Question

Me ayudan con este problema xfavor?

Answer 1

Respuesta:

            [tex]\frac{16}{5}[/tex]

Explicación paso a paso:

Expresamos los decimales periodicos puros en fracciones:

[tex]10(\frac{x}{y} ) = 1.111...[/tex]

[tex]-\frac{x}{y} =- 0.111...[/tex]

_______________

[tex]9 (\frac{x}{y} ) = 1[/tex]

[tex]\frac{x}{y} = \frac{1}{9}[/tex]

[tex]0.111... = \frac{1}{9}[/tex]

[tex]10(\frac{a}{b} ) = 3.333....[/tex]

[tex]-\frac{a}{b} =- 0.333...[/tex]

__________________

[tex]9(\frac{a}{b} ) = 3[/tex]

[tex]\frac{a}{b} = \frac{3}{9} = \frac{1}{3}[/tex]

[tex]0.333... = \frac{1}{3}[/tex]

Expremos el decimal terminar en fracción:

[tex]\frac{p}{q} = 2.2[/tex]

[tex]10(\frac{p}{q} ) =22[/tex]

[tex]\frac{p}{q} = \frac{22}{10}[/tex]

[tex]\frac{p}{q} = \frac{11}{5}[/tex]

LUEGO:

[tex](\frac{0.111...}{0.333..} X \sqrt[4]{81} )+ 2.2 = \frac{\frac{1}{9} }{\frac{1}{3} } X \sqrt[4]{3^{4} } +\frac{11}{5}[/tex]

[tex]= \frac{1*3}{1*9} * 3^{\frac{4}{4} } +\frac{11}{5} = \frac{3}{9} * 3 + \frac{11}{5}[/tex]

[tex]= \frac{9}{9} + \frac{11}{5} = 1 + \frac{11}{5}[/tex]

[tex]= \frac{5+11}{5}[/tex]

RESPUESTA:

         [tex]\frac{16}{5}[/tex]