User:ShadowWolf/Math example

Equations I have recently solved:

Drag Equation: <math>\mathrm{F} = \frac{1}{2} \rho \mathrm{v}^2 C_d A</math>

Barometric Formula for Air Density: <math>\rho = \rho_p \cdot \left[ \frac{T_b} { T_b + L_b \cdot ( h - h_b ) } \right]^{\left( \frac{g_0 \cdot M}{ R^* \cdot L_b } \right) +1}</math>

Einsteins Formula for Mass Equivalence: <math>E_{rest} = mc^2</math> (in the form of <math> m = \frac{E_{rest}}{c^2} </math>)

Fireball Radius of a Nuclear Weapon: <math> R = \left( { \frac{E t^2}{\rho} } \right)^{\begin{matrix}\frac{1}{5}\end{matrix}} </math>

Pythagoras: <math>x^2 + y^2 = z^2</math> hence <math>z = \sqrt{x^2 + y^2}</math>

Other Equations:

Einsteins formula for Mass Equivalence (complete and with all definitions): <math>E = \gamma m c^2</math> where γ is <math>\gamma = \frac{1}{\sqrt{1-\beta^2}}</math> and β is the velocity expressed as a ratio of the speed of light.

Approximation of Mass-Equivalence: <math>E \approx m c^2 + \begin{matrix} \frac{1}{2} \end{matrix} m v^2</math>

Lorentz Transformation: <math>L_1 = \frac{L_0}{\gamma}</math> where γ is <math>\gamma \ \stackrel{\mathrm{def}}{=} \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}</math>

Time Dilation Equation: <math>\Delta t^' = \gamma \left( {\Delta t - \frac{v \Delta x}{c^2} } \right)</math> where γ is <math>\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}</math>