Matematika

Pertanyaan

Tolong dong dikerjakan dengan caranya 1-5 ya,kalo gabisa semua gapapa
Tolong dong dikerjakan dengan caranya 1-5 ya,kalo gabisa semua gapapa

1 Jawaban

  • 1.)
    [tex]\frac{(2^{n+2})^{2}-(2^{2})(2^{2n})}{(2^{n})(2^{n+2})} = \frac{2^{2n+4}-2^{2n+2}}{2^{2n+2}} \\ \frac{(2^{n+2})^{2}-(2^{2})(2^{2n})}{(2^{n})(2^{n+2})} = (2^{2n+4}-2^{2n+2})(2^{-(2n+2)}) \\ \frac{(2^{n+2})^{2}-(2^{2})(2^{2n})}{(2^{n})(2^{n+2})} = 2^{2}-2^{0} \\ \frac{(2^{n+2})^{2}-(2^{2})(2^{2n})}{(2^{n})(2^{n+2})} = 4 - 1 \\ \frac{(2^{n+2})^{2}-(2^{2})(2^{2n})}{(2^{n})(2^{n+2})} = 3[/tex]

    2.) 
    Jika [tex]\sqrt{2011} + \sqrt{2009} = p[/tex],
    tentukan [tex]\sqrt{2011}-\sqrt{2009}[/tex] dalam bentuk p!

    [tex]\sqrt{2011}-\sqrt{2009} = \sqrt{2011}-\sqrt{2009}\frac{\sqrt{2011}+\sqrt{2009}}{\sqrt{2011}+\sqrt{2009}} \\ \sqrt{2011}-\sqrt{2009} = \frac{2011-2009}{\sqrt{2011}+\sqrt{2009}} \\ \sqrt{2011}-\sqrt{2009} = \frac{2}{p} [/tex]

    5.)
    [tex]V_{o} = E[1-e^{-\frac{t}{RC}}] \\ E = 270 \\ R = 6 \\ C = 2 \\ e = 2,7 \\ V_{o} = 170 \\[/tex]
    Tentukan [tex]t[/tex]

    [tex]170 = (270)[1-(2,7)^{-\frac{t}{(6)(2)}}] \\ \frac{17}{27} = 1-(2,7)^{-\frac{t}{(6)(2)}} \\ \frac{17}{27} - \frac{27}{27} = -(2,7)^{-\frac{t}{12}} \\ -\frac{10}{27} = -(2,7)^{-\frac{t}{12}} \\ \frac{10}{27} = (2,7)^{-\frac{t}{12}} \\ \frac{27}{10} = (2,7)^{\frac{t}{12}} \\ (2,7)^{1} = (2,7)^{\frac{t}{12}} \\ 1 = \frac{t}{12} \\ 12 = t[/tex]