%% AMS-LaTeX Created with the Wolfram Language for Students - Personal Use Only : www.wolfram.com

\documentclass{article}
\usepackage{amsmath, amssymb, graphics, setspace}

\newcommand{\mathsym}[1]{{}}
\newcommand{\unicode}[1]{{}}

\newcounter{mathematicapage}
\begin{document}

\begin{doublespace}
\noindent\(\pmb{\text{data1}=\{\{1,4.79\},\{2,5.09\},\{78,29.79\},\{111,40.50\},\{112,40.82\}\}}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\{\{1,4.79\},\{2,5.09\},\{78,29.79\},\{111,40.5\},\{112,40.82\}\}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{line1}=\text{Fit}[\text{data1},\{1,x\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.69004\, +0.323914 x\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{quad1}=\text{Fit}[\text{data1},\{1,x,x{}^{\wedge}2\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.69669\, +0.322347 x+0.0000143086 x^2\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{polynomial1}=\text{Fit}[\text{data1},\{1,x,x{}^{\wedge}2,x{}^{\wedge}3\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.65523\, +0.351087 x-0.000597139 x^2+\text{3.2020092706825565$\grave{ }$*${}^{\wedge}$-6} x^3\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{Show}[\text{ListPlot}[\text{data},\text{PlotStyle}\to \text{Red}],\text{Plot}[\{\text{line}\},\{x,0,113\}]]}\)
\end{doublespace}

\includegraphics{Mathematica_Fits_gr1.eps}



\begin{doublespace}
\noindent\(\pmb{\text{data2}=\{\{1,5.03\},\{2,5.33\},\{78,29.93\},\{111,40.59\},\{112,40.90\}\}}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\{\{1,5.03\},\{2,5.33\},\{78,29.93\},\{111,40.59\},\{112,40.9\}\}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{line2}=\text{Fit}[\text{data2},\{1,x\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.69699\, +0.323339 x\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{quad2}=\text{Fit}[\text{data2},\{1,x,x{}^{\wedge}2\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.69411\, +0.324017 x-\text{6.194898309323661$\grave{ }$*${}^{\wedge}$-6} x^2\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{polynomial2}=\text{Fit}[\text{data2},\{1,x,x{}^{\wedge}2,x{}^{\wedge}3\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.73225\, +0.297577 x+0.000556333 x^2-\text{2.945830047483431$\grave{ }$*${}^{\wedge}$-6} x^3\)
\end{doublespace}



\begin{doublespace}
\noindent\(\pmb{\text{data3}=\{\{1,4.98\},\{2,5.27\},\{78,29.74\},\{111,40.36\},\{112,40.67\}\}}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\{\{1,4.98\},\{2,5.27\},\{78,29.74\},\{111,40.36\},\{112,40.67\}\}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{line3}=\text{Fit}[\text{data3},\{1,x\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.64285\, +0.321729 x\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{quad3}=\text{Fit}[\text{data3},\{1,x,x{}^{\wedge}2\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.64242\, +0.32183 x-\text{9.144762911982003$\grave{ }$*${}^{\wedge}$-7} x^2\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{polynomial3}=\text{Fit}[\text{data3},\{1,x,x{}^{\wedge}2,x{}^{\wedge}3\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.6901\, +0.288777 x+0.000702313 x^2-\text{3.682639279500495$\grave{ }$*${}^{\wedge}$-6} x^3\)
\end{doublespace}



\begin{doublespace}
\noindent\(\pmb{\text{data4}=\{\{1,5.22\},\{2,5.51\},\{78,29.88\},\{111,40.44\},\{112,40.75\}\}}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\{\{1,5.22\},\{2,5.51\},\{78,29.88\},\{111,40.44\},\{112,40.75\}\}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{line4}=\text{Fit}[\text{data4},\{1,x\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.88633\, +0.320291 x\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{quad4}=\text{Fit}[\text{data4},\{1,x,x{}^{\wedge}2\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.88387\, +0.320871 x-\text{5.3013135336868355$\grave{ }$*${}^{\wedge}$-6} x^2\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{polynomial4}=\text{Fit}[\text{data4},\{1,x,x{}^{\wedge}2,x{}^{\wedge}3\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.9292\, +0.289447 x+0.00066326 x^2-\text{3.5011013392316933$\grave{ }$*${}^{\wedge}$-6} x^3\)
\end{doublespace}



\begin{doublespace}
\noindent\(\pmb{\text{data5}=\{\{1,5.16\},\{2,5.45\},\{78,29.69\},\{111,40.21\},\{112,40.52\}\}}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\{\{1,5.16\},\{2,5.45\},\{78,29.69\},\{111,40.21\},\{112,40.52\}\}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{line5}=\text{Fit}[\text{data5},\{1,x\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.82727\, +0.318729 x\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{quad5}=\text{Fit}[\text{data5},\{1,x,x{}^{\wedge}2\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.82694\, +0.318808 x-\text{7.177794900717407$\grave{ }$*${}^{\wedge}$-7} x^2\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{polynomial5}=\text{Fit}[\text{data5},\{1,x,x{}^{\wedge}2,x{}^{\wedge}3\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(4.86904\, +0.289627 x+0.000620118 x^2-\text{3.2511751947096687$\grave{ }$*${}^{\wedge}$-6} x^3\)
\end{doublespace}



\begin{doublespace}
\noindent\(\pmb{\text{data6}=\{\{1,5.40\},\{2,5.69\},\{78,29.83\},\{111,40.29\},\{112,40.60\}\}}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\{\{1,5.4\},\{2,5.69\},\{78,29.83\},\{111,40.29\},\{112,40.6\}\}\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{line6}=\text{Fit}[\text{data6},\{1,x\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(5.07076\, +0.31729 x\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{quad6}=\text{Fit}[\text{data6},\{1,x,x{}^{\wedge}2\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(5.06839\, +0.317849 x-\text{5.104616732556557$\grave{ }$*${}^{\wedge}$-6} x^2\)
\end{doublespace}

\begin{doublespace}
\noindent\(\pmb{\text{polynomial6}=\text{Fit}[\text{data6},\{1,x,x{}^{\wedge}2,x{}^{\wedge}3\},x]}\)
\end{doublespace}

\begin{doublespace}
\noindent\(5.10813\, +0.290298 x+0.000581066 x^2-\text{3.0696372544396152$\grave{ }$*${}^{\wedge}$-6} x^3\)
\end{doublespace}

\end{document}
