User talk:Steg55

Complex
$$ Z=\left ((\frac{-i}{\omega C})^{-1}+(R+i\omega L)^{-1}\right )^{-1} $$

$$ Z=\left (i\omega C+\frac{1}{R+i\omega L}\right )^{-1} == \frac{R+i\omega L}{1-\omega^{2}LC+i\omega RC} $$

$$ Z=\left (\frac{i\omega C}{R+i\omega L}\right )^{-1} $$

$$ \frac{1}{R+i\omega L} \times \frac{R-i\omega L}{R-i\omega L} == \frac{R-i\omega L}{R^{2}+\omega^{2}L^{2}} $$

$$ Answer == \frac{L}{CR}-\frac{i}{\omega C} $$

Millikan
$$ Q=\frac{18\pi d\eta^{3/2}}{U\sqrt{2\rho g}}(v_1+v_2)\sqrt{v_1} $$

$$ \eta_r=\frac{\eta_0}{1+\frac{b}{P\cdot r}} $$

$$ Q_{corr}=\frac{Q}{\sqrt{\left(1+\frac{b}{P\cdot r}\right)^3}} $$

$$ n\cdot2.857\times10^{-19}=m\cdot4.738\times10^{-19}=2n\cdot5.771\times10^{-19}=3n\cdot1.026\times10^{-18} $$

Conduction Cooling
$$ \frac{0.1}{86.9}\times100=0.1150\dots $$

$$ \frac{0.1}{4.7}\times100=2.1276\dots $$

$$ \frac{dT}{dt}=-k(T-T_{amb}) $$

$$ T_t=T_{amb}+(T_0-T_{amb})e^{-kt}\; $$

$$ T_t=295.15+(355.15-295.15)e^{-0.000330751\dots\times3600} $$

$$ t=\frac{1}{k}ln\left (\frac{T_{0}-T_{amb}}{T_t-T_{amb}}\right ) $$

$$ k=\frac{1}{t}ln\left (\frac{T_{0}-T_{amb}}{T_t-T_{amb}}\right ) $$

$$ k=\frac{1}{600}ln\left (\frac{355.15-295.15}{344.35-295.15}\right ) $$

$$ \frac{heat\;\;dissapated}{energy\;\;input}\times100=\%\;\;Efficiency $$

$$ \frac{96.68}{2.4}\times100=4028.33\dots\% $$

Pattern Analysis
$$h=(x-\mu)^{T}C^{-1}(x-\mu)$$

$$p(x) = \frac{1}{\left|C\right|^{\frac{1}{2}}(2\pi)^{\frac{n}{2}}}exp\left(\frac{-1}{2}(x-\mu)^{T}C^{-1}(x-\mu)\right)$$

$$p(A|x) = \frac{p(x|A)p(A)}{p(x|A)+p(x|B)}$$