1). P1 : jika
saya tidak makan, maka saya sakit
P2 : saya
tidak maka
Kesimpulan
: saya sakit
2 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 (45o+60o)=cos 45o+cos 60o
$=\frac{1}{2}\sqrt{2}+\frac{1}{2}$
$=\frac{1}{2}\sqrt{2}$
8).
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=
$[Tb\frac{\left( \frac{n}{2}-Fk \right)}{Fme}.I$
=
$52,5+\frac{1}{1+3}.3$
=
$52,5+\frac{1}{4}.3$
=
$52,5+\frac{3}{4}=60$
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).
$\int{\left( x-2 \right)}\left( x+3 \right)dx=$
$\int{\left( {{x}^{2}}+3x-2x-6 \right)dx}$
=
$\frac{1}{3}{{x}^{3}}+\frac{1}{2}{{x}^{2}}-6x$
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
