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)
=\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}
8. NS = $\begin{align}
6. \sin \left( a+b \right)=\sin a.\cos b+\cos a.\sin b
=\sin 30.\cos 45+\sin 30.\cos 45
=\frac{1}{2}.\frac{1}{2}\sqrt{2}+\frac{1}{2}\sqrt{3}.\frac{1}{2}\sqrt{2}
=\frac{1}{4}\sqrt{2}+\frac{1}{4}\sqrt{6}
7. \cos \left( 45{}^\circ +60{}^\circ \right)=\cos 45{}^\circ +\cos 60{}^\circ
=\frac{1}{2}\sqrt{2}+\frac{1}{2}
=\frac{1}{2}\sqrt{2}
& 10C3=\frac{10!}{7!3!}=\frac{10.9.8.7!}{7!.5!}=120 \\
& \\
\end{align}$
NA = $\begin{align}
& 3C2.1C1 \\
& 3.1=3 \\
\end{align}$ Peluangnya \[\frac{5}{120}=\frac{1}{2}\]
9. Dadu 5=4 Kemungkinan =36
9. Dadu 5=4 Kemungkinan =36
Dadu 8=\frac{5}{9} Peluang \frac{9}{36}=\frac{1}{4}
10. Me = \[\begin{align}
13. y = 9-{{x}^{2}}
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= \\
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}
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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