Respuestas Yahoo answers 6 de Marzo 2014

Aquí tenéis las soluciones a vuestros ejercicios


Hallar coordenadas cartesianas

$\bullet e^{3\pi +i}=\cos 3\pi +i\sin 3\pi=-1+0i$

$\bullet e^{2\pi +i}=\cos 2\pi+i\sin 2\pi=1+0i$

$\bullet \dfrac {1} {2}e^{-3\pi i/4}=\dfrac {1} {2}\left[ \cos \left( -\dfrac {3} {4}\pi \right) +i\sin \left( -\dfrac {3} {4}\pi \right) \right] =\dfrac {-\sqrt {2}} {4}-\dfrac {\sqrt {2}} {4}i$

$\bullet \sqrt {2}e^{-\pi i /{4}}=\sqrt {2}\left[ \cos \left( -\dfrac {\pi } {4}\right) +i\sin \left( -\dfrac {\pi} {4}\right) \right] =1-i$

Hallar la ecuación

$\bullet \sqrt [5] {x^{2}}\cdot x^{-7/5}=7$

$x^{2 / 5}\cdot x^{-7 / 5}=7$

$x^{-5 / 5}=7$

$x^{-1}=7$

$\boxed{x=\dfrac {1} {7}}$

$\bullet \dfrac {x\cdot x^{-1 / 2}} {x^{1/3}}=\dfrac {1} {2}$

$x^{1-1 / 2-1 / 3}=\dfrac {1} {2}$

$x^{1 / 6}=\dfrac {1} {2}$

$x=\dfrac {1} {2^{6}}=\dfrac {1} {64}$

$\boxed{x=\dfrac {1} {64}}$

$\bullet \dfrac {x^{3/2}\cdot x^{-3/5}} {x}=\dfrac {1} {3}$

$x^{3/2 -3/5-1}=\dfrac {1} {3}$

$x^{-1/10}=\dfrac {1} {3}$

$x=\left( \dfrac {1} {3}\right) ^{-10}=3^{10}$

$\boxed{x=3^{10}}$

Sistemas de ecuaciones

$\begin{cases} 5x & -2y & = & 8 \\ & & & \\ 3x & -4y & = & -6\end{cases}$ $\xrightarrow[]{-2\cdot f_{1}}$ $\begin{cases} -10x & 4y & = & -16 \\ & & & \\ 3x & -4y & = & -6\end{cases}$

$$7x=-22$$
$$\boxed{x=\dfrac {22} {7}}$$
$$-4y=-\dfrac {66} {7}-6$$
$$4y= \dfrac {108} {7}$$
$$\boxed{x=\dfrac {27} {7}}$$

$\begin{cases} 3x & y & = & 4 \\ & & & \\ 2x & 4y & = & 16\end{cases}$ $\xrightarrow[]{-4\cdot f_{1}}$ $\begin{cases} -12x & -4y & = & -16 \\ & & & \\ 2x & 4y & = & 16\end{cases}$

$$-10x=0$$
$$\boxed{x=0}$$
$$\boxed{y=4}$$