Math Help - Test

1. Test

. . $\Large\begin{array}{c} \curlyvee\!\! \curlyvee\!\! \curlyvee\! \curlyvee \\ [-3.6mm] \curlywedge\!\! \curlywedge\!\! \curlywedge\! \curlywedge \\ [-3.3mm] \curlyvee\!\! \curlyvee\!\! \curlyvee\! \curlyvee \\ [-3.6mm] \curlywedge\!\! \curlywedge\!\! \curlywedge\! \curlywedge \end{array}$

. . . $\huge\begin{array}{c}\top\!\!\!\! \dashv \\ [-6.5mm] \vdash\:\!\!\!\!\! \bot \end{array}$

. . $\large \begin{array}{cc}\backslash\text{curlyvee} & \curlyvee \\ \backslash\text{curlywedge} & \curlywedge \\ \backslash\text{top} & \top \\ \backslash\text{bot} & \bot \\ \backslash\text{vdash} & \vdash \\ \backslash\text{dashv} & \dashv \\ \backslash\text{maltese} & \maltese \\ \backslash\text{multimap} & \multimap \\ \backslash\text{circledcirc} & \circledcirc \\ \backslash\text{boxdot} & \boxdot \\ \backslash\text{boxplus} & \boxplus \\ \backslash\text{boxtimes} & \boxtimes \end{array} \qquad\begin{array}{cc} \backslash\text{varkappa} & \varkappa \\ \backslash\text{Cup} & \Cup \\ \backslash\text{Cap} & \Cap \\ \backslash\text{Subset} & \Subset \\ \backslash\text{Supset} & \Supset \\ \backslash S & \S \\ \backslash\text{between} & \between \\ \backslash\text{checkmark} & \checkmark \\ \backslash\text{bowtie} & \bowtie \\ \backslash\text{divideontimes} & \divideontimes \\ \backslash\text{Rrightarrow} & \Rrightarrow \\ \backslash\text{Lleftarrow} & \Lleftarrow \end{array}$

2. Re: Test

$\frac { 5(x^2 y^3 z ^{1/2})^{-4} }{20(x^3 y^{-2} z^1)^5}$

$= \frac { 1 x^{-8}y^{-12}z^{-2}}{4x^{15}y^{-10}z^5}$

$= \frac {1}{4}x^{-8-15}y^{-12-(-10)}z^{-2-5}$

$= \frac {1}{4}x^{-23}y^{-2}z^{-7}$

$= \frac {1}{4x^{23}y^2z^7}$

3. Re: Test

TEST
I try to do the following integral

$\left \int_0^t v(t) = \int_0^t v_0 + v_c \{sin(\omega t + \phi) - sin(\phi)\} \right$

I end up with $x(t) = x_0 + (\frac{v_c}{\omega}) \{cos \phi - cos(\omega t + \phi)\}$

$x(t) = x_0 + (\frac{v_c}{\omega}) \[\{(\frac{v_o}{v_c}) - sin \phi\} \omega t + cos \phi - cos(\omega t + \phi)\}$
$\{(\frac{v_o}{v_c}) - sin \phi\} \omega t$