Question

Sendo x = 0,444então o valor de x será



a)(  )4.

b)(  )9.

c) (  )2/9.

d) (  )2/3.

preciso de ajuda e pra hoje ​

Answer 1

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$\Large\boxed{\sf{\underline{soma~dos~termos~da~PG~infinita}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S_n=\dfrac{a_1}{1-q}}}}}$

$\sf 0,444...=\underbrace{0,4...+0,04...+0,004....+....}_{soma~dos~termos~da~PG~infinita}\\\sf a_1=0,4=\frac{4}{10}\\\sf a_2=0,04=\dfrac{4}{100}\\\sf q=\dfrac{a_2}{a_1}\\\sf q=\dfrac{\frac{4}{100}}{\frac{4}{10}}\\\sf q=\dfrac{4}{100}\div\dfrac{4}{10}\\\sf q=\dfrac{\diagup\!\!\!4}{10\diagup\!\!\!0}\cdot\dfrac{1\diagup\!\!\!0}{\diagup\!\!\!4}=\dfrac{1}{10}$

$\sf S_n=\dfrac{\frac{4}{10}}{1-\frac{1}{10}}\\\sf S_n=\dfrac{\frac{4}{10}}{\frac{10-1}{10}}\\\sf S_n=\dfrac{\frac{4}{10}}{\frac{9}{10}}\\\sf S_n=\dfrac{4}{\diagdown\!\!\!\!\!\!10}\cdot\dfrac{\diagdown\!\!\!\!\!\!10}{9}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S_n=\dfrac{4}{9}}}}}$

Answer 2

Resposta:

d)2/3

Explicação passo-a-passo:

√0,444...= √4/9= √4/√9= 2/3