Online Help

$\mathrm{distance}≔55⟦\mathrm{mph}⟧\cdot 35⟦\mathrm{minutes}⟧$

$\mathrm{distance}≔\frac{1290828}{25}⟦m⟧$

$\mathrm{convert}\left(\mathrm{distance}\,\mathrm{units}\,\mathrm{mi}\right)$

$\frac{385}{12}⟦\mathrm{mi}⟧$

$\mathrm{evalf}\left(\right)$

$32.08333333⟦\mathrm{mi}⟧$

$\mathrm{convert}\left(3⟦\mathrm{week}⟧\,\mathrm{units}\,s\right)$

$1814400⟦s⟧$

$\mathrm{convert}\left(5⟦\mathrm{ft}⟧+4⟦\mathrm{inches}⟧\,\mathrm{units}\,\mathrm{inches}\right)$

$64⟦\mathrm{in}⟧$

$\mathrm{convert}\left(50⟦\frac{\mathrm{km}}{h}⟧\,\mathrm{units}\,\frac{\mathrm{cm}}{s}\right)$

$\frac{12500}{9}⟦\frac{\mathrm{cm}}{s}⟧$

$\mathrm{evalf}\left(\right)$

$1388.888889⟦\frac{\mathrm{cm}}{s}⟧$

$\mathrm{elapsed\_time}≔\sqrt{2\frac{\mathrm{dist}}{\mathrm{accel}}}$

$\mathrm{elapsed\_time}≔\sqrt{2}\sqrt{\frac{\mathrm{dist}}{\mathrm{accel}}}$

$\mathrm{eval}\left(\mathrm{elapsed\_time}\,\left[\mathrm{dist}\=20⟦m⟧\,\mathrm{accel}\=⟦\mathrm{gn}⟧\right]\right)$

$\frac{\sqrt{2}\sqrt{400000}\sqrt{196133}}{196133}⟦s⟧$

$\mathrm{evalf}\left(\right)$

$2.019619976⟦s⟧$

$\mathrm{mass}≔9.11{10}^{\mathrm{-31}}⟦\mathrm{kg}⟧$

$\mathrm{mass}≔9.110000000{10}^{\mathrm{-31}}⟦\mathrm{kg}⟧$

$c≔3.00{10}^8⟦\frac{'m'}{\'s\'}⟧$

$c≔3.000000000{10}^8⟦\frac{m}{s}⟧$

$E≔\mathrm{mass}{c}^2$

$E≔8.199000000{10}^{\mathrm{-14}}⟦J⟧$

$\mathrm{convert}\left(⟦\mathrm{em}⟧\,\mathrm{units}\,J\,\mathrm{energy}\right)$

$8.187104141{10}^{\mathrm{-14}}⟦J⟧$

$\mathrm{cost}≔1210.00⟦\frac{\mathrm{USD}}{\mathrm{oz}\left[\mathrm{troy}\right]}⟧\;\#\mathrm{November\; 18th,\; 2016}$

$\mathrm{cost}≔1210.00⟦\frac{\mathrm{USD}}{{\mathrm{oz}}_{\mathrm{troy}}}⟧$

$\mathrm{density}≔19.3⟦\frac{g}{{\mathrm{cm}}^3}⟧$

$\mathrm{density}≔19.3⟦\frac{g}{{\mathrm{cm}}^3}⟧$

$\mathrm{mass}≔\frac{{10}^9⟦\mathrm{USD}⟧}{\mathrm{cost}}$

$\mathrm{mass}≔25705.35273⟦\mathrm{kg}⟧$

$\mathrm{volume}≔\frac{\mathrm{mass}}{\mathrm{density}}$

$\mathrm{volume}≔1.331883561⟦m^3⟧$

$\mathrm{length\_side}≔\sqrt[3]{\mathrm{volume}}$

$\mathrm{length\_side}≔1.100243351⟦m⟧$

$\mathrm{convert}\left(1.1⟦M⟧\,\mathrm{units}\,\mathrm{mph}\right)$

$815.6003937⟦\mathrm{mph}⟧$

$\mathrm{convert}\left(1.1⟦M⟧\,\mathrm{units}\,\frac{\mathrm{mi}}{s}\right)$

$0.2265556649⟦\frac{\mathrm{mi}}{s}⟧$

$\mathrm{convert}\left(1.1⟦M⟧\,\mathrm{units}\,\frac{m}{s}\right)$

$364.606⟦\frac{m}{s}⟧$

$\mathrm{convert}\left(3.5⟦\mathrm{mi}⟧\,\mathrm{units}\,m\right)$

$5632.704000⟦m⟧$

$\mathrm{round}\left(\right)$

$5633⟦m⟧$

$\frac{50⟦\mathrm{gal}\left[\mathrm{US\_liquid}\right]⟧}{750⟦\mathrm{mL}⟧}$

$\frac{157725491}{625000}$

$\mathrm{floor}\left(\right)$

$252$

$\frac{12⟦g⟧}{20⟦\mathrm{deniers}⟧}$

$5400⟦m⟧$

$\mathrm{convert}\left(2⟦L⟧\,\mathrm{units}\,{\mathrm{inches}}^3\right)$

$\frac{250000000}{2048383}⟦{\mathrm{in}}^3⟧$

$\mathrm{evalf}\left(\right)$

$122.0474882⟦{\mathrm{in}}^3⟧$

$\mathrm{frequency}≔1.420405761⟦\mathrm{GHz}⟧$

$\mathrm{frequency}≔1.420405761⟦\mathrm{GHz}⟧$

$\frac{1}{\mathrm{frequency}}$

$0.7040241792⟦\frac{1}{\mathrm{GHz}}⟧$

$\mathrm{convert}\left(\,\mathrm{units}\,\mathrm{nanoseconds}\right)$

$0.7040241792⟦\mathrm{ns}⟧$

$\mathrm{convert}\left(\mathrm{frequency}\,\mathrm{units}\,\frac{1}{\mathrm{yr}}\right)$

$4.482363838{10}^{16}⟦\frac{1}{\mathrm{yr}}⟧$

$\mathrm{frequency}\cdot 10000000000⟦\mathrm{yr}⟧$

$4.482363838{10}^{26}$

$\mathrm{resistance}≔\sqrt{\frac{\mathrm{inductance}}{\mathrm{capacitance}}}$

$\mathrm{resistance}≔\sqrt{\frac{\mathrm{inductance}}{\mathrm{capacitance}}}$

$\mathrm{eval}\left(\mathrm{resistance}\,\left[\mathrm{inductance}\=124.⟦\mathrm{nH}⟧\,\mathrm{capacitance}\=3.52⟦\mathrm{uF}⟧\right]\right)$

$0.1876892984⟦\mathrm{\Omega }⟧$

$\mathrm{evalf}\left(\right)$

$0.1876892984⟦\mathrm{\Omega }⟧$

$\mathrm{convert}\left(\,\mathrm{units}\,\mathrm{uOmega}\right)$

$187689.2984⟦\mathrm{\mu \Omega }⟧$

$\mathrm{molar\_energy}≔523.432⟦\frac{\mathrm{Btu}}{\mathrm{mol}\left(\mathrm{carbon}\right)}⟧$

$\mathrm{molar\_energy}≔523.432⟦\frac{\mathrm{Btu}}{\mathrm{mol}\left(\mathrm{carbon}\right)}⟧$

$\mathrm{carbon\_mass}≔12⟦\frac{\mathrm{kg}}{\mathrm{mol}\left(\mathrm{carbon}\right)}⟧$

$\mathrm{carbon\_mass}≔12⟦\frac{\mathrm{kg}}{\mathrm{mol}\left(\mathrm{carbon}\right)}⟧$

$\mathrm{mass\_energy}≔\frac{\mathrm{molar\_energy}}{\mathrm{carbon\_mass}}$

$\mathrm{mass\_energy}≔45990.05563⟦\frac{m^2}{s^2}⟧$

$\mathrm{convert}\left(\,\mathrm{units}\,\frac{\mathrm{Btu}}{\mathrm{lb}}\right)$

$19.78539678⟦\frac{\mathrm{Btu}}{\mathrm{lb}}⟧$

$\mathrm{distance}≔\frac{5}{1+4{\ⅇ}^{-\frac{3t}{⟦s⟧}}}⟦m⟧$

$\mathrm{distance}≔\frac{5}{1+4{\ⅇ}^{-3t⟦\frac{1}{s}⟧}}⟦m⟧$

$\mathrm{speed}≔\mathrm{diff}\left(\mathrm{distance}\,t\right)$

$\mathrm{speed}≔\frac{60{\ⅇ}^{-3t⟦\frac{1}{s}⟧}}{{\left(1+4{\ⅇ}^{-3t⟦\frac{1}{s}⟧}\right)}^2}⟦\frac{m}{s}⟧$

$\genfrac{}{}{0ex}{}{\mathrm{speed}}{\phantom{t\=2.5}}|\genfrac{}{}{0ex}{}{\phantom{\mathrm{speed}}}{t\=2.5⟦s⟧}$

$0.03303871496⟦\frac{m}{s}⟧$

$\genfrac{}{}{0ex}{}{\mathrm{speed}}{\phantom{y}}|\genfrac{}{}{0ex}{}{\phantom{x}}{t\=5.⟦\mathrm{blink}⟧}$

$0.0001411518555⟦\frac{m}{s}⟧$

$\mathrm{int}\left(\mathrm{speed}\,t\=1⟦s⟧..2.5⟦s⟧\right)$

$0.8193365798⟦m⟧$

$\mathrm{evalf}\left(\right)$

$0.8193365798⟦m⟧$

$\genfrac{}{}{0ex}{}{\mathrm{distance}}{\phantom{x\=a}}|\genfrac{}{}{0ex}{}{\phantom{\mathrm{f(x)}}}{t\=2.5⟦s⟧}-\genfrac{}{}{0ex}{}{\mathrm{distance}}{\phantom{x\=a}}|\genfrac{}{}{0ex}{}{\phantom{\mathrm{f(x)}}}{t\=1⟦s⟧}$

$\left(4.988962733-\frac{5}{1+4{\ⅇ}^{\mathrm{-3}}}\right)⟦m⟧$

$\mathrm{evalf}\left(\right)$

$0.819336584⟦m⟧$

$\min \left(1.2⟦\mathrm{yd}⟧\,⟦m⟧\,3.2⟦\mathrm{ft}⟧\,0.6⟦\mathrm{fathom}⟧\right)$

$0.9753600000⟦m⟧$

$\max \left(1.2⟦\mathrm{yd}⟧\,⟦m⟧\,3.2⟦\mathrm{ft}⟧\,0.6⟦\mathrm{fathom}⟧\right)$

$1.097280000⟦m⟧$

$\mathrm{energy}≔\mathrm{torque}\cdot \mathrm{angle}$

$\mathrm{energy}≔\mathrm{torque}\mathrm{angle}$

$\mathrm{eval}\left(\mathrm{energy}\,\left[\mathrm{torque}\=3⟦Nm⟧\,\mathrm{angle}\=10⟦\mathrm{deg}⟧\right]\right)$

$\frac{\mathrm{\pi }}{6}⟦J⟧$

$\mathrm{convert}\left(\,\mathrm{system}\right)$

$\frac{\mathrm{\pi }}{6}⟦J⟧$

$\mathrm{evalf}\left(\right)$

$0.5235987758⟦J⟧$

$\frac{40000⟦\mathrm{km}⟧}{7200⟦\mathrm{mph}⟧}$

$\frac{156250000}{12573}⟦s⟧$

$\mathrm{convert}\left(\,\mathrm{units}\,h\right)$

$\frac{390625}{113157}⟦h⟧$

$\mathrm{evalf}\left(\right)$

$3.452062179⟦h⟧$

$7200⟦\mathrm{mph}⟧\cdot 10⟦s⟧$

$\frac{804672}{25}⟦m⟧$

$\mathrm{evalf}\left(\right)$

$32186.88000⟦m⟧$

$\mathrm{convert}\left(\,\mathrm{units}\,\mathrm{km}\right)$

$32.18688000⟦\mathrm{km}⟧$

$\mathrm{vol}≔\mathrm{convert}\left(1.2⟦\mathrm{ft}⟧\cdot \mathrm{\π}\cdot {\left(\frac{.9⟦\mathrm{ft}⟧}{2}\right)}^2\,\mathrm{units}\,\mathrm{gal}\left[\mathrm{UK}\right]\right)$

$\mathrm{vol}≔4.755136685⟦{\mathrm{gal}}_{\mathrm{UK}}⟧$

$\frac{1032⟦\mathrm{gal}\left[\mathrm{UK}\right]⟧}{\mathrm{vol}}$

$217.0284617$

$\mathrm{evalf}\left(\frac{681.8150208}{\mathrm{\π}}\right)$

$217.0284616$

$\mathrm{gain}≔\frac{23⟦\mathrm{mW}⟧}{332⟦\mathrm{uW}⟧}$

$\mathrm{gain}≔\frac{5750}{83}$

$10\cdot \mathrm{log10}\left(\mathrm{gain}\right)$

$\frac{10\ln \left(\frac{5750}{83}\right)}{\ln \left(10\right)}$

$\mathrm{evalf}\left(\right)$

$18.40589752$

$\mathrm{voltage\_gain}≔\frac{23⟦\mathrm{mV}⟧}{332⟦\mathrm{uV}⟧}$

$\mathrm{voltage\_gain}≔\frac{5750}{83}$

$20\cdot \mathrm{log10}\left(\mathrm{gain}\right)$

$\frac{20\ln \left(\frac{5750}{83}\right)}{\ln \left(10\right)}$

$\mathrm{evalf}\left(\right)$

$36.81179504$

$v≔\mathrm{v0}\+a\cdot t$

$v≔at+\mathrm{v0}$

$\mathrm{vs}≔\genfrac{}{}{0ex}{}{v}{\phantom{y}}|\genfrac{}{}{0ex}{}{\phantom{x}}{\mathrm{v0}\=2.4⟦\frac{m}{s}⟧}$

$\mathrm{vs}≔at+2.4⟦\frac{m}{s}⟧$

$x≔\mathrm{x0}\+{\int }_0^{\mathrm{t0}}\mathrm{vs}\ⅆt$

$x≔\mathrm{x0}+\left(0.5000000000a{\mathrm{t0}}^2{\left(⟦\frac{s}{m}⟧\right)}^2+2.400000000\mathrm{t0}⟦\frac{s}{m}⟧\right)⟦\frac{m^2}{s^2}⟧$

$\mathrm{gravity}≔\mathrm{evalf}\left(\mathrm{ScientificConstants}:-\mathrm{Constant}\left(g\,\mathrm{units}\right)\right)\;$

$\mathrm{gravity}≔9.80665⟦\frac{m}{s^2}⟧$

$\genfrac{}{}{0ex}{}{x}{\phantom{y}}|\genfrac{}{}{0ex}{}{\phantom{x}}{\left[\mathrm{x0}\=0⟦m⟧\,a\=-\mathrm{gravity}\right]}$

$\left(-4.903325000{\mathrm{t0}}^2⟦\frac{1}{m}⟧+2.400000000\mathrm{t0}⟦\frac{s}{m}⟧\right)⟦\frac{m^2}{s^2}⟧$

$\genfrac{}{}{0ex}{}{\phantom{y}}{}|\genfrac{}{}{0ex}{}{\phantom{x}}{\mathrm{t0}\=0.4⟦s⟧}$

$0.1754680000⟦m⟧$