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.