User:PuzzleMeister/sandbox

Help With Formulæ

$f(x)={\frac {log_{10}n}{log_{10}(2006n-n^{2})}}$

$f(1),f(2),f(3),...,f(2005)$

$\left\{{\sqrt[{3}]{27+\overbrace {3+57+99} }}\right\}$

${\sqrt {2}}$

$\Delta x=x_{f}-x_{0}$

$x={\bar {v}}t$

${\bar {v}}={\frac {\Delta x}{\Delta t}}$

$v_{f}=v_{0}+at$

${\bar {v}}={\frac {v_{0}+v_{f}}{2}}\iff {\bar {a}}constant$

$x=v_{0}t+{\frac {1}{2}}at^{2}$

${v_{f}}^{2}={v_{0}}^{2}+2ax$

${\vec {v_{x}}}={\vec {v_{0}}}\cos {\Theta _{0}}$

$p_{final}$ ${\vec {v_{y}}}={\vec {v_{0}}}\sin {\Theta _{0}}$

$\Delta x=v_{x0}t=t\left(v_{0}\cos {\Theta _{0}}\right)$

$v_{y}=v_{y0}-gt$

$\Delta y=v_{y0}t-{\frac {1}{2}}gt^{2}$

${\textrm {Time\ to\ top\ of\ parabola}}={\frac {v_{0}\sin {\Theta _{0}}-v_{y}}{g}}$

$t={\sqrt {\frac {2\Delta y}{g}}}\iff v_{0}=0$

${v_{y}}^{2}={v_{y0}}^{2}-2g\Delta y={v_{y0}}^{2}-2g\left(v_{y0}t-{\frac {1}{2}}gt^{2}\right)$

${\textrm {Magnitude\ of\ }}{\vec {v}}={\sqrt {{v_{x}}^{2}+{v_{y}}^{2}}}$

$\Theta {\textrm {\ from\ positive\ }}x{\textrm {-axis}}=\arctan {\frac {v_{y}}{v_{x}}}$

$\Sigma F=F_{net}=m{\bar {a}}={\frac {m\Delta v}{\Delta t}}=F_{a}-F_{f}$

$Ft=m\Delta v{\textrm {\ (impulse=momentum)}}$

$T-F_{f}=ma$

$\Sigma F_{x}=0=T_{1x}-T_{2x}$

$\Sigma F_{y}=0=\left(T_{1y}+T_{2y}\right)-Newtons$

$\mu \left({\textrm {coefficient\ of\ friction}}\right)={\frac {friction}{normal}}$

$f_{k}=\mu _{k}n$

$f_{s}\leq \mu _{s}n,f_{s{\textrm {\ max}}}=\mu _{s}n$

${\textrm {Atwood\ Machines:\ }}m_{1}<m_{2}$

$T_{1}-N_{1}=m_{1}a$

$T_{2}+N_{2}=m_{2}a$

$a^{2}=b^{2}+c^{2}-2bc\cos {\alpha }$

${\frac {a}{\sin {\alpha }}}={\frac {b}{\sin {\beta }}}={\frac {c}{\sin {\gamma }}}$

$1N\equiv 1kg*m/s^{2}=0.225lb$

$g=9.8m/s_{2}=32ft/s^{2}$

$1lb=4.44N$

$1kg=2.2lbs\iff g=9.m/s^{2}$

${\vec {R}}={\sqrt {37.65^{2}+22.9^{2}}}\approx 44.1$

$2+p_{final}$

$\lim _{x\to \infty }f(x)=\mathbb {M} {\textrm {\ where\ }}\mathbb {M} \equiv {\textrm {madness.}}$