Processing math: 100%

Kamis, 16 Maret 2017

Jawaban Matematika Mid Semester

Nama : Dimas Fadli Saputra
Kelas : 12 TKJ 1

1. P1 : jika saya tidak makan, maka saya sakit
    P2 : saya tidak makan
    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 =Arc\tan \frac{\sqrt{3}}{-1}
      =Arc\tan -\sqrt{3}
      =-60{}^\circ
\left( 2,-60{}^\circ  \right)

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=2\left( \frac{1}{2} \right)

y=1 
\left( 2\sqrt{3},1 \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 30.\cos 45
=\frac{1}{2}.\frac{1}{2}\sqrt{2}+\frac{1}{2}\sqrt{3}.\frac{1}{2}\sqrt{2}
=\frac{1}{4}\sqrt{2}+\frac{1}{4}\sqrt{6}
=\frac{1}{4}\left( \sqrt{2}+\sqrt{6} \right) 

7.    \cos \left( 45{}^\circ +60{}^\circ  \right)=\cos 45{}^\circ +\cos 60{}^\circ  

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


8.    NS = $\begin{align}
 & 10C3=\frac{10!}{7!3!}=\frac{10.9.8.7!}{7!.5!}=120 \\
  &  \\
  \end{align}$
            NA =  $\begin{align}
  & 3C2.1C1 \\
 & 3.1=3 \\
\end{align}$ Peluangnya \[\frac{5}{120}=\frac{1}{2}\]

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

10.   Me = \[\begin{align}
& Tb\frac{\left( \frac{n}{2}-Fk \right)}{Fme}.I \\
\end{align}\]
            = 55,5\frac{\left( \frac{20}{2}-9 \right)3}{3}
            = \frac{55,5.10-9.3}{3}=55,5
            Mo = \[\begin{align}
  & Tb\frac{d1}{d1+d2}.I \\
 &  \\
\end{align}\]
            = 52,5+\frac{1}{1+3}.3
            = 52,5+\frac{1}{4}.3
            = 52,5+\frac{3}{4}=60
      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{15-4}{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

11. $\begin{align}
 & \int{\left( x-2 \right)}\left( x+3 \right)dx= \\
 & \int{\left( {{x}^{2}}+3x-2x-6 \right)dx} \\
 \end{align}$ 
 = \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

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