Rabu, 01 Agustus 2012
Solusi Soal Nomor 2 Uji Sertifikasi Pendidikan Menengah
$latex 2.\ \ \ (a)\ \ x^2-4x+6=0\quad \rightarrow \quad \alpha +\beta=4\ dan\ \alpha \beta=6\\\begin{matrix} & & & \ \end{matrix}\begin{array}{rcl}\alpha ^2+\beta ^2&=&(\alpha +\beta)^2-2\alpha \beta\\&=&4^2-2.6\\&=&16-12\\&=&4\end{array}\\\\\begin{matrix} & \ \ \end{matrix}(b)\ \ \frac{2x-5}{3x+1}>0\\\\\begin{matrix} & & & \ \end{matrix}Pembuat\ nol\ pada\ pembilang:\\\begin{matrix} & & & \ \end{matrix}\begin{array}{rcl}2x-5&=&0\\2x&=&5\\x&=&\frac{5}{2}\end{array}\\\begin{matrix} & & & \ \end{matrix}Pembuat\ nol\ pada\ penyebut:\\\begin{matrix} & & & \ \end{matrix}\begin{array}{rcl}3x+1&=&0\\3x&=&-1\\x&=&-\frac{1}{3}\end{array}\\\\\begin{matrix} & & & \ \end{matrix}Pada\ interval\ -\frac{1}{3}< x < \frac{5}{2}\ dipilih\ titik\ uji\ x=0,\ maka:\\\\\begin{matrix} & & & \ \end{matrix}\frac{2x-5}{3x+1}=\frac{2.0-5}{3.0+1}=\frac{-5}{1}=-5\ (bernilai\ negatif)\\\\\begin{matrix} & & & \ \end{matrix}Jadi\ batasan\ nilai\ x\ yang\ memenuhi\ adalah\\\\\begin{matrix} & & & \ \end{matrix}x<-\frac{1}{3}\ atau\ x>\frac{5}{2}\\\\\begin{matrix} & \ \ \end{matrix}(c)\ \ Ini\ masalah\ deret\ aritmatika\ dengan\\\begin{matrix} & & & \ \end{matrix}beda\ (b)=x,\ U_{5}=50,\ dan\ U_{9}=70\\\\\begin{matrix} & & & \ \end{matrix}U_{m}-U_{n}=(m-n)b\\\\\begin{matrix} & & & \ \end{matrix}U_{9}-U_{5}=(9-5)x\\\begin{matrix} & & & \ \end{matrix}70-50=4x\\\begin{matrix} & & & \ \end{matrix}20=4x\\\begin{matrix} & & & \ \end{matrix}x=5\\\\\begin{matrix} & & & \ \end{matrix}U_{5}=50\\\begin{matrix} & & & \ \end{matrix}a+4b=50\\\begin{matrix} & & & \ \end{matrix}a+20=50\\\begin{matrix} & & & \ \end{matrix}a=30\\\\\begin{matrix} & & & \ \end{matrix}\begin{array}{rcl}S_{24}&=&\frac{24}{2}(2a+23b)\\&=&12(2.30+23.5)\\&=&12(60+115)\\&=&12(175)\\&=&2100\end{array}\\\begin{matrix} & & & \ \end{matrix}Jadi\ jumlah\ TOTAL\ tersebut\ adalah\ \textdollar 2100.$
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