Question

1. determinati N O N stiind că :

1/9<1/2n+1<1


2.calculati

[3/4+2/3:(3/4-1/2)]×6/41​

Answer 1

Explicație pas cu pas:

1. n ∈ N

$\frac{1}{9} < \frac{1}{2n + 1}< 1 \\ 9 > 2n + 1 > 1 \\ 8 > 2n > 0 \\ 4 > n > 0$

=> n ∈ {1; 2; 3}

2.

$[ \frac{3}{4}+ \frac{2}{3} \div ( \frac{3}{4} - \frac{1}{2} )] \times \frac{6}{41} \\ = (\frac{3}{4}+ \frac{2}{3} \div \frac{3 - 2}{4}) \times \frac{6}{41} \\ = (\frac{3}{4}+ \frac{2}{3} \div \frac{1}{4}) \times \frac{6}{41} \\ = (\frac{3}{4}+ \frac{2}{3} \times 4) \times \frac{6}{41} \\ = (\frac{3}{4}+ \frac{8}{3}) \times \frac{6}{41} \\ = \frac{3 \times 3 + 8 \times 4}{4 \times 3} \times \frac{6}{41} \\ = \frac{9 + 32}{12} \times \frac{6}{41} \\ = \frac{41}{12} \times \frac{6}{41} = \frac{1}{2}$