Question

4. Calculaţi media geometrică a numerelor a=3,5:(-0,5)¯⁴ şi b=
$\frac{5}{3} - \frac{1}{7} \div \frac{9}{7}$

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Answer 1

Răspuns:

$\frac{7}{12}$

Explicație pas cu pas:

$a=3,5:(-0,5)^{-4}=\frac{35}{10} :(-\frac{5}{10})^{-4}=\frac{7}{2}:(-\frac{10}{5})^{4}$

$=> a=\frac{7}{2}:(-2)^{4} =\frac{7}{2}:2^{4} =\frac{7}{2}*\frac{1}{16}=\frac{7}{32}$

$b=\frac{5}{3} -\frac{1}{7}:\frac{9}{7}=\frac{5}{3}-\frac{1}{7}*\frac{7}{9}=\frac{5}{3}-\frac{1}{9}$

$=> b=\frac{5*3-1}{9}=\frac{15-1}{9}=\frac{14}{9}$

Formula mediei geometrice a doua numere este: $mg=\sqrt{a*b}$

$=> mg=\sqrt{\frac{7}{32}*\frac{14}{9} }=\sqrt{\frac{7*7}{16*9} }=\sqrt{\frac{7^{2} }{4^{2}*3^{2} }} =\frac{7}{4*3}=\frac{7}{12}$