User:Plutor/Math sandbox
I use this page to create LaTeX math images for random things. See Help:Formula for documentation.
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\sigma_0 = \langle\sigma_m\rangle
\approx
\int_0^{\varepsilon_0}
{\rm d}\varepsilon_0
\left\lbrace
2\kappa\frac{n(\varepsilon_0)-n(\infty)}{n(0)-n(\infty)}
+\alpha\left[
v_p(\varepsilon_0)-v_p^\max(\varepsilon_0)
\right]
\right\rbrace
Carrying change
2.7 miles = 1.35 hours
1 lb = 453.59237 g
penny = 2.5g = 250 g/$
= 0.551155655 lb/$ * 1.35 cal/lb*day
= 0.74406013425 cal/$*day
Value-density of a penny:
:
\begin{matrix} \mathbb{D} & = & \frac{2.5g}{\$0.01} \\
\ & = & 250\;g/\$ \\
\ & \approx & 0.551\;lb/\$
\end{matrix}
Energy used carrying a penny around for a day:
:
\begin{matrix} \mathbb{E} & = & \mathbb{D} * \frac{2.7\;mi}{2\;mph} * \frac{1\;cal}{lb * hr} \\
\ & = & \mathbb{D} * 1.35\;cal/lb \\
\ & \approx & 0.744\;cal/\$
\end{matrix}
When is [[Powerball]] worth it?
For http://plutor.org/blog/2006/02/15/when-is-powerball-worth-it/
:
\
\begin{matrix}
v_{ticket} & > & \$1.00 \\
\\
v_{ticket} & = & \frac{v_{jackpot}}{p_{jackpot}} + \frac{v_2}{p_2}+ \frac{v_3}{p_3} + \cdots + \frac{v_n}{p_n} \\
\\
\$1.00 & < & \frac{v_{jackpot}}{146,107,962.00} + \frac{\$200,000}{3,563,608.83} + \frac{\$10,000}{584,431.85} + \frac{\$100}{14,254.44} + \\
& & \frac{\$100}{11,927.18} + \frac{\$7}{290.91} + \frac{\$7}{745.45} + \frac{\$4}{126.88} + \frac{\$3}{68.96} \\
\$1.00 & < & \frac{v_{jackpot}}{146,107,962.00} + \sim 0.19711512 \\
\\
\$117,307,873 & < & v_{jackpot}
\end{matrix}
\