Question

ayuda porfavor es muy urgente​

Answer 1

Respuestas:

a)  $\left(-\frac{4}{5}\right)^2\sqrt{\frac{9}{16}}-\left(\frac{1}{5}+\left(\left(\frac{2}{3}+\frac{4}{6}\right)\left(3-\frac{4}{7}\right)\right)\right)=-\frac{1553}{525}\quad \left(\mathrm{Decimal:\quad }\:-2.95809\dots \right)$

b) $\frac{\frac{\left(-2.5\right)^3}{\frac{2}{3}}}{\sqrt{\frac{1}{3}\cdot \frac{9}{10}+5.3}}=-9.90415\dots$

Explicación paso a paso:

a) $\left(-\frac{4}{5}\right)^2\sqrt{\frac{9}{16}}-\left(\frac{1}{5}+\left(\left(\frac{2}{3}+\frac{4}{6}\right)\left(3-\frac{4}{7}\right)\right)\right)$

$\mathrm{Quitar\:los\:parentesis}:\quad \left(a\right)=a$

$=\left(-\frac{4}{5}\right)^2\sqrt{\frac{9}{16}}-\left(\frac{1}{5}+\left(\frac{2}{3}+\frac{4}{6}\right)\left(3-\frac{4}{7}\right)\right)$

$\left(-\frac{4}{5}\right)^2\sqrt{\frac{9}{16}}=\frac{12}{25}$

$-\left(\frac{1}{5}+\left(\frac{2}{3}+\frac{4}{6}\right)\left(3-\frac{4}{7}\right)\right)=-\frac{361}{105}$

$=\frac{12}{25}-\frac{361}{105}$

$\mathrm{Ya\:que\:los\:denominadores\:son\:iguales,\:combinar\:las\:fracciones}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{252-1805}{525}$

$\mathrm{Restar:}\:252-1805=-1553$

$=\frac{-1553}{525}$

$\mathrm{Aplicar\:las\:propiedades\:de\:las\:fracciones}:\quad \frac{-a}{b}=-\frac{a}{b}$

$=-\frac{1553}{525}$

b) $\frac{\frac{\left(-2.5\right)^3}{\frac{2}{3}}}{\sqrt{\frac{1}{3}\cdot \frac{9}{10}+5.3}}$

$\frac{\left(-2.5\right)^3}{\frac{2}{3}}=-\frac{3\cdot \:2.5^3}{2}$

$=\frac{-\frac{3\cdot \:2.5^3}{2}}{\sqrt{\frac{1}{3}\cdot \frac{9}{10}+5.3}}$

$\mathrm{Aplicar\:las\:propiedades\:de\:las\:fracciones}:\quad \frac{-a}{b}=-\frac{a}{b}$

$=-\frac{\frac{2.5^3\cdot \:3}{2}}{\sqrt{\frac{1}{3}\cdot \frac{9}{10}+5.3}}$

$\mathrm{Aplicar\:las\:propiedades\:de\:las\:fracciones}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}$

$\frac{\frac{2.5^3\cdot \:3}{2}}{\sqrt{\frac{1}{3}\cdot \frac{9}{10}+5.3}}=\frac{2.5^3\cdot \:3}{2\sqrt{\frac{1}{3}\cdot \frac{9}{10}+5.3}}$

$=-\frac{2.5^3\cdot \:3}{2\sqrt{\frac{1}{3}\cdot \frac{9}{10}+5.3}}$

$2.5^3\cdot \:3=46.875$

$=-\frac{3\cdot \:2.5^3}{2\sqrt{5.6}}$

$\mathrm{Simplificar}\:\frac{46.875}{2\sqrt{5.6}}:\quad 9.90415\dots$

$=-9.90415\dots$