Matemáticas, pregunta formulada por jonassurcocapatinta, hace 4 meses

Ayuden con resoluciones plisss

Adjuntos:

Respuestas a la pregunta

Contestado por Usuario anónimo
14

Explicación paso a paso:

¡¡Hola un cordial saludo!!

Respuesta:

 \boxed{ \bold{ \huge{E =  \frac{9}{2} }}}

 \boxed{ \mathcal{NOTA:}}

No daré mucha explicación debido a que el desarrollo del ejercicio es muy largo, espero me comprendas. Okey

Solucion:

E =  \frac{ \frac{6}{5}(1 +  \frac{1}{6}  )(1 +  \frac{1}{7} )(1 +  \frac{1}{8})(1 +  \frac{1}{9} ) }{(1 -  \frac{1}{5})(1 -  \frac{1}{6} )(1 -  \frac{1}{7} )(1 -  \frac{1}{8})(1 -  \frac{1}{9} )  }  \\ \\  E =  \frac{ \frac{6}{5} \times  \frac{7}{6}  (1 +  \frac{1}{7})(1 +  \frac{1}{8} )(1 +  \frac{1}{9} ) }{(1 -  \frac{1}{5})(1 -  \frac{1}{6} )(1 -  \frac{1}{7} )(1 -  \frac{1}{8} )(1 -  \frac{1}{9}  )}  \\  \\ E =  \frac{ \frac{6}{5} \times  \frac{7}{6}   \times  \frac{8}{7}(1 +  \frac{1}{8})(1 +  \frac{1}{9} )  }{(1 -  \frac{1}{5})(1 -  \frac{1}{6} )(1 -  \frac{1}{7})(1 -  \frac{1}{8})(1 -  \frac{1}{9}  ) }  \\  \\ E =  \frac{ \frac{6}{5} \times  \frac{7}{6} \times  \frac{8}{7}  \times  \frac{9}{8}  (1 +  \frac{1}{9})  }{(1 -  \frac{1}{5})(1 -   \frac{1}{6}  )(1 -  \frac{1}{7} ) (1 -  \frac{1}{8})(1 -  \frac{1}{9} ) }  \\  \\ E =  \frac{ \frac{6}{5}  \times  \frac{7}{6} \times  \frac{8}{7}  \times  \frac{9}{8}  \times  \frac{10}{9}  }{(1 -  \frac{1}{5})(1 -  \frac{1}{6})(1 -  \frac{1}{7})(1 -  \frac{1}{8}  )(1 -  \frac{1}{9}  ) }  \\

Ahora cancelamos 9

E =  \frac{ \frac{5}{6}  \times  \frac{7}{6}  \times  \frac{8}{7} \times  \frac{1}{8}   \times 10}{(1 -  \frac{1}{5})(1 -  \frac{1}{6}  )(1 -  \frac{1}{7} )(1 -  \frac{1}{8} )(1 -  \frac{1}{9}) }  \\

Cancelamos 8

E =  \frac{ \frac{6}{5} \times  \frac{7}{6}  \times  \frac{1}{7} \times 10  }{(1 -  \frac{1}{5})(1 -  \frac{1}{6})( 1 -  \frac{1}{7} )(1 -  \frac{1}{8})(1 -  \frac{1}{9} )  }  \\

Cancelamos 7 y 6.

E =  \frac{ \frac{1}{5} \times 10 }{(1 -  \frac{1}{5})(1 - \frac{1}{6} )(1 -  \frac{1}{7} )(1 -  \frac{1}{8})(1 -  \frac{1}{9}   ) }  \\

Multiplicamos 1/5 x 10.

E =  \frac{ \frac{10}{5} }{(1 -  \frac{1}{5} )(1 -  \frac{1}{6})(1 -  \frac{1}{7} )(1 -  \frac{1}{8})(1 -  \frac{1}{9}   )}  \\

Simplificamos 10/5 que es igual a 2.

E =  \frac{2}{(1 -  \frac{1}{5})(1 -  \frac{1}{6} )(1 -  \frac{1}{7})(1 -  \frac{1}{8} )(1 -  \frac{1}{9} ) }   \\

Ahora seguimos desarrollando.

E =  \frac{ 2 }{ \frac{4}{5} (1 -  \frac{1}{6} )(1 -  \frac{1}{7} )(1 -  \frac{1}{8} )(1 -  \frac{1}{9} ) }  \\  \\ E =  \frac{2}{ \frac{4}{5} \times  \frac{5}{6} (1 -  \frac{1}{7} )(1 -  \frac{1}{8}  )(1 -  \frac{1}{9}) }  \\  \\ E =  \frac{2}{ \frac{4}{5} \times  \frac{5}{6}   \times  \frac{6}{7}(1 -  \frac{1}{8} )(1 -  \frac{1}{9})  }  \\  \\ E =  \frac{2}{ \frac{4}{5} \times  \frac{5}{6}   \times  \frac{6}{7}  \times  \frac{7}{8} (1 -  \frac{1}{9} )}  \\  \\ E =  \frac{2}{ \frac{4}{5}  \times  \frac{5}{6} \times  \frac{6}{5}  \times  \frac{6}{7}  \times  \frac{7}{8}   \times  \frac{8}{9} }

Cancelamos 8, 7, 6 y 5.

E =  \frac{2}{ \frac{4}{5} \times  \frac{5}{6}  \times  \frac{6}{7} \times 7 \times  \frac{1}{9}   }  \\  \\ E =  \frac{2}{ \frac{4}{5}  \times  \frac{5}{6}  \times 6 \times  \frac{1}{9} }  \\  \\ E =  \frac{2}{ \frac{4}{5} \times 5 \times  \frac{1}{9}  }  \\  \\ E =  \frac{2}{4  \times  \frac{1}{9} }  \\

Como ya cancelamos 8, 7, 6 y 5. Entonces ahora multiplicamos.

E =  \frac{2}{ \frac{4}{9} }  \\

Invertimos y multiplicamos.

E = 2 \times  \frac{9}{4}  \\

Usamos esta regla: a x b/c = ab/c

E =  \frac{2  \times 9}{4}  \\

Multiplicamos.

E =  \frac{18}{4}  \\

Y finalmente simplificamos.

 \boxed{E =  \frac{9}{2} } \:  <  =  \bold{ resultado}

Por lo que:

La opción correcta es el literal B

Hasta pronto!!

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