Question

valoarea lui x din proportia x/radical de 0,07(1)=radical de 1,13(7)/radical de 0,4096 este egal cu????imi trebuie super urgent. p.s nu stiu sa scriu radical...dau si 74 de puncte!!!!!

Answer 1

x/√0,07(1)=√1,13(7)/√0,4096
0,07(1)=(71-7) /900=64/900
1,13(7)=(1137-113)/900=1024/900

x/√64/900=√1024/900/√0,4096
x/(8/30)=(32/30)/0,64
15x/4=16/15 ×1/0,64
15x/4=16/9,6
x=4*16/15*9,6
x=64/144
x=4/9
x=0,(4)

Answer 2

$\it \sqrt{0,07(1)} = \sqrt{\dfrac{71-7}{900}} = \sqrt{\dfrac{64}{900}} =\dfrac{8}{30}=\dfrac{4}{15}$

$\it \sqrt{1,13(7)} =\sqrt{1\dfrac{137-13}{900}} =\sqrt {1\dfrac{124}{900}}=\sqrt{\dfrac{1024}{900}} =\dfrac{32}{30} =\dfrac{16}{15}$

$\it \sqrt{0, 4096} =\sqrt{ \dfrac{4096}{10000}} =\sqrt{\dfrac{1024}{2500}}=\dfrac{32}{50} =\dfrac{16}{25}$

Ecuația din enunț devine:

[tex]\it \dfrac{x}{\dfrac{4}{15}} =\dfrac{\dfrac{16}{15}}{\dfrac{16}{25}} \Rightarrow \dfrac{x}{\dfrac{4}{15}} = \dfrac{16}{15} \cdot\dfrac{25}{16 }\Rightarrow \dfrac{x}{\dfrac{4}{15}} = \dfrac{5}{3} \Rightarrow \\\;\\ \\\;\\ \Rightarrow x = \dfrac{5\cdot\dfrac{4}{15}}{3} = \dfrac{\dfrac{4}{3}}{3} =\dfrac{4}{9} =0,(4)[/tex]