Question

Sendo f(x)=5x²/4 -5, g(x)=2x/5 -c é f(0)-g(0)=1/2, o valor de f(1/2)-10g(1/4) arredondando somente no resultado final, com três algarismos decimais após a vírgula, é:

Answer 1

Resposta:

Explicação passo a passo:

$f(x)=\frac{5x^{2} }{4}-5$

$g(x)=\frac{2x}{5}-C$

$f(0)=\frac{5.(0)^{2} }{4}-5$

$f(0)=\frac{5\:.\:0 }{4}-5$

$f(0)=\frac{\:0 }{4}-5$

$f(0)=0-5$

$f(0)=-5$

$g(0)=\frac{2\:.\:(0)}{5}-C$

$g(0)=\frac{0}{5}-C$

$g(0)=0-C$

$g(0)=-C$

$f(0)-g(0)=\frac{1}{2}$

$-5-(-C)=\frac{1}{2}$

$-5+C=\frac{1}{2}$

$C=\frac{1}{2}+5$

$C=\frac{1}{2}+\frac{10}{2}$

$C=\frac{11}{2}$

$g(x)=\frac{2x}{5}-C$

$g(x)=\frac{2x}{5}-\frac{11}{2}$

$f(x)=\frac{5x^{2} }{4}-5$

$f(\frac{1}{2} )=\frac{5\:.\:(\frac{1}{2}) ^{2} }{4}-5$

$f(\frac{1}{2} )=\frac{5.(\frac{1}{4}) }{4}-5$

$f(\frac{1}{2} )=\frac{(\frac{5}{4}) }{4}-5$

$f(\frac{1}{2})= (\frac{5}{4})\:.\:(\frac{1}{4})-5$

$f(\frac{1}{2})=\frac{5}{16}-5$

$f(\frac{1}{2})=\frac{5}{16}-\frac{80}{16}$

$f(\frac{1}{2})=-\frac{75}{16}$

$g(x)=\frac{2x}{5}-\frac{11}{2}$

$g(\frac{1}{4} )=\frac{2.(\frac{1}{4}) }{5}-\frac{11}{2}$

$g(\frac{1}{4} )=\frac{(\frac{2}{4}) }{5}-\frac{11}{2}$

$g(\frac{1}{4})= (\frac{2}{4})\:.\:(\frac{1}{5}) -\frac{11}{2}$

$g(\frac{1}{4})=\frac{2}{20}-\frac{11}{2}$

$g(\frac{1}{4})=\frac{2}{20}-\frac{110}{20}$

$g(\frac{1}{4})=-\frac{108}{20}$

$Portanto...$

 $f(\frac{1}{2})-10\:.\:g(\frac{1}{4})=$

$-\frac{75}{16}-10\:.\:(-\frac{108}{20})=$

$-\frac{75}{16}+\frac{108}{2} =$

$-\frac{75}{16}+\frac{864}{16} =$

    $\frac{864-75}{16} =$

       $\frac{789}{16}=$

   $49,3125$

  $Arredondando\:para\:3\:casas\;decimais\:temos...$    

              $Resposta:49,313$

             $Alternativa:(a)$