\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Use 5 rectangles to approximate \(\displaystyle \int\limits_{3}^{5} \frac{1}{x}\, dx\) using the right endpoint. Draw a graph showing the sum.
\(\displaystyle \Delta x = \frac{b-a}{n}=\frac{2}{5}\) and \(\displaystyle x_i = a+i\Delta x = \frac{2 i}{5} + 3\). Drawing a graph gives:
\begin{tikzpicture}[yscale=5]
\draw[very thick, color=blue, opacity=0.3, xstep=1, ystep=1] (-1,-1) grid (6,1.05);
\draw[latex-latex, very thick] (-1.4,0)--(6.4,0) node[right]{$x$};
\draw[latex-latex, very thick] (0,-1.1)--(0,1.1) node[above]{$y$};
\foreach \x in { -1,1,...,6 }{
\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={3.0}:{5.0}, samples=200, samples =350] plot(\x, {1/(\x)});
\draw[fill=blue, opacity=0.3](3.00, 0) rectangle (3.40, 0.294);
\draw[thick](3.00, 0) rectangle (3.40, 0.294);
\draw[fill=blue, opacity=0.3](3.40, 0) rectangle (3.80, 0.263);
\draw[thick](3.40, 0) rectangle (3.80, 0.263);
\draw[fill=blue, opacity=0.3](3.80, 0) rectangle (4.20, 0.238);
\draw[thick](3.80, 0) rectangle (4.20, 0.238);
\draw[fill=blue, opacity=0.3](4.20, 0) rectangle (4.60, 0.217);
\draw[thick](4.20, 0) rectangle (4.60, 0.217);
\draw[fill=blue, opacity=0.3](4.60, 0) rectangle (5.00, 0.200);
\draw[thick](4.60, 0) rectangle (5.00, 0.200);
\end{tikzpicture}
\begin{question}Use 5 rectangles to approximate $\int\limits_{3}^{5} \frac{1}{x}\, dx$ using the right endpoint. Draw a graph showing the sum.
\soln{9cm}{$\Delta x = \frac{b-a}{n}=\frac{2}{5}$ and $x_i = a+i\Delta x = \frac{2 i}{5} + 3$. 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 (6,1.05);
\draw[latex-latex, very thick] (-1.4,0)--(6.4,0) node[right]{$x$};
\draw[latex-latex, very thick] (0,-1.1)--(0,1.1) node[above]{$y$};
\foreach \x in { -1,1,...,6 }{
\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={3.0}:{5.0}, samples=200, samples =350] plot(\x, {1/(\x)});
\draw[fill=blue, opacity=0.3](3.00, 0) rectangle (3.40, 0.294);
\draw[thick](3.00, 0) rectangle (3.40, 0.294);
\draw[fill=blue, opacity=0.3](3.40, 0) rectangle (3.80, 0.263);
\draw[thick](3.40, 0) rectangle (3.80, 0.263);
\draw[fill=blue, opacity=0.3](3.80, 0) rectangle (4.20, 0.238);
\draw[thick](3.80, 0) rectangle (4.20, 0.238);
\draw[fill=blue, opacity=0.3](4.20, 0) rectangle (4.60, 0.217);
\draw[thick](4.20, 0) rectangle (4.60, 0.217);
\draw[fill=blue, opacity=0.3](4.60, 0) rectangle (5.00, 0.200);
\draw[thick](4.60, 0) rectangle (5.00, 0.200);
\end{tikzpicture}
\end{center}
The sum is $\sum_{i=1}^{5} \frac{2}{5 \left(\frac{2 i}{5} + 3\right)} = 0.48511$. }
\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 5 rectangles to approximate <img class="equation_image" title=" \displaystyle \int\limits_{3}^{5} \frac{1}{x}\, dx " src="/equation_images/%20%5Cdisplaystyle%20%5Cint%5Climits_%7B3%7D%5E%7B5%7D%20%5Cfrac%7B1%7D%7Bx%7D%5C%2C%20dx%20" alt="LaTeX: \displaystyle \int\limits_{3}^{5} \frac{1}{x}\, dx " data-equation-content=" \displaystyle \int\limits_{3}^{5} \frac{1}{x}\, dx " /> using the right endpoint. Draw a graph showing the sum. </p> </p><p> <p> <img class="equation_image" title=" \displaystyle \Delta x = \frac{b-a}{n}=\frac{2}{5} " src="/equation_images/%20%5Cdisplaystyle%20%5CDelta%20x%20%3D%20%5Cfrac%7Bb-a%7D%7Bn%7D%3D%5Cfrac%7B2%7D%7B5%7D%20" alt="LaTeX: \displaystyle \Delta x = \frac{b-a}{n}=\frac{2}{5} " data-equation-content=" \displaystyle \Delta x = \frac{b-a}{n}=\frac{2}{5} " /> and <img class="equation_image" title=" \displaystyle x_i = a+i\Delta x = \frac{2 i}{5} + 3 " src="/equation_images/%20%5Cdisplaystyle%20x_i%20%3D%20a%2Bi%5CDelta%20x%20%3D%20%5Cfrac%7B2%20i%7D%7B5%7D%20%2B%203%20" alt="LaTeX: \displaystyle x_i = a+i\Delta x = \frac{2 i}{5} + 3 " data-equation-content=" \displaystyle x_i = a+i\Delta x = \frac{2 i}{5} + 3 " /> . 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="234.632pt" height="325.876pt" viewBox="0 0 234.632 325.876" 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 4.578125 -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="glyph2-5">
<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="glyph2-6">
<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 170.080281 -141.733469 M -28.3455 0.00090625 L 170.080281 0.00090625 M -28.3455 141.735281 L 170.080281 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 170.072469 -141.733469 L 170.072469 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 175.681844 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 221.703125 169.371094 C 220.003906 169.054688 217.238281 168.097656 215.328125 166.980469 L 215.328125 171.761719 C 217.238281 170.648438 220.003906 169.691406 221.703125 169.371094 "/>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-1" x="225.618" 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 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="#glyph2-4" 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="#glyph2-5" 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="#glyph2-4" 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="#glyph2-4" 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="#glyph2-6" 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="#glyph2-4" 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="#glyph2-6" 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="#glyph2-4" 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="#glyph2-4" 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="#glyph2-5" 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 85.041219 47.243094 L 85.201375 47.15325 L 85.365437 47.063406 L 85.525594 46.977469 L 85.689656 46.883719 L 85.849812 46.797781 L 86.013875 46.707937 L 86.174031 46.622 L 86.338094 46.532156 L 86.502156 46.446219 L 86.662312 46.360281 L 86.826375 46.274344 L 86.986531 46.188406 L 87.150594 46.098562 L 87.31075 46.016531 L 87.474812 45.930594 L 87.634969 45.844656 L 87.799031 45.762625 L 87.959187 45.676687 L 88.12325 45.594656 L 88.283406 45.508719 L 88.447469 45.426687 L 88.607625 45.336844 L 88.771687 45.262625 L 88.931844 45.172781 L 89.095906 45.094656 L 89.256062 45.012625 L 89.420125 44.930594 L 89.580281 44.848562 L 89.744344 44.770437 L 89.908406 44.6845 L 90.068562 44.606375 L 90.232625 44.524344 L 90.392781 44.450125 L 90.556844 44.368094 L 90.717 44.289969 L 90.881062 44.207937 L 91.041219 44.129812 L 91.205281 44.051687 L 91.365437 43.973562 L 91.5295 43.895437 L 91.689656 43.817312 L 91.853719 43.743094 L 92.013875 43.661062 L 92.177937 43.586844 L 92.338094 43.512625 L 92.502156 43.4345 L 92.662312 43.360281 L 92.826375 43.282156 L 92.986531 43.211844 L 93.150594 43.133719 L 93.31075 43.055594 L 93.638875 42.907156 L 93.799031 42.832937 L 93.963094 42.758719 L 94.12325 42.6845 L 94.287312 42.610281 L 94.447469 42.536062 L 94.611531 42.46575 L 94.771687 42.391531 L 94.93575 42.317312 L 95.095906 42.247 L 95.259969 42.180594 L 95.420125 42.102469 L 95.584187 42.032156 L 95.744344 41.961844 L 95.908406 41.891531 L 96.068562 41.821219 L 96.232625 41.750906 L 96.392781 41.676687 L 96.556844 41.614187 L 96.717 41.539969 L 96.881062 41.473562 L 97.045125 41.40325 L 97.205281 41.336844 L 97.369344 41.262625 L 97.5295 41.192312 L 97.693562 41.122 L 97.853719 41.0595 L 98.017781 40.989187 L 98.177937 40.918875 L 98.342 40.856375 L 98.502156 40.789969 L 98.666219 40.719656 L 98.826375 40.649344 L 98.990437 40.586844 L 99.150594 40.520437 L 99.314656 40.454031 L 99.474812 40.387625 L 99.638875 40.325125 L 99.799031 40.258719 L 99.963094 40.192312 L 100.12325 40.129812 L 100.287312 40.063406 L 100.451375 40.000906 L 100.611531 39.9345 L 100.775594 39.872 L 100.93575 39.805594 L 101.099812 39.743094 L 101.259969 39.680594 L 101.424031 39.618094 L 101.584187 39.547781 L 101.74825 39.489187 L 101.908406 39.422781 L 102.072469 39.360281 L 102.232625 39.301687 L 102.396687 39.235281 L 102.556844 39.176687 L 102.720906 39.110281 L 102.881062 39.047781 L 103.045125 38.993094 L 103.205281 38.926687 L 103.369344 38.868094 L 103.5295 38.805594 L 103.693562 38.747 L 103.857625 38.6845 L 104.017781 38.622 L 104.181844 38.563406 L 104.342 38.512625 L 104.506062 38.446219 L 104.666219 38.387625 L 104.830281 38.325125 L 104.990437 38.270437 L 105.1545 38.211844 L 105.314656 38.149344 L 105.478719 38.09075 L 105.638875 38.036062 L 105.802937 37.973562 L 105.963094 37.914969 L 106.127156 37.856375 L 106.287312 37.801687 L 106.451375 37.747 L 106.611531 37.688406 L 106.775594 37.625906 L 106.93575 37.575125 L 107.099812 37.512625 L 107.263875 37.457937 L 107.424031 37.40325 L 107.588094 37.348562 L 107.74825 37.289969 L 107.912312 37.235281 L 108.072469 37.180594 L 108.236531 37.122 L 108.396687 37.063406 L 108.56075 37.008719 L 108.720906 36.954031 L 108.884969 36.90325 L 109.045125 36.848562 L 109.209187 36.789969 L 109.369344 36.735281 L 109.533406 36.6845 L 109.693562 36.625906 L 109.857625 36.575125 L 110.017781 36.520437 L 110.181844 36.469656 L 110.342 36.414969 L 110.506062 36.352469 L 110.670125 36.301687 L 110.830281 36.247 L 110.994344 36.196219 L 111.1545 36.141531 L 111.318562 36.086844 L 111.478719 36.039969 L 111.642781 35.985281 L 111.802937 35.9345 L 111.967 35.879812 L 112.127156 35.832937 L 112.291219 35.77825 L 112.451375 35.723562 L 112.615437 35.672781 L 112.775594 35.622 L 112.939656 35.571219 L 113.099812 35.520437 L 113.263875 35.469656 L 113.424031 35.422781 L 113.588094 35.368094 L 113.74825 35.321219 L 114.076375 35.219656 L 114.236531 35.168875 L 114.400594 35.118094 L 114.56075 35.071219 L 114.724812 35.024344 L 114.884969 34.96575 L 115.049031 34.918875 L 115.209187 34.872 L 115.37325 34.821219 L 115.533406 34.774344 L 115.697469 34.723562 L 115.857625 34.672781 L 116.021687 34.629812 L 116.181844 34.575125 L 116.345906 34.532156 L 116.506062 34.485281 L 116.670125 34.438406 L 116.830281 34.387625 L 116.994344 34.34075 L 117.1545 34.289969 L 117.318562 34.247 L 117.482625 34.200125 L 117.642781 34.149344 L 117.806844 34.102469 L 117.967 34.0595 L 118.131062 34.012625 L 118.291219 33.96575 L 118.455281 33.918875 L 118.615437 33.875906 L 118.7795 33.821219 L 118.939656 33.77825 L 119.103719 33.735281 L 119.263875 33.6845 L 119.427937 33.641531 L 119.588094 33.598562 L 119.752156 33.547781 L 119.912312 33.504812 L 120.076375 33.457937 L 120.236531 33.411062 L 120.400594 33.368094 L 120.56075 33.325125 L 120.888875 33.231375 L 121.049031 33.188406 L 121.213094 33.145437 L 121.37325 33.098562 L 121.537312 33.055594 L 121.697469 33.012625 L 121.861531 32.969656 L 122.021687 32.926687 L 122.18575 32.879812 L 122.345906 32.836844 L 122.509969 32.793875 L 122.670125 32.750906 L 122.834187 32.707937 L 122.994344 32.664969 L 123.158406 32.622 L 123.318562 32.575125 L 123.482625 32.536062 L 123.642781 32.489187 L 123.806844 32.450125 L 123.967 32.407156 L 124.131062 32.364187 L 124.295125 32.325125 L 124.455281 32.282156 L 124.619344 32.239187 L 124.7795 32.196219 L 124.943562 32.15325 L 125.103719 32.114187 L 125.267781 32.071219 L 125.427937 32.032156 L 125.592 31.989187 L 125.752156 31.946219 L 125.916219 31.907156 L 126.076375 31.864187 L 126.240437 31.825125 L 126.400594 31.786062 L 126.564656 31.743094 L 126.724812 31.704031 L 126.888875 31.664969 L 127.049031 31.622 L 127.213094 31.582937 L 127.37325 31.543875 L 127.537312 31.500906 L 127.701375 31.46575 L 127.861531 31.418875 L 128.025594 31.379812 L 128.18575 31.34075 L 128.349812 31.301687 L 128.509969 31.262625 L 128.674031 31.223562 L 128.834187 31.1845 L 128.99825 31.145437 L 129.158406 31.102469 L 129.322469 31.067312 L 129.482625 31.02825 L 129.646687 30.989187 L 129.806844 30.950125 L 129.970906 30.914969 L 130.131062 30.872 L 130.295125 30.836844 L 130.455281 30.797781 L 130.619344 30.758719 L 130.7795 30.723562 L 130.943562 30.680594 L 131.107625 30.645437 L 131.267781 30.610281 L 131.431844 30.571219 L 131.592 30.532156 L 131.756062 30.493094 L 131.916219 30.457937 L 132.080281 30.418875 L 132.240437 30.379812 L 132.4045 30.344656 L 132.564656 30.305594 L 132.728719 30.270437 L 132.888875 30.231375 L 133.052937 30.196219 L 133.213094 30.157156 L 133.377156 30.122 L 133.537312 30.086844 L 133.701375 30.047781 L 133.861531 30.012625 L 134.025594 29.977469 L 134.18575 29.938406 L 134.513875 29.868094 L 134.674031 29.832937 L 134.838094 29.797781 L 134.99825 29.762625 L 135.162312 29.727469 L 135.322469 29.688406 L 135.486531 29.65325 L 135.646687 29.618094 L 135.81075 29.582937 L 135.970906 29.551687 L 136.134969 29.512625 L 136.295125 29.481375 L 136.459187 29.446219 L 136.619344 29.407156 L 136.783406 29.372 L 136.943562 29.336844 L 137.107625 29.301687 L 137.267781 29.266531 L 137.431844 29.231375 L 137.592 29.200125 L 137.920125 29.129812 L 138.080281 29.098562 L 138.244344 29.063406 L 138.4045 29.02825 L 138.568562 28.997 L 138.728719 28.961844 L 138.892781 28.926687 L 139.052937 28.891531 L 139.217 28.860281 L 139.377156 28.825125 L 139.541219 28.789969 L 139.701375 28.762625 L 139.865437 28.727469 L 140.025594 28.692312 L 140.189656 28.657156 L 140.349812 28.629812 L 140.513875 28.59075 L 140.674031 28.5595 L 140.838094 28.524344 L 140.99825 28.493094 L 141.162312 28.461844 L 141.322469 28.426687 L 141.650594 28.364187 " 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 85.041219 0.00090625 L 85.041219 41.668875 L 96.377156 41.668875 L 96.377156 0.00090625 Z M 85.041219 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 85.041219 0.00090625 L 85.041219 41.668875 L 96.377156 41.668875 L 96.377156 0.00090625 Z M 85.041219 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 96.377156 0.00090625 L 96.377156 37.274344 L 107.717 37.274344 L 107.717 0.00090625 Z M 96.377156 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 96.377156 0.00090625 L 96.377156 37.274344 L 107.717 37.274344 L 107.717 0.00090625 Z M 96.377156 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 107.717 0.00090625 L 107.717 33.735281 L 119.056844 33.735281 L 119.056844 0.00090625 Z M 107.717 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 107.717 0.00090625 L 107.717 33.735281 L 119.056844 33.735281 L 119.056844 0.00090625 Z M 107.717 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 119.056844 0.00090625 L 119.056844 30.754812 L 130.396687 30.754812 L 130.396687 0.00090625 Z M 119.056844 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 119.056844 0.00090625 L 119.056844 30.754812 L 130.396687 30.754812 L 130.396687 0.00090625 Z M 119.056844 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 130.396687 0.00090625 L 130.396687 28.344656 L 141.732625 28.344656 L 141.732625 0.00090625 Z M 130.396687 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 130.396687 0.00090625 L 130.396687 28.344656 L 141.732625 28.344656 L 141.732625 0.00090625 Z M 130.396687 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=1}^{5} \frac{2}{5 \left(\frac{2 i}{5} + 3\right)} = 0.48511 " src="/equation_images/%20%5Cdisplaystyle%20%5Csum_%7Bi%3D1%7D%5E%7B5%7D%20%5Cfrac%7B2%7D%7B5%20%5Cleft%28%5Cfrac%7B2%20i%7D%7B5%7D%20%2B%203%5Cright%29%7D%20%3D%200.48511%20" alt="LaTeX: \displaystyle \sum_{i=1}^{5} \frac{2}{5 \left(\frac{2 i}{5} + 3\right)} = 0.48511 " data-equation-content=" \displaystyle \sum_{i=1}^{5} \frac{2}{5 \left(\frac{2 i}{5} + 3\right)} = 0.48511 " /> . </p> </p>