\[\boxed{\text{42\ (42).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ y = \frac{x - \sqrt{x + 6}}{x + 5}\]
\[\left\{ \begin{matrix} x + 6 \geq 0 \\ x + 5 \neq 0 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x \geq - 6 \\ x \neq - 5 \\ \end{matrix} \right.\ \]
\[Область\ определения:\ \ \ \]
\[x \in \lbrack - 6;\ - 5) \cup ( - 5;\ + \infty);\]
\[x - \sqrt{x + 6} = 0\]
\[x = \sqrt{x + 6},\ \ x > 0\]
\[x^{2} = x + 6\]
\[x^{2} - x - 6 = 0\]
\[D = 1 + 24 = 25 = 5^{2}\]
\[x_{1.2} = \frac{1 \pm 5}{2} = 3;\ - 2.\]
\[Так\ как\ x > 0;\ \ то\ x =\]
\[= - 2 \Longrightarrow не\ подходит.\]
\[Ноль\ функции:\ \ \ x = 3.\]
\[\textbf{б)}\ y = \frac{4x^{2} + 25x}{2x - \sqrt{10 - 6x}}\]
\[\left\{ \begin{matrix} 10 - 6x \geq 0\ \ \ \ \ \ \ \ \ \ \ \ \\ 2x - \sqrt{10 - 6x} \neq 0 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 6x \leq 10\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x \neq \sqrt{10 - 6x} \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x \leq \frac{10}{6}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 4x^{2} \neq 10 - 6x \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} x \leq \frac{5}{3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ 2x^{2} + 3x - 5 = 0 \\ \end{matrix} \right.\ \]
\[2x^{2} + 3x - 5 = 0\]
\[D = 9 + 4 \cdot 2 \cdot 5 = 49 = 7^{2}\]
\[x_{1,2} = \frac{- 3 \pm 7}{4} = 1;\ - 2,5.\]
\[Но\ при\ x = - 2,5:\ \ \ \ \]
\[2x = - 5,а\ \]
\[\sqrt{10 - 6x} = 5.\]
\[Область\ определения:\ \ \ \]
\[x \in ( - \infty;1) \cup \left( 1;\frac{5}{3} \right\rbrack.\]
\[Нули\ функции:\]
\[4x^{2} + 25x = 0\]
\[x(4x + 25) = 0\]
\[x_{1} = 0\ \ \ и\ \ \ \ 4x_{2} = - 25,\ \ \]
\[\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }x_{2} = - 6\frac{1}{4}\]
\[y = 0\ \ \ при\ \ x_{1} = 0\ \ \ и\ \ x_{2} =\]
\[= - 6\frac{1}{4}\text{\ .\ \ }\]
\[\boxed{\text{42.\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[m = 420\ г \pm 3\%:\]
\[3\%\ от\ 420\ г = 420 \cdot \frac{3}{100} =\]
\[= \frac{1260}{100} = 12,6\ грамм;\]
\[m = 420 \pm 12,6\ (г).\]
\[420 - 12,6 \leq m \leq 420 + 12,6\]
\[407,4 \leq m \leq 432,6\ (грамм) -\]
\[граница\ массы\ товара.\]