heureka

SIN X/2=0.145424   X=?

$$\small{\text{
$
\begin{array}{rcl}
\sin{( \dfrac{x_1}{2} )} & = & 0.145424 \\
x_1 & = & 2*\sin^{-1}{( 0.145424 )}\\
\textcolor[rgb]{1,0,0}{ x_1} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{16.7236657093\ensurement{^{\circ}} }
\end{array}
$
}}$\\$
\hline
$\\$
\small{\text{
$
\begin{array}{rcl}
\sin{( \dfrac{x_1}{2} )} = \sin{( 180\ensurement{^{\circ}}- \dfrac{x_2}{2} )} & = & 0.145424 \\\\
180\ensurement{^{\circ}} - \dfrac{x_2}{2} & = & \sin^{-1}{( 0.145424 )}\\\\
180\ensurement{^{\circ}} - \dfrac{x_2}{2} & = &8.36183285464\ensurement{^{\circ}} \\
\textcolor[rgb]{1,0,0}{x_2} & \textcolor[rgb]{1,0,0}{=} & \textcolor[rgb]{1,0,0}{343.276334291\ensurement{^{\circ}} }
\end{array}
$
}}$$

Ein Vater war vor 8 Jahren 3-mal so alt wie seine Tochter. In 2 Jahren wird die Tochter halb so alt wie ihr Vater sein. Wie alt sind beide heute?

$$\small{\text{
V = Vater und T = Tochter.
$
\begin{array}{lcr}
(1) & (V-8) = 3*(T-8) & \text{ vor 8 Jahren}\\
(2) & (V+2) = 2*(T+2) & \text{ in 2 Jahren}\\
\end{array}
$
}}$\\$
\small{\text{
$
(1): V = 3T -16
$
}}$\\$
\small{\text{
$
(2) : V = 2T + 2
$
}}\hline
$\\$
\small{\text{
(1) = (2):
$
\begin{array}{rclr}
3T -16 &=& 2T + 2 \\
\textcolor[rgb]{1,0,0}{T} &\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{18}
\end{array}
$
}}
}}\hline
$\\$
\small{\text{
$
\begin{array}{rclr}
V&=& 2T+2\\
V&=& 2*18+2\\
\textcolor[rgb]{1,0,0}{V} &\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{38}
\end{array}
$
}}$$

Die Tochter ist 18 Jahre und ihr Vater ist 38 Jahre.

Vielen Dank. Frohe Weihnachten und

ein friedliches neues Jahr 2015. 

$$\small{\text{
$15500-12\% $
}}
$\\$
\small{\text{
$=15500-(12\%\ of \ 15500) $
}}
$\\$
\small{\text{
$=15500-15500*12\% $
}}
$\\$
\small{\text{
$=15500*1-15500*12\% \quad | \quad 1 = \frac{100}{100}=100*\frac{1}{100}=100\%
$
}}
$\\$
\small{\text{
$=15500*100\%-15500*12\%$
}}
$\\$
\small{\text{
$=15500*(100\%-12\%)$
}}
$\\$
\small{\text{
$=15500*88\% $
}}
$\\$
\small{\text{
$=15500*\frac{88}{100}$
}}
$\\$
\small{\text{
$=155*88 $
}}
$\\$
\small{\text{
$=13640$
}}$$

1. Suppose you and a friend are working for a nursery plating trees. Together you can play 8 trees per hour. Qhat is the greatest number of hours that you and your friend would need to plant at most 40 trees?

$$\small{
$ \dfrac{ 40 \text{ trees } } { \dfrac{ 8 \text{ trees } } {1\ h} }
= \dfrac{40}{8} = 5\ h$
}$$

2. The Garcias are putting a brick border along one edge of their flower garden. The garden is no more than 31 ft long. If each brick is 6 in. long, what is the greates number of bricks needed?

$$\dfrac{ 31\ ft * \dfrac{12\ in }{ 1\ ft } }{ 6\ in } = \dfrac{31*12}{6}= 62\text{ bricks}$$

 8z^2=6z^2+38

$$\small{\text{
$
\begin{array}{rcl}
8z^2 &=& 6z^2+38 \quad | \quad -6z^2 \\
8z^2-6z^2 &=& 38 \\
(8-6)z^2 &=& 38 \\
2z^2 &=& 38 \quad | \quad :2 \\\\
z^2 &=& \dfrac{38}{2} \\\\
z^2 &=& 19\quad | \quad \pm\sqrt \\
z_{1,2} &=& \pm\sqrt{19} \\
\end{array}
$
}} $\\\\$
\small{\text{
$
z_1 &=& 4.35889894354 $ and $ z_2 &=& -4.35889894354
$
}}$$

9 to the 4th power over 9 to the 6th power

$$\small{\text{
Set $ 9^4 = \dfrac{ 1 }{ 9^{-4} } $. We have
$
\dfrac{ 9^4 }{ 9^6 } = \dfrac{1 }{ 9^6 }*9^4 = \dfrac{1 }{ 9^6 }*\dfrac{ 1 }{ 9^{-4} } = \dfrac{1 }{ 9^{6-4} } = \dfrac{1 }{ 9^{2} } = \dfrac{1}{81} = 0.01234567901
$
}}$$

(2+5j)/(3+j)

$$\small{\text{
$
\dfrac{ (2+5j) } { (3+j) } * \dfrac{ (3-j) } { (3-j) } =
\dfrac{ 6-2j+15j-5j^2 } {9-j^2 } $
}} \\\\
\quad \boxed{j^2=-1}
\\\\
\small{\text{
$
=\dfrac{ (6+13j+5) } { (9+1) }
=\dfrac{ 11+13j } {10 }
=1.1+1.3j $
}}$$

Which equation represents the relationship between h, the number of hours she drives and m the number of miles she completes?

m = 45 * h

Example: m(6) = 45 * 6 = 270  okay!

I need to make a graph for an equation regarding BMI index. How can i solve an equation where a man weighs 85 kg and is between 130 cm and 200 cm? Eventually make graph for it.