\[t,\ ч\] | \[V,\ \frac{км}{ч}\] | \[S,\ км\] | |
---|---|---|---|
\[По\ течению\] | \[4\ часа\ \left\{ \begin{matrix} \frac{54}{x + 3} \\ \frac{42}{x - 3} \\ \end{matrix} \right.\ \] | \[x + 3\] | \[54\] |
\[Против\ течения\] | \[x - 3\] | \[42\] |
\[\mathbf{Составим\ уравнение:}\]
\[\frac{54}{x + 3} + \frac{42}{x - 3} = 4\]
\[\frac{54 \cdot (x - 3) + 42 \cdot (x + 3)}{(x - 3)(x + 3)} = 4\]
\[54x - 162 + 42x + 126 = 4 \cdot \left( x^{2} - 9 \right)\]
\[4x^{2} - 96x - 36 + 36 = 0\]
\[4x^{2} - 96x = 0\]
\[4x(x - 24) = 0\]
\[x = 0\ \ \ \ \ \ \ \ x - 24 = 0\]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 24\]
\[Ответ:собственная\ скорость\ теплохода\ \]
\[24\ \frac{км}{ч}.\]
\[y = - 2x^{2} + 5x + 3\ \ \ и\ \ \ y = - 4\]
\[- 4 = - 2x^{2} + 5x + 3\]
\[2x^{2} - 5x - 3 - 4 = 0\]
\[2x^{2} - 5x - 7 = 0\]
\[D = 25 + 56 = 81\]
\[x_{1} = \frac{5 + 9}{4} = \frac{14}{4} = 3,5;\]
\[x_{2} = \frac{5 - 9}{4} = - \frac{4}{4} = - 1.\]
\[Ответ:\ \ x = 3,5\ \ \ \ и\ \ \ x = - 1.\]
\[y = x^{2} - 2x - 8\]
\[1)\ x_{0} = \frac{- b}{2a} = \frac{2}{2} = 1\]
\[y_{0}(1) = 1 - 2 - 8 = - 9.\]
\[2)\ x^{2} - 2x - 8 = 0\]
\[x_{1} + x_{2} = 2\]
\[x_{1} \cdot x_{2} = - 8 \Longrightarrow x_{1} = 4\ \ \ \ и\ \ \ x_{2} = - 2.\]
\[\ x = - 1,5 \Longrightarrow y = - 2,75.\]