\[\boxed{\text{614}\text{\ (614)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x_{1} = 5,\ \ d = 10:\]
\[S_{5} = \frac{2x_{1} + d(n - 1)}{2} \cdot 5 = \frac{10 + 10 \cdot 4}{2} \cdot 5 = 25 \cdot 5 = 125\ (м) - глубина\ \]
\[шахты.\]
\[Ответ:125\ м.\]
\[\boxed{\text{614.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ 2x² - 13x - 34 \geq 0\]
\[2x^{2} - 13x - 34 = 0\]
\[D = 169 + 4 \cdot 2 \cdot 34 = 441\]
\[x_{1,2} = \frac{13 \pm 21}{4} = - 2;\ 8,5;\]
\[\Longrightarrow 2 \cdot (x + 2)(x - 8,5) \geq 0.\]
\[x \in ( - \infty; - 2\rbrack \cup \lbrack 8,5; + \infty).\]
\[\textbf{б)}\ 10x - 4x^{2} < 0\]
\[4x^{2} - 10x > 0\]
\[x(2x - 5) > 0\]
\[x(x - 2,5) > 0\]
\[x \in ( - \infty;0) \cup (2,5;\ + \infty).\]
\[\textbf{в)}\ \frac{x - 4}{2x + 5} \leq 0\]
\[x \in ( - 2,5;4\rbrack.\]