# Sample Latex

$^nC_r = \frac{n!}{(n-r)! r! }$$\frac{1}{2}$$\sqrt{1}$$\frac{n(E)}{n(S)}$$\frac{1}{n}$

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$\frac{\frac{150}{100} x }{ \frac{90}{100} y}$$\frac{1}{2}$$Calculate (144^{-312}) ?$$144^(-312)^1/6$$\frac{1}{2} \$

$$\frac{(1+2)}{(2 +\frac{4}{3})}\\$$

$x^2$$\frac{1}{2} \$

$\frac{(1+2)}{(2 +\frac{4}{3})}\\$

$\frac{1}{7}=0.\overline{142857}$$(\frac{1}{2})^2 \$$\implies$$\neq$$\ a_1 + a_5 \$$\overline{A}$$c^20$$18*\tfrac{\pi }{180^{\circ}}$$\frac{Pl}{2}$$\frac{\alpha ^{n}+\beta ^{n}}{\frac{1}{\alpha ^{n}}+\frac{1}{\beta ^{n}}}$

n * βn)

$t\frac{\partial x}{\partial t} + x = t \text{ is }$$IF = e^{\int Pdt} = e^{\int \frac{1}{t}dt} = e^{lnt} = t$$x^{x} = (e^{i\tfrac{\pi }{2}})^{x}$$A−\left ( \forall x p(x)\Rightarrow \forall x q(x) \right )\Rightarrow \left ( \exists x \neg p(x) \vee \forall x q(x) \right )$$\frac{1}{2\pi j}\oint_{C} f(z)dz$$\frac{\partial^2y(t) }{\partial t^2} + 2\frac{\partial y(t)}{\partial t} + y(t) = \delta (t) \text{ with } y(t)|_{t=0^{-}} = -2 \text{ and } \frac{\partial y}{\partial t}\mid _{t = 0^{-}} = 0$$\iint_{s} 5\vec{r}\cdot \hat{n}dS \text{ is}$

To write Augmented matrix:

${\left[\begin{array}{ccc|c}1 & 1 & 1 & 1 \\a & -a & 3 & 5 \\5 & -3 & a & 6 \\\end{array}\right]}$$\begin{vmatrix}1& 1& 1& :& 6\\1& 4& 6& :& 20\\1& 4& \lambda & :& \mu \\\end{vmatrix}$$=L^{−1}\left ( \begin{bmatrix}S& 0\\S& 0\end{bmatrix}−\begin{bmatrix}0& 1\\ −2& −3\end{bmatrix} \right )^{−1}$$L^{−1}\left ( \begin{bmatrix}\frac{s+3}{(s+1)(s+2)}& \frac{1}{(s+1)(s+2)}\\ \frac{−2}{(s+1)(s+2)}& \frac{s}{(s+1)(s+2)}\end{bmatrix} \right )$$=\left [ x^{4}+32x^{5} \right ]^{1}_{0}=33$$\iiint \bigtriangledown\cdot Pdv$

$A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0$

A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha

$A_{10} =0, A_{11} =1, A_{14} =0, A_{15 }=0\alpha$

$15\frac{1}{2}$${12}^C_{3} = 220$$\frac{2}{4}$$\begin{bmatrix}2 &4\\ 2 & 5\end{bmatrix}$

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_{}
$\frac{1}{2}$
$\frac{1}{\sqrt{3}}$
$\sqrt{3}$
$x^{\frac{1}{a}}$

$\frac{P × R × T}{100}$

$\mathbf{\frac{P × R × T}{100}}$

$P (1+ \mathbf{\frac{r}{100}})^{n}$

$P (1+ \frac{r}{100})^{n}$

$(\frac{A}{P})^{\frac{1}{t}}$

$\mathbf{ P (1+ \frac{{\frac{r}{2}}}{100})^{2n}}$

$(1+ \mathbf{\frac{\frac{3}{2}r}{100}})$

$\frac{r_{1}}{100}$

$\frac{P × (R)^2}{(100)^2} × \frac{(300 + R) }{100}$

$\frac{P × (R)^2}{(100)^2}$

==========linear equation ===========
$\frac{}{}$
$– \frac{b}{a}$
$p_{1}x +q_{1}y = r_{1}$
$\frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$
$\sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2}$
$\sqrt{2}$$\frac{(y_{1}- y_{2})}{(x_{1}- x_{2}}$$\frac{ m x_{2} + nx_{1}}{m + n}$$\frac{my_{2} + ny_{1} }{m + n}$$\frac{x_{1}+ x_{2} + x_{3}}{3}$$\frac{y_{1}+ y_{2} + y_{3}}{3}$$\frac{1}{2} × (x_{1}(y_{2}-y_{3}) + (x_{2}(y_{3}-y_{1}) ) + (x_{3}(y_{1}-y_{2}) )$