Jawaban UTS Matematika

nomor :



1) . P1 : jika saya tidak makan, maka saya sakit

            P2 : saya tidak maka

            Kesimpulan : saya sakit
2). P1 : jika panen berhasil maka kesejahteraan petani meningkat

      P2 : kesejahteraan petani tidak meningkat

      Kesimpulan : panen tidak berhasil


3). P1 : jika 2x2 = 4 maka faktor dari 20

      P2 : jika 4 faktor dari 20 maka 20 bilangan genap

      Kesimpulan : jika 2x2 = 4 maka 20 bilangan genap


4).  $\left( -1,\sqrt{3} \right)$

      ${{r}^{2}}={{x}^{2}}+{{y}^{2}}$

      $[{{r}^{2}}=-{{1}^{2}}+{{\left( \sqrt{3} \right)}^{2}}$

      ${{r}^{2}}=1+3$

      $r=\sqrt{4}=2$


 $\alpha {}^\circ =\tan \frac{\sqrt{3}}{-1}$

      $=\tan -\sqrt{3}$

      $=120{}^\circ $

        =(2,120o)   





5).  $\left( 4,30{}^\circ \right)$

      $[x=r\cos \alpha {}^\circ $

      $x=4\cos 30{}^\circ $

      $x=4.\frac{1}{2}\sqrt{3}$

      $x=2\sqrt{3}$


      $y=r\sin \alpha {}^\circ $

      $y=4\sin 30{}^\circ $

      $y=4\left( \frac{1}{2} \right)$

      $y=2$

      $\left( 2\sqrt{3},2 \right)$



6). $\sin \left( a+b \right)=\sin a.\cos b+\cos a.\sin b$

      $\sin 75=\sin \left( 30+45 \right)$

      $=\sin 30.\cos 45+\sin 45.\cos 30$

      $=\frac{1}{2}.\frac{1}{2}\sqrt{2}+\frac{1}{2}\sqrt{2}.\frac{1}{2}\sqrt{3}$

      $=\frac{1}{4}\sqrt{2}+\frac{1}{4}\sqrt{6}$

       $=\frac{1}{4}\sqrt{2}+2\frac{1}{4}\sqrt{2}$

       $=2\frac{1}{2}\sqrt{2}$




7). cos 45o+cos 60o

     $=\frac{1}{2}\sqrt{2}+\frac{1}{2}$

      $=\sqrt{2}$

     


8). NS=10C3=120

     NA=3C2 x 1C1=3

     Peluangnya $=\frac{3}{120}=\frac{1}{40}$





9). Dadu 5=4                 Kemungkinan $=36$

     Dadu 8=5                      Peluang $\frac{9}{36}=\frac{1}{4}$



     10). Me=      $[Tb\frac{\left( \frac{n}{2}-Fk \right)}{Fme}.I$




                   $=55,5+\frac{10-5}{3}x3$

                   $=55,5+5=60,5$

      Q1 = ….

      Letak = $\frac{20}{4}=5$

      FQ = 5

      Tb = $52,5$

      Fk = 4

      I = 3

      Q1 = $52,5+\frac{5-4}{5}.3$

            = $52,5+\frac{1}{5}.3$

            = $52,5+0,2.3$

            = $52,5+6,6$

            = $53,1$

      Q3 = ….

      Letak = $\frac{20.3}{4}=15$

      FQ = 6

      Tb = $61,5$

      Fk = $14$

      I = 3

      Q1 = $61,5+\frac{15-14}{6}.3$

            = $61,5+\frac{1}{6}.3$

            = $61,5+0,5$

            = $62$

 

   Mean = $\frac{\sum\limits_{{}}^{{}}{F1.X1}}{\sum\limits_{{}}^{{}}{F1}}$

            = $\frac{1143}{20}$

            = $57,15$


   Modus

              $=TB\frac{d1}{d1+d2}.I$

               d1=4

             d2= -

                 =Tb+I

                 =61,5+3

                 =64,5  



11).

$\int{\left( x-2 \right)}\left( x+3 \right)dx=$



                 $\int{\left( {{x}^{2}}+3x-2x-6 \right)dx}$

             = $\frac{1}{3}{{x}^{3}}+\frac{1}{2}{{x}^{2}}-6x$



12).   $\int\limits_{1}^{2}{\left( 2x-3 \right)dx}$

       = ${{x}^{2}}-3x\int\limits_{1}^{2}{{}}$

       = $\left( {{2}^{2}}-3.2 \right)-\left( {{1}^{2}}-3.1 \right)$

       = $\left( 4-6 \right)-\left( 1-3 \right)$

       = $-2--2=0$



13).    y = $9-{{x}^{2}}$


$\int\limits_{-1}^{1}{\left( {{x}^{3}} \right)}dx=\frac{1}{4}.{{x}^{4}}$

            = $\frac{1}{4}{{.1}^{4}}-\frac{1}{4}-{{1}^{4}}$

            = $\frac{1}{4}--\frac{1}{4}$

            = $\frac{1}{2}$ satuan



14).   Soalnya tidak jelas atau tak terbaca

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