:\]
\[\overrightarrow{a} \bullet \overrightarrow{b} = x \bullet 3 + ( - 1) \bullet 2 = 0\]
\[3x - 2 = 0\]
\[x = \frac{2}{3}.\]
\[\textbf{в)}\ \overrightarrow{a}\left\{ 0; - 3 \right\};\ \overrightarrow{b}\left\{ 5;x \right\}:\]
\[\overrightarrow{a} \bullet \overrightarrow{b} = 0 \bullet 5 + ( - 3)x = 0\]
\[- 3x = 0\]
\[x = 0.\]
\[\boxed{\mathbf{1047.еуроки - ответы\ на\ пятёрку}}\]
\[\mathbf{Дан}о:\]
\[A( - 2;4);B( - 5; - 3);\]
\[C( - 7; - 2);D(1;5);\]
\[(x + 5)^{2} + (y - 1)^{2} = 16 \Longrightarrow\]
\[\Longrightarrow O( - 5;1);\ R = 4.\]
\[1)\ A( - 2;4):\]
\[( - 2 + 5)^{2} + (4 - 1)^{2} \neq 16;\]
\[9 + 9 \neq 16;\]
\[18 \neq 16 \Longrightarrow \ A( - 2;4) -\]
\[вне\ круга.\]
\[2)\ B( - 5; - 3):\]
\[( - 5 + 5)^{2} + ( - 3 - 1)^{2} = 16;\]
\[16 = 16 \Longrightarrow B( - 5; - 3) -\]
\[на\ окружности.\]
\[3)\ C( - 7; - 2):\]
\[( - 7 + 5)^{2} + ( - 2 - 1)^{2} \neq 16;\ \]
\[4 + 9 \neq 16;\]
\[13 \neq 16 \Longrightarrow C( - 7; - 2) -\]
\[внутри\ круга.\]
\[4)\ D(1;5):\]
\[(1 + 5)^{2} + (5 - 1)^{2} \neq 16;\]
\[36 + 16 \neq 16\]
\[52 \neq 16 \Longrightarrow \ D(1;5) -\]
\[вне\ круга.\]
\[Ответ:а)\ C;б)\ B;в)\ A\ и\ \text{D.}\]