heureka

how do i hex a number?

Hex numbers are: $\begin{array}{lrrrrrrrrrrrrrrr} \text{Hex-Numbers} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & A & B & C & D & E & F\\ &0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \end{array}$

Example:

$\begin{array}{rrrrr} 1234_{10} &=& 4D2_{16} \\ \\ \hline \\ && q & r & r_{\text{hex}}\\ \\ \hline 1234 & : 16 & 2 & 2 & 2\\ 77 & : 16 & 4 & (13) & D\\ 4 & : 16 & 0 & 4 & 4\\ \end{array}$

Solve the following equation!

$\begin{array}{rcl} \sqrt{x-4} -\sqrt[4]{x-4} &=& 12 \\ \end{array}$

The solution(s) of the given equation is/are x=??

$\begin{array}{rcll} \sqrt{x-4} -\sqrt[4]{x-4} &=& 12 \qquad &| \qquad +\sqrt[4]{x-4}\\ \sqrt{x-4} &=& 12 + \sqrt[4]{x-4} \qquad &| \qquad -12\\ \sqrt{x-4}-12 &=& \sqrt[4]{x-4} \qquad &| \qquad()^2\\ ( \sqrt{x-4}-12 )^2 &=& ( \sqrt[4]{x-4} )^2 \\ x-4 - 24\sqrt{x-4} + 144 &=& (x-4)^{\frac24 } \\ x-4 - 24\sqrt{x-4} + 144 &=& (x-4)^{\frac12 } \\ x-4 - 24\sqrt{x-4} + 144 &=& \sqrt{x-4} \qquad &| \qquad + 24\sqrt{x-4}\\ x-4 + 144 &=& \sqrt{x-4}+ 24\sqrt{x-4}\\ x-4 + 144 &=& 25\sqrt{x-4}\\ x + 140 &=& 25\sqrt{x-4}\qquad &| \qquad()^2\\ ( x + 140 )^2 &=& ( 25\sqrt{x-4} )^2 \\ x^2+280x+140^2 &=& 625 ( x-4)\\ x^2+280x+19600 &=& 625x-2500 \qquad &| \qquad -625x\\ x^2-345x +19600 &=& -2500 \qquad &| \qquad +2500\\ x^2-345x +22100 &=& 0 \\ \end{array}$

$\begin{array}{rcll} x^2-345x +22000 &=& 0\\ \qquad \boxed{ ~ x = {-b \pm \sqrt{b^2-4ac} \over 2a} ~}\\ x &=& {345 \pm \sqrt{345^2-4\cdot22100} \over 2}\\ x &=& {345 \pm \sqrt{30625} \over 2}\\ x &=& {345 \pm 175 \over 2}\\ \hline x_1 &=& {345 + 175 \over 2}\\ \mathbf{x_1} &\mathbf{=} & \mathbf{260}\\ \hline x_2 &=& {345 - 175 \over 2}\\ x_2 &=& 85 \quad \text{ no solution}\\ \end{array}$

The solution is x = 260

Was ist die Wurzel aus 17 hoch8 ?

$\sqrt{17^8}=17^{ \frac82}=17^4=83\ 521$

solve for LD: w = 0.002(2000-LD)

Having some trouble with this one, the LD equation I'm getting has some interesting signs (I get LD = -2000-500w) which I don't think makes intuitive sense.

$\begin{array}{rcll} w &=& 0.002\cdot (2000-LD) \qquad &|\qquad :0.002\\\\ \dfrac{w}{0.002} &=& 2000-LD \qquad &|\qquad +LD\\\\ LD + \dfrac{w}{0.002} &=& 2000 \qquad &|\qquad - \dfrac{w}{0.002}\\\\ LD &=& 2000 - \dfrac{w}{0.002}\\\\ LD &=& 2000 - \dfrac{1}{0.002}\cdot w\\\\ LD &=& 2000 - \dfrac{1}{\frac{2}{1000}}\cdot w\\\\ LD &=& 2000 - \dfrac{1000}{2}\cdot w\\\\ \mathbf{LD} &\mathbf{=}& \mathbf{2000 - 500\cdot w} \end{array}$

5nCr2(.5)^2(.5)^3

$\begin{array}{rcl} 5Cr2(0.5)^2(0.5)^3 \\ &=& \binom{5}{2}\cdot 0.5^2\cdot 0.5^3\\ &=& \binom{5}{2}\cdot 0.5^{2+3}\\ &=& \binom{5}{2}\cdot 0.5^{5}\\ &=& \frac{5}{2}\cdot\frac{4}{1}\cdot 0.5^{5}\\ &=& \frac{5}{2}\cdot\frac{4}{1}\cdot 0.03125\\ &=& 10\cdot 0.03125\\ &=& 0.3125\\ \mathbf{5Cr2(0.5)^2(0.5)^3 }& \mathbf{=} & \mathbf{0.3125}\\ \end{array}$

Wie berechnet man die Kantenlänge eines Würfels bzw. volumen

Wenn das Volumen(V) eines Würfels gegeben ist, dann berechnet sich die Kantenlänge(a) aus: $a=\sqrt[3]{V}$

Wenn die Kantenlänge(a) eines Würfels gegeben ist, dann berechnet sich das Volumen(V) zu: $V=a^3$

Beispiel:

$V = 1000 cm^3\\ a = \sqrt[3]{1000\ cm^3}\\ a = 10\ cm$

-3(y+8)-7(y-7)

Simplifiy by removing paraenthses and combining like terms

$\begin{array}{rcl} -3(y+8)-7(y-7)\\ &=& -[ 3(y+8)+7(y-7)] \\ &=& -[ 3\cdot y + 3\cdot 8 + 7\cdot y +7\cdot(-7) ]\\ &=& -( 3\cdot y + 24 + 7\cdot y -49 )\\ &=& -( 3\cdot y + 7\cdot y + 24 - 49 )\\ &=& -( 10\cdot y - 25 )\\ &=& - 10\cdot y + 25 \\ &=& 25 - 10\cdot y \\ \mathbf{ -3(y+8)-7(y-7) }&\mathbf{=} & \mathbf{ 25 - 10\cdot y }\\ \end{array}$

max muskelmann hat auf seinem fahrradtrainer mit 80 umdrehungen insgesamt 96 m geschafft.wie viele umdrehungen benötigt er,wenn er 5 km weit fahren will?

$\begin{array}{rcl} 80~\text{Umdrehungen} &=& 96~\text{m}\\ x~\text{Umdrehungen} &=& 5000~\text{m} \qquad | \qquad 5~\text{km} = 5000~\text{m}\\ \\ \hline \\ \dfrac{80}{x} &=& \dfrac{96}{5000} \\ \dfrac{x}{80} &=& \dfrac{5000}{96} \\ x &=& 80\cdot \dfrac{5000}{96} \\ x &=& 4166.66666667 ~\text{Umdrehungen}\\ \end{array}$

Er benötigt rund 4167 Umdrehungen, wenn er 5 km weit fahren will.

which are the steps of this thing 24-x=-16

$\begin{array}{rcl} 24-x &=&-16 \qquad | \qquad \cdot (-1)\\ -24+x &=& 16 \qquad | \qquad +24\\ x &=& 16+24\\ \mathbf{ x} & \mathbf{=} & \mathbf{40} \end{array}$

Which of the following is irrational?

square root of 6

square root of 0.16

square root of 900 or

square root of 25

square root of 6 is irrational, because

square root of 0.16 = 0.4,

square root of 900 = 30,

square root of 25 = 5,

but square root of 6 = 2.44948974278...