\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Use 2 rectangles to approximate \(\displaystyle \int\limits_{5}^{12} \frac{1}{x}\, dx\) using the midpoint. Draw a graph showing the sum.
\(\displaystyle \Delta x = \frac{b-a}{n}=\frac{7}{2}\) and \(\displaystyle x_i = a+i\Delta x +\frac{\Delta x}{2} = \frac{7 i}{2} + \frac{27}{4}\). Drawing a graph gives:
\begin{tikzpicture}[yscale=5]
\draw[very thick, color=blue, opacity=0.3, xstep=1, ystep=1] (-1,-1) grid (13,1.05);
\draw[latex-latex, very thick] (-1.4,0)--(13.4,0) node[right]{$x$};
\draw[latex-latex, very thick] (0,-1.1)--(0,1.1) node[above]{$y$};
\foreach \x in { -1,1,...,13 }{
\pgfmathsetmacro{\xtick}{\x != 0 ? "\x" : ""}
\draw (\x, .2) -- (\x,-.2) node[below]{$\xtick$};
}
\foreach \y in { -1,-0.75,...,1.05 }{
\pgfmathsetmacro{\ytick}{\y != 0 ? "\y" : ""}
\draw (.2, \y) -- (-.2, \y) node[left]{$\ytick$};
}
\draw[thick, color=blue, domain={5.0}:{12.0}, samples=200, samples =350] plot(\x, {1/(\x)});
\draw[fill=blue, opacity=0.3](5.0000, 0) rectangle (8.5000, 0.14815);
\draw[thick](5.0000, 0) rectangle (8.5000, 0.14815);
\draw[fill=blue, opacity=0.3](8.5000, 0) rectangle (12.000, 0.097561);
\draw[thick](8.5000, 0) rectangle (12.000, 0.097561);
\end{tikzpicture}
\begin{question}Use 2 rectangles to approximate $\int\limits_{5}^{12} \frac{1}{x}\, dx$ using the midpoint. Draw a graph showing the sum.
\soln{9cm}{$\Delta x = \frac{b-a}{n}=\frac{7}{2}$ and $x_i = a+i\Delta x +\frac{\Delta x}{2} = \frac{7 i}{2} + \frac{27}{4}$. Drawing a graph gives:
\begin{center}\begin{tikzpicture}[yscale=5]
\draw[very thick, color=blue, opacity=0.3, xstep=1, ystep=1] (-1,-1) grid (13,1.05);
\draw[latex-latex, very thick] (-1.4,0)--(13.4,0) node[right]{$x$};
\draw[latex-latex, very thick] (0,-1.1)--(0,1.1) node[above]{$y$};
\foreach \x in { -1,1,...,13 }{
\pgfmathsetmacro{\xtick}{\x != 0 ? "\x" : ""}
\draw (\x, .2) -- (\x,-.2) node[below]{$\xtick$};
}
\foreach \y in { -1,-0.75,...,1.05 }{
\pgfmathsetmacro{\ytick}{\y != 0 ? "\y" : ""}
\draw (.2, \y) -- (-.2, \y) node[left]{$\ytick$};
}
\draw[thick, color=blue, domain={5.0}:{12.0}, samples=200, samples =350] plot(\x, {1/(\x)});
\draw[fill=blue, opacity=0.3](5.0000, 0) rectangle (8.5000, 0.14815);
\draw[thick](5.0000, 0) rectangle (8.5000, 0.14815);
\draw[fill=blue, opacity=0.3](8.5000, 0) rectangle (12.000, 0.097561);
\draw[thick](8.5000, 0) rectangle (12.000, 0.097561);
\end{tikzpicture}
\end{center}
The sum is $\sum_{i=0}^{1} \frac{7}{2 \left(\frac{7 i}{2} + \frac{27}{4}\right)} = 0.85998$. }
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Use 2 rectangles to approximate <img class="equation_image" title=" \displaystyle \int\limits_{5}^{12} \frac{1}{x}\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B5%7D%5E%7B12%7D%20%5Cfrac%7B1%7D%7Bx%7D%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{5}^{12} \frac{1}{x}\, dx " data-equation-content=" \displaystyle \int\limits_{5}^{12} \frac{1}{x}\, dx " /> using the midpoint. Draw a graph showing the sum. </p> </p><p> <p> <img class="equation_image" title=" \displaystyle \Delta x = \frac{b-a}{n}=\frac{7}{2} " src="/equation_images/%20%5Cdisplaystyle%20%5CDelta%20x%20%3D%20%5Cfrac%7Bb-a%7D%7Bn%7D%3D%5Cfrac%7B7%7D%7B2%7D%20" alt="LaTeX: \displaystyle \Delta x = \frac{b-a}{n}=\frac{7}{2} " data-equation-content=" \displaystyle \Delta x = \frac{b-a}{n}=\frac{7}{2} " /> and <img class="equation_image" title=" \displaystyle x_i = a+i\Delta x +\frac{\Delta x}{2} = \frac{7 i}{2} + \frac{27}{4} " src="/equation_images/%20%5Cdisplaystyle%20x_i%20%3D%20a%2Bi%5CDelta%20x%20%2B%5Cfrac%7B%5CDelta%20x%7D%7B2%7D%20%3D%20%5Cfrac%7B7%20i%7D%7B2%7D%20%2B%20%5Cfrac%7B27%7D%7B4%7D%20" alt="LaTeX: \displaystyle x_i = a+i\Delta x +\frac{\Delta x}{2} = \frac{7 i}{2} + \frac{27}{4} " data-equation-content=" \displaystyle x_i = a+i\Delta x +\frac{\Delta x}{2} = \frac{7 i}{2} + \frac{27}{4} " /> . Drawing a graph gives:
<center><?xml version="1.0" encoding="UTF-8"?>
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="433.057pt" height="325.876pt" viewBox="0 0 433.057 325.876" version="1.1">
<defs>
<g>
<symbol overflow="visible" id="glyph0-0">
<path style="stroke:none;" d=""/>
</symbol>
<symbol overflow="visible" id="glyph0-1">
<path style="stroke:none;" d="M 3.328125 -3.015625 C 3.390625 -3.265625 3.625 -4.1875 4.3125 -4.1875 C 4.359375 -4.1875 4.609375 -4.1875 4.8125 -4.0625 C 4.53125 -4 4.34375 -3.765625 4.34375 -3.515625 C 4.34375 -3.359375 4.453125 -3.171875 4.71875 -3.171875 C 4.9375 -3.171875 5.25 -3.34375 5.25 -3.75 C 5.25 -4.265625 4.671875 -4.40625 4.328125 -4.40625 C 3.75 -4.40625 3.40625 -3.875 3.28125 -3.65625 C 3.03125 -4.3125 2.5 -4.40625 2.203125 -4.40625 C 1.171875 -4.40625 0.59375 -3.125 0.59375 -2.875 C 0.59375 -2.765625 0.703125 -2.765625 0.71875 -2.765625 C 0.796875 -2.765625 0.828125 -2.796875 0.84375 -2.875 C 1.1875 -3.9375 1.84375 -4.1875 2.1875 -4.1875 C 2.375 -4.1875 2.71875 -4.09375 2.71875 -3.515625 C 2.71875 -3.203125 2.546875 -2.546875 2.1875 -1.140625 C 2.03125 -0.53125 1.671875 -0.109375 1.234375 -0.109375 C 1.171875 -0.109375 0.953125 -0.109375 0.734375 -0.234375 C 0.984375 -0.296875 1.203125 -0.5 1.203125 -0.78125 C 1.203125 -1.046875 0.984375 -1.125 0.84375 -1.125 C 0.53125 -1.125 0.296875 -0.875 0.296875 -0.546875 C 0.296875 -0.09375 0.78125 0.109375 1.21875 0.109375 C 1.890625 0.109375 2.25 -0.59375 2.265625 -0.640625 C 2.390625 -0.28125 2.75 0.109375 3.34375 0.109375 C 4.375 0.109375 4.9375 -1.171875 4.9375 -1.421875 C 4.9375 -1.53125 4.859375 -1.53125 4.828125 -1.53125 C 4.734375 -1.53125 4.71875 -1.484375 4.6875 -1.421875 C 4.359375 -0.34375 3.6875 -0.109375 3.375 -0.109375 C 2.984375 -0.109375 2.828125 -0.421875 2.828125 -0.765625 C 2.828125 -0.984375 2.875 -1.203125 2.984375 -1.640625 Z M 3.328125 -3.015625 "/>
</symbol>
<symbol overflow="visible" id="glyph0-2">
<path style="stroke:none;" d="M 4.84375 -3.796875 C 4.890625 -3.9375 4.890625 -3.953125 4.890625 -4.03125 C 4.890625 -4.203125 4.75 -4.296875 4.59375 -4.296875 C 4.5 -4.296875 4.34375 -4.234375 4.25 -4.09375 C 4.234375 -4.03125 4.140625 -3.734375 4.109375 -3.546875 C 4.03125 -3.296875 3.96875 -3.015625 3.90625 -2.75 L 3.453125 -0.953125 C 3.421875 -0.8125 2.984375 -0.109375 2.328125 -0.109375 C 1.828125 -0.109375 1.71875 -0.546875 1.71875 -0.921875 C 1.71875 -1.375 1.890625 -2 2.21875 -2.875 C 2.375 -3.28125 2.421875 -3.390625 2.421875 -3.59375 C 2.421875 -4.03125 2.109375 -4.40625 1.609375 -4.40625 C 0.65625 -4.40625 0.296875 -2.953125 0.296875 -2.875 C 0.296875 -2.765625 0.390625 -2.765625 0.40625 -2.765625 C 0.515625 -2.765625 0.515625 -2.796875 0.5625 -2.953125 C 0.84375 -3.890625 1.234375 -4.1875 1.578125 -4.1875 C 1.65625 -4.1875 1.828125 -4.1875 1.828125 -3.875 C 1.828125 -3.625 1.71875 -3.359375 1.65625 -3.171875 C 1.25 -2.109375 1.078125 -1.546875 1.078125 -1.078125 C 1.078125 -0.1875 1.703125 0.109375 2.296875 0.109375 C 2.6875 0.109375 3.015625 -0.0625 3.296875 -0.34375 C 3.171875 0.171875 3.046875 0.671875 2.65625 1.203125 C 2.390625 1.53125 2.015625 1.828125 1.5625 1.828125 C 1.421875 1.828125 0.96875 1.796875 0.796875 1.40625 C 0.953125 1.40625 1.09375 1.40625 1.21875 1.28125 C 1.328125 1.203125 1.421875 1.0625 1.421875 0.875 C 1.421875 0.5625 1.15625 0.53125 1.0625 0.53125 C 0.828125 0.53125 0.5 0.6875 0.5 1.171875 C 0.5 1.671875 0.9375 2.046875 1.5625 2.046875 C 2.578125 2.046875 3.609375 1.140625 3.890625 0.015625 Z M 4.84375 -3.796875 "/>
</symbol>
<symbol overflow="visible" id="glyph0-3">
<path style="stroke:none;" d="M 1.90625 -0.53125 C 1.90625 -0.8125 1.671875 -1.0625 1.390625 -1.0625 C 1.09375 -1.0625 0.859375 -0.8125 0.859375 -0.53125 C 0.859375 -0.234375 1.09375 0 1.390625 0 C 1.671875 0 1.90625 -0.234375 1.90625 -0.53125 Z M 1.90625 -0.53125 "/>
</symbol>
<symbol overflow="visible" id="glyph1-0">
<path style="stroke:none;" d=""/>
</symbol>
<symbol overflow="visible" id="glyph1-1">
<path style="stroke:none;" d="M 6.5625 -2.296875 C 6.734375 -2.296875 6.921875 -2.296875 6.921875 -2.5 C 6.921875 -2.6875 6.734375 -2.6875 6.5625 -2.6875 L 1.171875 -2.6875 C 1 -2.6875 0.828125 -2.6875 0.828125 -2.5 C 0.828125 -2.296875 1 -2.296875 1.171875 -2.296875 Z M 6.5625 -2.296875 "/>
</symbol>
<symbol overflow="visible" id="glyph2-0">
<path style="stroke:none;" d=""/>
</symbol>
<symbol overflow="visible" id="glyph2-1">
<path style="stroke:none;" d="M 2.9375 -6.375 C 2.9375 -6.625 2.9375 -6.640625 2.703125 -6.640625 C 2.078125 -6 1.203125 -6 0.890625 -6 L 0.890625 -5.6875 C 1.09375 -5.6875 1.671875 -5.6875 2.1875 -5.953125 L 2.1875 -0.78125 C 2.1875 -0.421875 2.15625 -0.3125 1.265625 -0.3125 L 0.953125 -0.3125 L 0.953125 0 C 1.296875 -0.03125 2.15625 -0.03125 2.5625 -0.03125 C 2.953125 -0.03125 3.828125 -0.03125 4.171875 0 L 4.171875 -0.3125 L 3.859375 -0.3125 C 2.953125 -0.3125 2.9375 -0.421875 2.9375 -0.78125 Z M 2.9375 -6.375 "/>
</symbol>
<symbol overflow="visible" id="glyph2-2">
<path style="stroke:none;" d="M 2.890625 -3.515625 C 3.703125 -3.78125 4.28125 -4.46875 4.28125 -5.265625 C 4.28125 -6.078125 3.40625 -6.640625 2.453125 -6.640625 C 1.453125 -6.640625 0.6875 -6.046875 0.6875 -5.28125 C 0.6875 -4.953125 0.90625 -4.765625 1.203125 -4.765625 C 1.5 -4.765625 1.703125 -4.984375 1.703125 -5.28125 C 1.703125 -5.765625 1.234375 -5.765625 1.09375 -5.765625 C 1.390625 -6.265625 2.046875 -6.390625 2.40625 -6.390625 C 2.828125 -6.390625 3.375 -6.171875 3.375 -5.28125 C 3.375 -5.15625 3.34375 -4.578125 3.09375 -4.140625 C 2.796875 -3.65625 2.453125 -3.625 2.203125 -3.625 C 2.125 -3.609375 1.890625 -3.59375 1.8125 -3.59375 C 1.734375 -3.578125 1.671875 -3.5625 1.671875 -3.46875 C 1.671875 -3.359375 1.734375 -3.359375 1.90625 -3.359375 L 2.34375 -3.359375 C 3.15625 -3.359375 3.53125 -2.6875 3.53125 -1.703125 C 3.53125 -0.34375 2.84375 -0.0625 2.40625 -0.0625 C 1.96875 -0.0625 1.21875 -0.234375 0.875 -0.8125 C 1.21875 -0.765625 1.53125 -0.984375 1.53125 -1.359375 C 1.53125 -1.71875 1.265625 -1.921875 0.984375 -1.921875 C 0.734375 -1.921875 0.421875 -1.78125 0.421875 -1.34375 C 0.421875 -0.4375 1.34375 0.21875 2.4375 0.21875 C 3.65625 0.21875 4.5625 -0.6875 4.5625 -1.703125 C 4.5625 -2.515625 3.921875 -3.296875 2.890625 -3.515625 Z M 2.890625 -3.515625 "/>
</symbol>
<symbol overflow="visible" id="glyph2-3">
<path style="stroke:none;" d="M 4.46875 -2 C 4.46875 -3.1875 3.65625 -4.1875 2.578125 -4.1875 C 2.109375 -4.1875 1.671875 -4.03125 1.3125 -3.671875 L 1.3125 -5.625 C 1.515625 -5.5625 1.84375 -5.5 2.15625 -5.5 C 3.390625 -5.5 4.09375 -6.40625 4.09375 -6.53125 C 4.09375 -6.59375 4.0625 -6.640625 3.984375 -6.640625 C 3.984375 -6.640625 3.953125 -6.640625 3.90625 -6.609375 C 3.703125 -6.515625 3.21875 -6.3125 2.546875 -6.3125 C 2.15625 -6.3125 1.6875 -6.390625 1.21875 -6.59375 C 1.140625 -6.625 1.125 -6.625 1.109375 -6.625 C 1 -6.625 1 -6.546875 1 -6.390625 L 1 -3.4375 C 1 -3.265625 1 -3.1875 1.140625 -3.1875 C 1.21875 -3.1875 1.234375 -3.203125 1.28125 -3.265625 C 1.390625 -3.421875 1.75 -3.96875 2.5625 -3.96875 C 3.078125 -3.96875 3.328125 -3.515625 3.40625 -3.328125 C 3.5625 -2.953125 3.59375 -2.578125 3.59375 -2.078125 C 3.59375 -1.71875 3.59375 -1.125 3.34375 -0.703125 C 3.109375 -0.3125 2.734375 -0.0625 2.28125 -0.0625 C 1.5625 -0.0625 0.984375 -0.59375 0.8125 -1.171875 C 0.84375 -1.171875 0.875 -1.15625 0.984375 -1.15625 C 1.3125 -1.15625 1.484375 -1.40625 1.484375 -1.640625 C 1.484375 -1.890625 1.3125 -2.140625 0.984375 -2.140625 C 0.84375 -2.140625 0.5 -2.0625 0.5 -1.609375 C 0.5 -0.75 1.1875 0.21875 2.296875 0.21875 C 3.453125 0.21875 4.46875 -0.734375 4.46875 -2 Z M 4.46875 -2 "/>
</symbol>
<symbol overflow="visible" id="glyph2-4">
<path style="stroke:none;" d="M 4.75 -6.078125 C 4.828125 -6.1875 4.828125 -6.203125 4.828125 -6.421875 L 2.40625 -6.421875 C 1.203125 -6.421875 1.171875 -6.546875 1.140625 -6.734375 L 0.890625 -6.734375 L 0.5625 -4.6875 L 0.8125 -4.6875 C 0.84375 -4.84375 0.921875 -5.46875 1.0625 -5.59375 C 1.125 -5.65625 1.90625 -5.65625 2.03125 -5.65625 L 4.09375 -5.65625 C 3.984375 -5.5 3.203125 -4.40625 2.984375 -4.078125 C 2.078125 -2.734375 1.75 -1.34375 1.75 -0.328125 C 1.75 -0.234375 1.75 0.21875 2.21875 0.21875 C 2.671875 0.21875 2.671875 -0.234375 2.671875 -0.328125 L 2.671875 -0.84375 C 2.671875 -1.390625 2.703125 -1.9375 2.78125 -2.46875 C 2.828125 -2.703125 2.953125 -3.5625 3.40625 -4.171875 Z M 4.75 -6.078125 "/>
</symbol>
<symbol overflow="visible" id="glyph2-5">
<path style="stroke:none;" d="M 3.65625 -3.171875 L 3.65625 -2.84375 C 3.65625 -0.515625 2.625 -0.0625 2.046875 -0.0625 C 1.875 -0.0625 1.328125 -0.078125 1.0625 -0.421875 C 1.5 -0.421875 1.578125 -0.703125 1.578125 -0.875 C 1.578125 -1.1875 1.34375 -1.328125 1.125 -1.328125 C 0.96875 -1.328125 0.671875 -1.25 0.671875 -0.859375 C 0.671875 -0.1875 1.203125 0.21875 2.046875 0.21875 C 3.34375 0.21875 4.5625 -1.140625 4.5625 -3.28125 C 4.5625 -5.96875 3.40625 -6.640625 2.515625 -6.640625 C 1.96875 -6.640625 1.484375 -6.453125 1.0625 -6.015625 C 0.640625 -5.5625 0.421875 -5.140625 0.421875 -4.390625 C 0.421875 -3.15625 1.296875 -2.171875 2.40625 -2.171875 C 3.015625 -2.171875 3.421875 -2.59375 3.65625 -3.171875 Z M 2.421875 -2.40625 C 2.265625 -2.40625 1.796875 -2.40625 1.5 -3.03125 C 1.3125 -3.40625 1.3125 -3.890625 1.3125 -4.390625 C 1.3125 -4.921875 1.3125 -5.390625 1.53125 -5.765625 C 1.796875 -6.265625 2.171875 -6.390625 2.515625 -6.390625 C 2.984375 -6.390625 3.3125 -6.046875 3.484375 -5.609375 C 3.59375 -5.28125 3.640625 -4.65625 3.640625 -4.203125 C 3.640625 -3.375 3.296875 -2.40625 2.421875 -2.40625 Z M 2.421875 -2.40625 "/>
</symbol>
<symbol overflow="visible" id="glyph2-6">
<path style="stroke:none;" d="M 4.578125 -3.1875 C 4.578125 -3.984375 4.53125 -4.78125 4.1875 -5.515625 C 3.734375 -6.484375 2.90625 -6.640625 2.5 -6.640625 C 1.890625 -6.640625 1.171875 -6.375 0.75 -5.453125 C 0.4375 -4.765625 0.390625 -3.984375 0.390625 -3.1875 C 0.390625 -2.4375 0.421875 -1.546875 0.84375 -0.78125 C 1.265625 0.015625 2 0.21875 2.484375 0.21875 C 3.015625 0.21875 3.78125 0.015625 4.21875 -0.9375 C 4.53125 -1.625 4.578125 -2.40625 4.578125 -3.1875 Z M 2.484375 0 C 2.09375 0 1.5 -0.25 1.328125 -1.203125 C 1.21875 -1.796875 1.21875 -2.71875 1.21875 -3.3125 C 1.21875 -3.953125 1.21875 -4.609375 1.296875 -5.140625 C 1.484375 -6.328125 2.234375 -6.421875 2.484375 -6.421875 C 2.8125 -6.421875 3.46875 -6.234375 3.65625 -5.25 C 3.765625 -4.6875 3.765625 -3.9375 3.765625 -3.3125 C 3.765625 -2.5625 3.765625 -1.890625 3.65625 -1.25 C 3.5 -0.296875 2.9375 0 2.484375 0 Z M 2.484375 0 "/>
</symbol>
<symbol overflow="visible" id="glyph2-7">
<path style="stroke:none;" d="M 1.265625 -0.765625 L 2.328125 -1.796875 C 3.875 -3.171875 4.46875 -3.703125 4.46875 -4.703125 C 4.46875 -5.84375 3.578125 -6.640625 2.359375 -6.640625 C 1.234375 -6.640625 0.5 -5.71875 0.5 -4.828125 C 0.5 -4.28125 1 -4.28125 1.03125 -4.28125 C 1.203125 -4.28125 1.546875 -4.390625 1.546875 -4.8125 C 1.546875 -5.0625 1.359375 -5.328125 1.015625 -5.328125 C 0.9375 -5.328125 0.921875 -5.328125 0.890625 -5.3125 C 1.109375 -5.96875 1.65625 -6.328125 2.234375 -6.328125 C 3.140625 -6.328125 3.5625 -5.515625 3.5625 -4.703125 C 3.5625 -3.90625 3.078125 -3.125 2.515625 -2.5 L 0.609375 -0.375 C 0.5 -0.265625 0.5 -0.234375 0.5 0 L 4.203125 0 L 4.46875 -1.734375 L 4.234375 -1.734375 C 4.171875 -1.4375 4.109375 -1 4 -0.84375 C 3.9375 -0.765625 3.28125 -0.765625 3.0625 -0.765625 Z M 1.265625 -0.765625 "/>
</symbol>
</g>
<clipPath id="clip1">
<path d="M 37 318 L 43 318 L 43 325.875 L 37 325.875 Z M 37 318 "/>
</clipPath>
</defs>
<g id="surface1">
<path style="fill:none;stroke-width:1.19553;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,100%);stroke-opacity:0.3;stroke-miterlimit:10;" d="M -28.3455 -141.733469 L 368.509969 -141.733469 M -28.3455 0.00090625 L 368.509969 0.00090625 M -28.3455 141.735281 L 368.509969 141.735281 M -28.3455 -141.733469 L -28.3455 148.821219 M -0.00175 -141.733469 L -0.00175 148.821219 M 28.345906 -141.733469 L 28.345906 148.821219 M 56.693562 -141.733469 L 56.693562 148.821219 M 85.041219 -141.733469 L 85.041219 148.821219 M 113.388875 -141.733469 L 113.388875 148.821219 M 141.732625 -141.733469 L 141.732625 148.821219 M 170.080281 -141.733469 L 170.080281 148.821219 M 198.427937 -141.733469 L 198.427937 148.821219 M 226.775594 -141.733469 L 226.775594 148.821219 M 255.119344 -141.733469 L 255.119344 148.821219 M 283.467 -141.733469 L 283.467 148.821219 M 311.814656 -141.733469 L 311.814656 148.821219 M 340.162312 -141.733469 L 340.162312 148.821219 M 368.49825 -141.733469 L 368.49825 148.821219 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<path style="fill:none;stroke-width:1.19553;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -33.947063 0.00090625 L 374.107625 0.00090625 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;" d="M 0.597656 169.371094 C 2.296875 169.691406 5.0625 170.648438 6.972656 171.761719 L 6.972656 166.980469 C 5.0625 168.097656 2.296875 169.054688 0.597656 169.371094 "/>
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;" d="M 420.128906 169.371094 C 418.429688 169.054688 415.667969 168.097656 413.753906 166.980469 L 413.753906 171.761719 C 415.667969 170.648438 418.429688 169.691406 420.128906 169.371094 "/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-1" x="424.043" y="171.517"/>
</g>
<path style="fill:none;stroke-width:1.19553;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -0.00175 -150.170969 L -0.00175 150.168875 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g clip-path="url(#clip1)" clip-rule="nonzero">
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;" d="M 40.28125 325.28125 C 40.601562 323.578125 41.558594 320.816406 42.675781 318.902344 L 37.890625 318.902344 C 39.007812 320.816406 39.964844 323.578125 40.28125 325.28125 "/>
</g>
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;" d="M 40.28125 13.464844 C 39.964844 15.164062 39.007812 17.925781 37.890625 19.839844 L 42.675781 19.839844 C 41.558594 17.925781 40.601562 15.164062 40.28125 13.464844 "/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-2" x="37.662" y="7.61"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -28.3455 28.344656 L -28.3455 -28.34675 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph1-1" x="5.571" y="207.658"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="13.32" y="207.658"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 28.345906 28.344656 L 28.345906 -28.34675 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="66.138" y="207.658"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 85.041219 28.344656 L 85.041219 -28.34675 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-2" x="122.831" y="207.658"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 141.732625 28.344656 L 141.732625 -28.34675 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-3" x="179.524" y="207.658"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 198.427937 28.344656 L 198.427937 -28.34675 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-4" x="236.217" y="207.658"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 255.119344 28.344656 L 255.119344 -28.34675 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-5" x="292.91" y="207.658"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 311.814656 28.344656 L 311.814656 -28.34675 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="347.112" y="207.658"/>
<use xlink:href="#glyph2-1" x="352.0933" y="207.658"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 368.509969 28.344656 L 368.509969 -28.34675 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="403.805" y="207.658"/>
<use xlink:href="#glyph2-2" x="408.7863" y="207.658"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 -141.733469 L -5.669719 -141.733469 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph1-1" x="18.364" y="313.899"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="26.112" y="313.899"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 -106.299875 L -5.669719 -106.299875 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph1-1" x="5.633" y="278.466"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-6" x="13.382" y="278.466"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-3" x="18.364" y="278.466"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-4" x="21.131" y="278.466"/>
<use xlink:href="#glyph2-3" x="26.1123" y="278.466"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 -70.866281 L -5.669719 -70.866281 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph1-1" x="10.615" y="243.033"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-6" x="18.364" y="243.033"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-3" x="23.345" y="243.033"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-3" x="26.112" y="243.033"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 -35.432688 L -5.669719 -35.432688 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph1-1" x="5.633" y="207.6"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-6" x="13.382" y="207.6"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-3" x="18.364" y="207.6"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-7" x="21.131" y="207.6"/>
<use xlink:href="#glyph2-3" x="26.1123" y="207.6"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 0.00090625 L -5.669719 0.00090625 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 35.4345 L -5.669719 35.4345 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-6" x="13.382" y="137.149"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-3" x="18.364" y="137.149"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-7" x="21.131" y="137.149"/>
<use xlink:href="#glyph2-3" x="26.1123" y="137.149"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 70.868094 L -5.669719 70.868094 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-6" x="18.364" y="101.716"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-3" x="23.345" y="101.716"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-3" x="26.112" y="101.716"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 106.301687 L -5.669719 106.301687 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-6" x="13.382" y="66.283"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-3" x="18.364" y="66.283"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-4" x="21.131" y="66.283"/>
<use xlink:href="#glyph2-3" x="26.1123" y="66.283"/>
</g>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 5.670125 141.735281 L -5.669719 141.735281 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="26.112" y="30.85"/>
</g>
<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,100%);stroke-opacity:1;stroke-miterlimit:10;" d="M 141.732625 28.344656 L 142.302937 28.235281 L 142.869344 28.122 L 143.439656 28.008719 L 144.006062 27.899344 L 144.576375 27.789969 L 145.142781 27.680594 L 145.713094 27.571219 L 146.2795 27.46575 L 146.849812 27.360281 L 147.416219 27.254812 L 147.986531 27.15325 L 148.552937 27.047781 L 149.12325 26.942312 L 149.689656 26.84075 L 150.259969 26.739187 L 150.826375 26.637625 L 151.396687 26.539969 L 151.963094 26.442312 L 152.533406 26.344656 L 153.099812 26.243094 L 153.670125 26.141531 L 154.236531 26.043875 L 154.806844 25.954031 L 155.37325 25.856375 L 155.943562 25.762625 L 156.509969 25.672781 L 157.080281 25.575125 L 157.646687 25.477469 L 158.217 25.391531 L 158.783406 25.301687 L 159.353719 25.211844 L 159.920125 25.122 L 160.490437 25.036062 L 161.056844 24.946219 L 161.627156 24.856375 L 162.193562 24.770437 L 162.763875 24.6845 L 163.330281 24.594656 L 163.900594 24.512625 L 164.467 24.430594 L 165.037312 24.344656 L 165.603719 24.258719 L 166.174031 24.176687 L 166.740437 24.094656 L 167.31075 24.012625 L 167.877156 23.930594 L 168.447469 23.852469 L 169.013875 23.766531 L 169.584187 23.688406 L 170.150594 23.614187 L 170.720906 23.532156 L 171.287312 23.454031 L 171.857625 23.379812 L 172.424031 23.301687 L 172.994344 23.223562 L 173.56075 23.145437 L 174.131062 23.075125 L 174.697469 22.997 L 175.267781 22.918875 L 175.834187 22.848562 L 176.4045 22.774344 L 176.970906 22.704031 L 177.541219 22.629812 L 178.107625 22.555594 L 178.677937 22.485281 L 179.244344 22.414969 L 179.814656 22.34075 L 180.381062 22.274344 L 180.951375 22.204031 L 181.517781 22.129812 L 182.088094 22.067312 L 182.6545 21.997 L 183.224812 21.926687 L 183.791219 21.860281 L 184.361531 21.793875 L 184.927937 21.727469 L 185.49825 21.657156 L 186.064656 21.59075 L 186.634969 21.52825 L 187.201375 21.461844 L 187.771687 21.399344 L 188.338094 21.329031 L 188.908406 21.266531 L 189.474812 21.204031 L 190.045125 21.141531 L 190.611531 21.079031 L 191.181844 21.016531 L 191.74825 20.954031 L 192.318562 20.891531 L 192.884969 20.829031 L 193.455281 20.766531 L 194.021687 20.704031 L 194.592 20.645437 L 195.158406 20.582937 L 195.728719 20.524344 L 196.295125 20.46575 L 196.865437 20.411062 L 197.431844 20.344656 L 198.002156 20.289969 L 198.568562 20.231375 L 199.138875 20.172781 L 199.705281 20.118094 L 200.275594 20.0595 L 200.842 20.004812 L 201.412312 19.946219 L 201.978719 19.891531 L 202.549031 19.832937 L 203.115437 19.77825 L 203.68575 19.723562 L 204.252156 19.668875 L 204.822469 19.618094 L 205.388875 19.563406 L 205.959187 19.504812 L 206.525594 19.454031 L 207.095906 19.399344 L 207.662312 19.348562 L 208.232625 19.293875 L 208.799031 19.243094 L 209.369344 19.188406 L 209.93575 19.137625 L 210.506062 19.082937 L 211.072469 19.032156 L 211.642781 18.981375 L 212.209187 18.930594 L 212.7795 18.883719 L 213.345906 18.832937 L 213.916219 18.782156 L 214.482625 18.731375 L 215.052937 18.680594 L 215.619344 18.629812 L 216.189656 18.582937 L 216.756062 18.536062 L 217.326375 18.489187 L 217.892781 18.438406 L 218.463094 18.391531 L 219.0295 18.344656 L 219.599812 18.293875 L 220.166219 18.247 L 220.736531 18.200125 L 221.302937 18.15325 L 221.87325 18.106375 L 222.439656 18.063406 L 223.009969 18.016531 L 223.576375 17.969656 L 224.146687 17.922781 L 224.713094 17.879812 L 225.283406 17.832937 L 225.849812 17.789969 L 226.420125 17.743094 L 226.986531 17.700125 L 227.556844 17.657156 L 228.12325 17.614187 L 228.693562 17.567312 L 229.259969 17.524344 L 229.830281 17.481375 L 230.396687 17.438406 L 230.967 17.395437 L 231.533406 17.352469 L 232.103719 17.3095 L 232.670125 17.266531 L 233.240437 17.227469 L 233.806844 17.1845 L 234.377156 17.145437 L 234.943562 17.102469 L 235.513875 17.0595 L 236.080281 17.016531 L 236.650594 16.973562 L 237.217 16.938406 L 237.787312 16.895437 L 238.353719 16.856375 L 238.924031 16.813406 L 239.490437 16.774344 L 240.06075 16.735281 L 240.627156 16.696219 L 241.197469 16.65325 L 241.763875 16.614187 L 242.334187 16.579031 L 242.900594 16.539969 L 243.470906 16.500906 L 244.037312 16.461844 L 244.607625 16.422781 L 245.174031 16.387625 L 245.744344 16.348562 L 246.31075 16.3095 L 246.881062 16.270437 L 247.447469 16.235281 L 248.017781 16.200125 L 248.584187 16.161062 L 249.1545 16.122 L 249.720906 16.086844 L 250.291219 16.051687 L 250.857625 16.016531 L 251.427937 15.981375 L 251.994344 15.942312 L 252.564656 15.907156 L 253.131062 15.868094 L 253.701375 15.836844 L 254.267781 15.801687 L 254.838094 15.766531 L 255.4045 15.727469 L 255.974812 15.696219 L 256.541219 15.661062 L 257.111531 15.625906 L 257.677937 15.59075 L 258.24825 15.555594 L 258.814656 15.524344 L 259.384969 15.489187 L 259.951375 15.454031 L 260.521687 15.422781 L 261.088094 15.387625 L 261.658406 15.356375 L 262.224812 15.321219 L 262.795125 15.286062 L 263.361531 15.254812 L 263.931844 15.223562 L 264.49825 15.192312 L 265.068562 15.157156 L 265.634969 15.125906 L 266.205281 15.094656 L 266.771687 15.0595 L 267.342 15.02825 L 267.908406 14.997 L 268.478719 14.961844 L 269.045125 14.9345 L 269.615437 14.899344 L 270.181844 14.868094 L 270.752156 14.836844 L 271.318562 14.8095 L 271.888875 14.774344 L 272.455281 14.747 L 273.025594 14.71575 L 273.592 14.6845 L 274.162312 14.657156 L 274.728719 14.625906 L 275.299031 14.594656 L 275.865437 14.563406 L 276.43575 14.532156 L 277.002156 14.504812 L 277.572469 14.473562 L 278.138875 14.446219 L 278.709187 14.414969 L 279.275594 14.387625 L 279.845906 14.356375 L 280.412312 14.329031 L 280.982625 14.297781 L 281.549031 14.270437 L 282.119344 14.243094 L 282.68575 14.211844 L 283.256062 14.1845 L 283.822469 14.15325 L 284.392781 14.125906 L 284.959187 14.098562 L 285.5295 14.071219 L 286.095906 14.043875 L 286.666219 14.012625 L 287.232625 13.985281 L 287.802937 13.957937 L 288.369344 13.930594 L 288.939656 13.90325 L 289.506062 13.879812 L 290.076375 13.848562 L 290.642781 13.825125 L 291.213094 13.793875 L 291.7795 13.766531 L 292.349812 13.743094 L 292.916219 13.71575 L 293.486531 13.688406 L 294.052937 13.664969 L 294.62325 13.637625 L 295.189656 13.610281 L 295.759969 13.582937 L 296.326375 13.5595 L 296.896687 13.532156 L 297.463094 13.504812 L 298.033406 13.481375 L 298.599812 13.457937 L 299.170125 13.426687 L 299.736531 13.40325 L 300.306844 13.379812 L 300.87325 13.352469 L 301.443562 13.325125 L 302.009969 13.301687 L 302.580281 13.27825 L 303.146687 13.254812 L 303.717 13.227469 L 304.283406 13.204031 L 304.853719 13.176687 L 305.420125 13.15325 L 305.990437 13.129812 L 306.556844 13.106375 L 307.127156 13.082937 L 307.693562 13.055594 L 308.263875 13.032156 L 308.830281 13.012625 L 309.400594 12.985281 L 309.967 12.961844 L 310.537312 12.938406 L 311.103719 12.914969 L 311.674031 12.891531 L 312.240437 12.864187 L 312.81075 12.844656 L 313.377156 12.821219 L 313.947469 12.797781 L 314.513875 12.774344 L 315.084187 12.750906 L 315.650594 12.731375 L 316.220906 12.704031 L 316.787312 12.6845 L 317.357625 12.661062 L 317.924031 12.637625 L 318.494344 12.614187 L 319.06075 12.59075 L 319.631062 12.571219 L 320.197469 12.547781 L 320.767781 12.524344 L 321.334187 12.500906 L 321.900594 12.481375 L 322.470906 12.457937 L 323.037312 12.438406 L 323.607625 12.414969 L 324.174031 12.391531 L 324.744344 12.372 L 325.31075 12.352469 L 325.881062 12.332937 L 326.447469 12.3095 L 327.017781 12.286062 L 327.584187 12.262625 L 328.1545 12.239187 L 328.720906 12.219656 L 329.291219 12.200125 L 329.857625 12.180594 L 330.427937 12.157156 L 330.994344 12.137625 L 331.564656 12.114187 L 332.131062 12.094656 L 332.701375 12.075125 L 333.267781 12.055594 L 333.838094 12.036062 L 334.4045 12.012625 L 334.974812 11.993094 L 335.541219 11.973562 L 336.111531 11.954031 L 336.677937 11.930594 L 337.24825 11.911062 L 337.814656 11.891531 L 338.384969 11.872 L 338.951375 11.852469 L 339.521687 11.832937 L 340.088094 11.813406 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<path style="fill-rule:nonzero;fill:rgb(0%,0%,100%);fill-opacity:0.3;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:0.3;stroke-miterlimit:10;" d="M 141.732625 0.00090625 L 141.732625 20.997 L 240.947469 20.997 L 240.947469 0.00090625 Z M 141.732625 0.00090625 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 141.732625 0.00090625 L 141.732625 20.997 L 240.947469 20.997 L 240.947469 0.00090625 Z M 141.732625 0.00090625 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<path style="fill-rule:nonzero;fill:rgb(0%,0%,100%);fill-opacity:0.3;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:0.3;stroke-miterlimit:10;" d="M 240.947469 0.00090625 L 240.947469 13.829031 L 340.162312 13.829031 L 340.162312 0.00090625 Z M 240.947469 0.00090625 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
<path style="fill:none;stroke-width:0.79701;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 240.947469 0.00090625 L 240.947469 13.829031 L 340.162312 13.829031 L 340.162312 0.00090625 Z M 240.947469 0.00090625 " transform="matrix(1,0,0,-1,40.283,169.372)"/>
</g>
</svg>
</center>
The sum is <img class="equation_image" title=" \displaystyle \sum_{i=0}^{1} \frac{7}{2 \left(\frac{7 i}{2} + \frac{27}{4}\right)} = 0.85998 " src="/equation_images/%20%5Cdisplaystyle%20%5Csum_%7Bi%3D0%7D%5E%7B1%7D%20%5Cfrac%7B7%7D%7B2%20%5Cleft%28%5Cfrac%7B7%20i%7D%7B2%7D%20%2B%20%5Cfrac%7B27%7D%7B4%7D%5Cright%29%7D%20%3D%200.85998%20" alt="LaTeX: \displaystyle \sum_{i=0}^{1} \frac{7}{2 \left(\frac{7 i}{2} + \frac{27}{4}\right)} = 0.85998 " data-equation-content=" \displaystyle \sum_{i=0}^{1} \frac{7}{2 \left(\frac{7 i}{2} + \frac{27}{4}\right)} = 0.85998 " /> . </p> </p>