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

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

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

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

\[-10x=0\]
\[\boxed{x=0}\]
\[\boxed{y=4}\]