Question

toate inafara de a). ​

Answer 1

Răspuns:

$a) [2,(6)-2]^{3} *x=0,4*10\\(\frac{26-2}{9}-2) ^{3} *x =4\\(\frac{24}{9}-\frac{18}{9}) ^{3}*x=4\\(\frac{6}{9}) ^{3}*x=4\\ \frac{216}{729}*x=4 \\x=4:\frac{216}{729} \\x= 4*\frac{216}{729} =4*\frac{24}{81}=4*\frac{8}{27} =\frac{32}{27}$

$b) x*0,8=[2-1,(3)]^{2} *1,2\\0,8x =(2-\frac{13-1}{9}) ^{2} *1,2\\0,8x=(\frac{18}{9}-\frac{12}{9}) ^{2} *1,2\\0,8x=(\frac{6}{9} )^{2} *1,2\\0,8x=\frac{36}{81} *\frac{12}{10}\\ 0,8x =\frac{18}{27} *\frac{4}{5} \\0,8x =\frac{2}{3} *\frac{4}{5} \\\frac{8}{10} *x=\frac{8}{15}\\ x=\frac{8}{15}:\frac{8}{10} =\frac{8}{15}*\frac{10}{8}=\frac{10}{15}=\frac{2}{3}$

$c)3,5*0,7=x*[1+0,1(6)]^{2} \\3,5*0,7 =x*(1+\frac{16-1}{90}) ^{2} \\3,5*0,7=x*(\frac{90}{90} +\frac{15}{90} )^{2} \\3,5*0,7=x*(\frac{6}{6}+\frac{1}{6} ) ^{2} \\3,5*0,7=x*(\frac{7}{6}) ^{2} \\\frac{35}{10}*\frac{7}{10}=x*\frac{49}{36} \\\frac{7}{10}*\frac{7}{2}=x*\frac{49}{36} \\\frac{49}{36}*x=\frac{49}{20}\\ x=\frac{49}{20}:\frac{49}{36}\\ x=\frac{49}{20}*\frac{36}{49}=\frac{1}{5}*\frac{9}{1} =\frac{9}{5}$

$d) [1-0,8(3)]^{2}*4,5= 6x\\(1-\frac{83-8}{90}) ^{2}*4,5=6x\\(\frac{90}{90}-\frac{75}{90}) ^{2} *4,5=6x\\6x=(\frac{6}{6}-\frac{5}{6}) ^{2} *4,5\\6x=(\frac{1}{6}) ^{2}*4,5\\6x=\frac{1}{36}*\frac{45}{10}\\ 6x=\frac{45}{360}\\ x=\frac{45}{360}:6\\ x=\frac{45}{360}*\frac{1}{6}\\ x=\frac{15}{360}*\frac{1}{2}=\frac{15}{720} =\frac{1}{48}$

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