A solution for CSI500 project 3
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\textbf{\huge Project III: \LaTeX\ Component\footnote[1]{Created \today}}
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My name is Francis Opoku. This is my second \LaTeX\ document.
\begin{enumerate}
\item$\fbox{$\left(
\begin{array}{c|c}
\overbrace{\int_1^3 \frac{1}{t} \, dt}\rule[-.15in]{0in}{.15in} & |-4|\\
\hline
\rule[-.15in]{0in}{.40in}
\oint \mathbf{B}\cdot d\mathbf{a}
& \mathbf{A}
\end{array} \right)
\stackrel{?}{=}
\left(
\begin{array}{c|c}
\underbrace{\ln{3}}\rule[-.15in]{0in}{.5in} & 4 \\\hline
0 \rule[-.15in]{0in}{.40in}& \frac{1}{4\pi}\int
\frac{\mathbf{B}\times \dot{R}}{R^2}\,d\tau^\prime\\
\end{array}
\right)$ }$
\item By completing the square, solve the equation $2x^2+8x+1=0$.
\indent {\textbf {Solution:}}
\end{enumerate}
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\begin{eqnarray}
2x^2 + 8x + 1 &=& 0\\
2x^2 + 8x &=& -1\\
2(x^2 + 4x) &=& -1\\
2\left( x^2 +4x + (2)^2 \right) &=& -1 + 2(2)^2\\
(x + 2)^2 &=& \frac{7}{2}\\
x + 2 &=& \pm \sqrt{\frac{7}{2}}\nonumber\\
x + 2 &=& \nonumber\pm
\sqrt{\frac{7}{2}}\sqrt{\frac{2}{2}}=\pm\frac{\sqrt{14}}{2}\nonumber\\
x &=& -2 \pm\frac{\sqrt{14}}{2}.
\end{eqnarray}
\end{center}
\medskip
\begin{table*}[h]
\begin{tabular}[b]{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
\multicolumn{1}{|c|}{} & \multicolumn{11}{|l|}{Number of Times Out of fifty Repetitions} & \multicolumn{1}{|c|}{}
\\
\cline{2-11} Outcome & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & Total & Frac \\
\hline TT & 12 & 14 & 10 & 8 & 12 & 11 & 13 & 15 & 9 & 13 & 117 & .234 \\
\hline HT & 12 & 12 & 13 & 14 & 15 & 14 & 14 & 11 & 15 & 12 & 132 & .264 \\
\hline TH & 14 & 13 & 15 & 13 & 10 & 13 & 10 & 11 & 11 & 14 & 124 & .248 \\
\hline HH & 12 & 11 & 12 & 15 & 13 & 12 & 13 & 13 & 15 & 11 & 127 & .254 \\
\hline Total & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 500 & 1.000 \\
\hline \multicolumn{13}{|c|}{Frac (Fraction) is the ratio of the number of heads divided by 500} \\
\hline
\end{tabular}
\caption{Summary of Data for 50 Samples of Size 2}
\label{tab:summary}
\end{table*}
\bigskip
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