User:PuzzleMeister/sandbox

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

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

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

$\sqrt2$

$Δ x = x f - x 0$

$x=\bar{v}t$

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

$v f = v 0 + a t$

$\bar{v}=\frac{v_0+v_f}{2} \iff \bar{a} constant$

$x=v_0t+\frac{1}{2}at^2$

${v_f}^2={v_0}^2+2ax$

$\vec{v_x} = \vec{v_0}\cos{\Theta_0}$

$p f i n a l$ $\vec{v_y} = \vec{v_0}\sin{\Theta_0}$

$\Delta x = v_{x0}t=t\left(v_0\cos{\Theta_0}\right)$

$v y = v y 0 - g t$

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

$\textrm{Time\ to\ top\ of\ parabola}=\frac{v_0\sin{\Theta_0}-v_y}{g}$

$t=\sqrt{\frac{2\Delta y}{g}}\iff v_0=0$

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

$\textrm{Magnitude\ of\ }\vec{v}=\sqrt{{v_x}^2+{v_y}^2}$

$\Theta\textrm{\ from\ positive\ }x\textrm{-axis}=\arctan{\frac{v_y}{v_x}}$

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

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

$T - F f = m a$

$Σ F x = 0 = T 1 x - T 2 x$

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

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

$f k = μ k n$

$f_s \leq \mu_sn, f_{s\textrm{\ max}} = \mu_sn$

$\textrm{Atwood\ Machines:\ }m_1<m_2$

$T 1 - N 1 = m 1 a$

$T 2 + N 2 = m 2 a$

$a 2 = b 2 + c 2 - 2 b c cosα$

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

$1N\equiv1kg*m/s^2=0.225lb$

$g = 9.8 m / s 2 = 32 f t / s 2$

$1 l b = 4.44 N$

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

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

$2 + p f i n a l$

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

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