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\colorlet{bg hours 1}{red!50} + \colorlet{hours color}{red!80!black} + % styles + \tikzset{ + minutes/.style={circle,inner sep=0,text width=5mm,align=center,font=\bfseries}, + minutes 0/.style={fill=minutes color,text=white,minutes}, + minutes 1/.style={text=minutes color,fill=white,minutes}, + minutes font/.style={font=\normalsize}, + hours/.style={font=\fontsize{60}{66}\selectfont\bfseries,text=hours color,align=center}, + mini hours font/.style={font=\fontsize{40}{46}\selectfont\bfseries}, + } + % radii + \def\bigradius{80mm} + \def\minuteradius{75mm} + \def\hourradius{60mm} + \def\minihourminradius{25mm} + \def\minihourmaxradius{45mm} + \pgfmathsetmacro\minihourradius{(\minihourmaxradius + \minihourminradius)*.5} + \def\hourwidth{2mm} + \def\minutewidth{1mm} + + % big circle + \filldraw [fill=white,draw=minutes color] (0,0) circle (\bigradius); + + % minutes marks + \foreach \angle[count=\c from 0,evaluate={\c as \hourmark using notequal(int(mod(\c,5)),0)}] + in {0,6,...,354}{ \path (-\angle:\minuteradius) node[minutes \hourmark]{\c}; } + + % hours marks + \foreach \angle[count=\c from 1,evaluate={\c as \col using int(mod(\c,2))}] in {30,60,...,360}{ + + \path (-\angle:\hourradius) node[hours]{\c}; + + \path[fill=bg hours \col] + (-\angle:\minihourminradius) -- (-\angle:\minihourmaxradius) + arc(-\angle:-\angle-30:\minihourmaxradius) -- (-\angle-30:\minihourminradius) + arc(-\angle-30:-\angle:\minihourminradius) -- cycle; + + \path (-\angle-15:\minihourradius pt) node[mini hours font]{\textcolor{white}{\contour{hours color}{\c}}}; + } + + % hands + \pgfmathsetmacro\hourangle{-#1*30-#2*.5} + \pgfmathsetmacro\minuteangle{-#2*6} + \fill[rotate=\hourangle,fill=hours color] ++(0,\hourwidth) arc(90:270:\hourwidth) -- ++(50mm,0) + -- ++(\hourwidth,\hourwidth) -- ++(-\hourwidth,\hourwidth) -- ++(-50mm,0) -- cycle ; + \fill[rotate=\minuteangle,fill=minutes color] ++(0,\minutewidth) arc(90:270:\minutewidth) -- ++(70mm,0) + -- ++(\minutewidth,\minutewidth) -- ++(-\minutewidth,\minutewidth) -- ++(-70mm,0) -- cycle ; +} + +\newcommand{\clockBTick}[2]{% + \draw (0,0) circle (2cm); + \foreach \angle / \label in + {0/3, 30/2, 60/1, 90/12, 120/11, 150/10, 180/9, + 210/8, 240/7, 270/6, 300/5, 330/4} + { + \draw (\angle:1.8cm) -- (\angle:2cm); + \draw (\angle:1.4cm) node{\textsf{\label}}; + } + \foreach \angle[count=\c from 0] in {0,6,...,354} + { + \draw (\angle:1.9cm) -- (\angle:2cm); + } + \draw[rotate=90] (0,0) -- (-#1*30-#2*30/60:0.7cm); % hours + \draw[rotate=90] (0,0) -- (-#2*6:1.2cm); % minutes + \path [fill=black] (0,0) circle (3pt); + \path [fill=red] (0,0) circle (1.5pt); +} + +\newcommand{\clockA}{% + % colors + \colorlet{minutes color}{blue!50!cyan!70!black} + \colorlet{bg hours 0}{yellow} + \colorlet{bg hours 1}{red!50} + \colorlet{hours color}{red!80!black} + % styles + \tikzset{ + minutes/.style={circle,inner sep=0,text width=5mm,align=center,font=\bfseries}, + minutes 0/.style={fill=minutes color,text=white,minutes}, + minutes 1/.style={text=minutes color,fill=white,minutes}, + minutes font/.style={font=\normalsize}, + hours/.style={font=\fontsize{60}{66}\selectfont\bfseries,text=hours color,align=center}, + mini hours font/.style={font=\fontsize{40}{46}\selectfont\bfseries}, + } + % radii + \def\bigradius{80mm} + \def\minuteradius{75mm} + \def\hourradius{60mm} + \def\minihourminradius{25mm} + \def\minihourmaxradius{45mm} + \pgfmathsetmacro\minihourradius{(\minihourmaxradius + \minihourminradius)*.5} + \def\hourwidth{2mm} + \def\minutewidth{1mm} + + % big circle + \filldraw [fill=white,draw=minutes color] (0,0) circle (\bigradius); + + % minutes marks + \foreach \angle[count=\c from 0,evaluate={\c as \hourmark using notequal(int(mod(\c,5)),0)}] + in {0,6,...,354}{ \path (-\angle:\minuteradius) node[minutes \hourmark]{\c}; } + + % hours marks + \foreach \angle[count=\c from 1,evaluate={\c as \col using int(mod(\c,2))}] in {30,60,...,360}{ + + \path (-\angle:\hourradius) node[hours]{\c}; + + \path[fill=bg hours \col] + (-\angle:\minihourminradius) -- (-\angle:\minihourmaxradius) + arc(-\angle:-\angle-30:\minihourmaxradius) -- (-\angle-30:\minihourminradius) + arc(-\angle-30:-\angle:\minihourminradius) -- cycle; + + \path (-\angle-15:\minihourradius pt) node[mini hours font]{\textcolor{white}{\contour{hours color}{\c}}}; + } + + \path [fill=black] (0,0) circle (3mm); + \path [fill=red] (0,0) circle (1.5mm); +} + +\newcommand{\clockB}{% + \draw (0,0) circle (2cm); + \foreach \angle / \label in + {0/3, 30/2, 60/1, 90/12, 120/11, 150/10, 180/9, + 210/8, 240/7, 270/6, 300/5, 330/4} + { + \draw (\angle:1.8cm) -- (\angle:2cm); + \draw (\angle:1.4cm) node{\textsf{\label}}; + } + \foreach \angle[count=\c from 0] in {0,6,...,354} + { + \draw (\angle:1.9cm) -- (\angle:2cm); + } + \path [fill=black] (0,0) circle (3pt); + \path [fill=red] (0,0) circle (1.5pt); +} + + \begin{document} \competencesStatement @@ -15,18 +156,142 @@ \bigskip \begin{exercise}[subtitle={Angle et mesures}] + \begin{enumerate} + \item \textbf{Mesurer} les angles de la figure. + + \includegraphics[scale=0.9]{./fig/mes_angles-1} + + \begin{center} + $\widehat{ABC} = ....$ \hfill + $\widehat{BCD} = ....$ \hfill + $\widehat{CDE} = ....$ + \end{center} + \item Tracer la droite (d) parallèle à la droite $(AB)$ passant par le point $C$ + + \includegraphics[scale=0.9]{./fig/paral-1} + \end{enumerate} \end{exercise} \begin{exercise}[subtitle={L'heure}] + \begin{enumerate} + \item Quelle heure indique ces deux horloges? + ~ + + \vspace{1.5cm} + \hspace{1cm} + \begin{tikzpicture}[cap=round, rotate=90, transform canvas={scale=0.25}] + \clockATick{7}{30} + \end{tikzpicture} + \hspace{2cm} + ............ + \hspace{2.5cm} + \begin{tikzpicture}[cap=round, transform canvas={scale=0.9}] + \clockBTick{11}{15} + \end{tikzpicture} + \hspace{2cm} + ............ + \hspace{2.5cm} + \begin{tikzpicture}[cap=round, transform canvas={scale=0.9}] + \clockBTick{3}{55} + \end{tikzpicture} + \hspace{2cm} + ............ + + \vspace{2cm} + \item Placer les aiguilles correctement. + ~ + + \vspace{1.5cm} + \hspace{1cm} + \begin{tikzpicture}[cap=round, rotate=90, transform canvas={scale=0.25}] + \clockA + \end{tikzpicture} + \hspace{2cm} + 10h20 + \hspace{2.5cm} + \begin{tikzpicture}[cap=round, transform canvas={scale=0.9}] + \clockB + \end{tikzpicture} + \hspace{2cm} + 9h54 + \hspace{2.5cm} + \begin{tikzpicture}[cap=round, transform canvas={scale=0.9}] + \clockB + \end{tikzpicture} + \hspace{2cm} + 1h34 + + \vspace{2cm} + \end{enumerate} \end{exercise} \clearpage -\begin{exercise}[subtitle={}] +\begin{exercise}[subtitle={Longueur d'un pas}] + \begin{enumerate} + \item Abdou a mesuré la longueur d'un de ses pas, 1 pas mesure 80cm. + \begin{enumerate} + \item Complète le tableau avec la mesure que vient de faire Abdou. + + \begin{tabular}{|c|*{5}{p{2cm}|}} + \hline + Nombre de pas & & & & & \\ + \hline + Distance (en cm) & & & & & \\ + \hline + \end{tabular} + \item Il a mesuré que pour sortir de la salle d'histoire, il devrait faire 6pas. Quelle distance parcourt il pour sortir? + \\[0.2cm] .\dotfill + \item Il a mesuré que pour aller du cours de français au cours de math, il faisait 20pas. Cela fait combien de cm? + \\[0.2cm] .\dotfill + \item Quand il est rentré chez lui, il a compté 554 pas. Combien de km a-t-il parcouru? + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \end{enumerate} + \end{enumerate} \end{exercise} -\begin{exercise}[subtitle={Taille d'élèves}] +\begin{exercise}[subtitle={Tailles des élèves}] + Dans le tableau ci-dessous, on a reporté les tailles des élèves d'une classe de 6e. + + \begin{tabular}{|c|*{5}{p{2cm}|}} + \hline + Élève & Mariam & Abdou & Roubouanti & Ikram & Faiz \\ + \hline + Taille & 1,5m & 1,45m & 1,63m & 1,4m & 1,53m \\ + \hline + \end{tabular} + \begin{enumerate} + \item Qui est la plus grande, Mariam ou Ikram? + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \item Ranger en ordre croissant la taille des élèves. + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \item Convertir la taille de Roubouanti en cm. + \\[0.2cm] .\dotfill + \item Convertir la taille de Abdou en km. + \\[0.2cm] .\dotfill + \end{enumerate} + + \vspace{3cm} + + \begin{tikzpicture}[scale=8] + \draw (0,0) -> (2.2, 0); + \foreach \x in {0,...,2} {% + \draw (\x,0) -- (\x, -0.1); + } + \foreach \x in {0,...,21} {% + \draw ({0.1*\x},0) -- ({0.1*\x}, -0.07); + } + \foreach \x in {0,...,210} {% + \draw ({0.01*\x},0) -- ({0.01*\x}, -0.03); + } + \end{tikzpicture} \end{exercise} + \end{document} diff --git a/6e/DS/DS_18_04_11/DS_18_04_11-2.pdf b/6e/DS/DS_18_04_11/DS_18_04_11-2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..88685a3ca1987f350a64b5878cea66a07b776a16 GIT binary patch literal 90457 zcmZtNWmH>1+bC?@-QC^Yp}0eFcXyZK?(R+r4h16F;L&m|u!Nx`Q z?+1ZZ+Sb9t(v6H&+QHPrQqt1g*}@V*L*%+h6R*Bdu`N z8LFJADL>cz)t&_REyHhKe;ij)8>AZ-3gjCF3Dyb!tdjP9O@^vgJ1exCH4rDP_lBfQxlaX@o+ttHc z)aT>iVQ&{iYYpnLHrw@NP(#qiqxWZg0eEA!BseGA zJ{PZhUha80Kllrd(sHyMUVQZuzU(LWw)@||1r;do?0T>LyzhBi41$_L{P?t+9myBT z4}6<$mC{KucRBkT@6Nm5O9=mZ&udNCqx1>2(D1z`Z$^p zhY*-dbcwEOJoc0OgOY#Gw)OL4A9s=86)1y+XG1UdX1&%2P_=p^M+)k+dqpB@12_vV zdzjZ=L`C+KX1L(qzh60I`ZV&YeG} zj~(h)WJ_Oxh4dnfLGl9`NsatJCmZ-Mqy~jd5iQIDevRRN*AXeVuKa%dD5UhmFw9?V 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zzjoNGnID?T;^I(8etk)gEV44Ag@gkEIsC3Uw^U|cP#!_NM}mr8w0-Rd?T?UmwEf54 rkksPVuu2zCyy!hXa2Ede#$bHyeS8Cbs9PZ|CI*24Zr_IMs{{TAJ>ssR literal 0 HcmV?d00001 diff --git a/6e/DS/DS_18_04_11/DS_18_04_11-2.tex b/6e/DS/DS_18_04_11/DS_18_04_11-2.tex new file mode 100644 index 0000000..c809e9c --- /dev/null +++ b/6e/DS/DS_18_04_11/DS_18_04_11-2.tex @@ -0,0 +1,302 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +\title{DS 9} +\tribe{Sixième} +\date{13 avril 2018} + +\sujet{2} + +\RequirePackage{contour} +\newcommand{\clockATick}[2]{% + % colors + \colorlet{minutes color}{blue!50!cyan!70!black} + \colorlet{bg hours 0}{yellow} + \colorlet{bg hours 1}{red!50} + \colorlet{hours color}{red!80!black} + % styles + \tikzset{ + minutes/.style={circle,inner sep=0,text width=5mm,align=center,font=\bfseries}, + minutes 0/.style={fill=minutes color,text=white,minutes}, + minutes 1/.style={text=minutes color,fill=white,minutes}, + minutes font/.style={font=\normalsize}, + hours/.style={font=\fontsize{60}{66}\selectfont\bfseries,text=hours color,align=center}, + mini hours font/.style={font=\fontsize{40}{46}\selectfont\bfseries}, + } + % radii + \def\bigradius{80mm} + \def\minuteradius{75mm} + \def\hourradius{60mm} + \def\minihourminradius{25mm} + \def\minihourmaxradius{45mm} + \pgfmathsetmacro\minihourradius{(\minihourmaxradius + \minihourminradius)*.5} + \def\hourwidth{2mm} + \def\minutewidth{1mm} + + % big circle + \filldraw [fill=white,draw=minutes color] (0,0) circle (\bigradius); + + % minutes marks + \foreach \angle[count=\c from 0,evaluate={\c as \hourmark using notequal(int(mod(\c,5)),0)}] + in {0,6,...,354}{ \path (-\angle:\minuteradius) node[minutes \hourmark]{\c}; } + + % hours marks + \foreach \angle[count=\c from 1,evaluate={\c as \col using int(mod(\c,2))}] in {30,60,...,360}{ + + \path (-\angle:\hourradius) node[hours]{\c}; + + \path[fill=bg hours \col] + (-\angle:\minihourminradius) -- (-\angle:\minihourmaxradius) + arc(-\angle:-\angle-30:\minihourmaxradius) -- (-\angle-30:\minihourminradius) + arc(-\angle-30:-\angle:\minihourminradius) -- cycle; + + \path (-\angle-15:\minihourradius pt) node[mini hours font]{\textcolor{white}{\contour{hours color}{\c}}}; + } + + % hands + \pgfmathsetmacro\hourangle{-#1*30-#2*.5} + \pgfmathsetmacro\minuteangle{-#2*6} + \fill[rotate=\hourangle,fill=hours color] ++(0,\hourwidth) arc(90:270:\hourwidth) -- ++(50mm,0) + -- ++(\hourwidth,\hourwidth) -- ++(-\hourwidth,\hourwidth) -- ++(-50mm,0) -- cycle ; + \fill[rotate=\minuteangle,fill=minutes color] ++(0,\minutewidth) arc(90:270:\minutewidth) -- ++(70mm,0) + -- ++(\minutewidth,\minutewidth) -- ++(-\minutewidth,\minutewidth) -- ++(-70mm,0) -- cycle ; +} + +\newcommand{\clockBTick}[2]{% + \draw (0,0) circle (2cm); + \foreach \angle / \label in + {0/3, 30/2, 60/1, 90/12, 120/11, 150/10, 180/9, + 210/8, 240/7, 270/6, 300/5, 330/4} + { + \draw (\angle:1.8cm) -- (\angle:2cm); + \draw (\angle:1.4cm) node{\textsf{\label}}; + } + \foreach \angle[count=\c from 0] in {0,6,...,354} + { + \draw (\angle:1.9cm) -- (\angle:2cm); + } + \draw[rotate=90] (0,0) -- (-#1*30-#2*30/60:0.7cm); % hours + \draw[rotate=90] (0,0) -- (-#2*6:1.2cm); % minutes + \path [fill=black] (0,0) circle (3pt); + \path [fill=red] (0,0) circle (1.5pt); +} + +\newcommand{\clockA}{% + % colors + \colorlet{minutes color}{blue!50!cyan!70!black} + \colorlet{bg hours 0}{yellow} + \colorlet{bg hours 1}{red!50} + \colorlet{hours color}{red!80!black} + % styles + \tikzset{ + minutes/.style={circle,inner sep=0,text width=5mm,align=center,font=\bfseries}, + minutes 0/.style={fill=minutes color,text=white,minutes}, + minutes 1/.style={text=minutes color,fill=white,minutes}, + minutes font/.style={font=\normalsize}, + hours/.style={font=\fontsize{60}{66}\selectfont\bfseries,text=hours color,align=center}, + mini hours font/.style={font=\fontsize{40}{46}\selectfont\bfseries}, + } + % radii + \def\bigradius{80mm} + \def\minuteradius{75mm} + \def\hourradius{60mm} + \def\minihourminradius{25mm} + \def\minihourmaxradius{45mm} + \pgfmathsetmacro\minihourradius{(\minihourmaxradius + \minihourminradius)*.5} + \def\hourwidth{2mm} + \def\minutewidth{1mm} + + % big circle + \filldraw [fill=white,draw=minutes color] (0,0) circle (\bigradius); + + % minutes marks + \foreach \angle[count=\c from 0,evaluate={\c as \hourmark using notequal(int(mod(\c,5)),0)}] + in {0,6,...,354}{ \path (-\angle:\minuteradius) node[minutes \hourmark]{\c}; } + + % hours marks + \foreach \angle[count=\c from 1,evaluate={\c as \col using int(mod(\c,2))}] in {30,60,...,360}{ + + \path (-\angle:\hourradius) node[hours]{\c}; + + \path[fill=bg hours \col] + (-\angle:\minihourminradius) -- (-\angle:\minihourmaxradius) + arc(-\angle:-\angle-30:\minihourmaxradius) -- (-\angle-30:\minihourminradius) + arc(-\angle-30:-\angle:\minihourminradius) -- cycle; + + \path (-\angle-15:\minihourradius pt) node[mini hours font]{\textcolor{white}{\contour{hours color}{\c}}}; + } + + \path [fill=black] (0,0) circle (3mm); + \path [fill=red] (0,0) circle (1.5mm); +} + +\newcommand{\clockB}{% + \draw (0,0) circle (2cm); + \foreach \angle / \label in + {0/3, 30/2, 60/1, 90/12, 120/11, 150/10, 180/9, + 210/8, 240/7, 270/6, 300/5, 330/4} + { + \draw (\angle:1.8cm) -- (\angle:2cm); + \draw (\angle:1.4cm) node{\textsf{\label}}; + } + \foreach \angle[count=\c from 0] in {0,6,...,354} + { + \draw (\angle:1.9cm) -- (\angle:2cm); + } + \path [fill=black] (0,0) circle (3pt); + \path [fill=red] (0,0) circle (1.5pt); +} + + +\begin{document} + +\competencesStatement + +\maketitle +\bigskip +\begin{exercise}[subtitle={L'heure}] + \begin{enumerate} + \item Quelle heure indique ces deux horloges? + ~ + + \vspace{1.5cm} + \hspace{1cm} + \begin{tikzpicture}[cap=round, rotate=90, transform canvas={scale=0.25}] + \clockATick{1}{30} + \end{tikzpicture} + \hspace{2cm} + ............ + \hspace{2.5cm} + \begin{tikzpicture}[cap=round, transform canvas={scale=0.9}] + \clockBTick{8}{5} + \end{tikzpicture} + \hspace{2cm} + ............ + \hspace{2.5cm} + \begin{tikzpicture}[cap=round, transform canvas={scale=0.9}] + \clockBTick{10}{34} + \end{tikzpicture} + \hspace{2cm} + ............ + + \vspace{2cm} + \item Placer les aiguilles correctement. + ~ + + \vspace{1.5cm} + \hspace{1cm} + \begin{tikzpicture}[cap=round, rotate=90, transform canvas={scale=0.25}] + \clockA + \end{tikzpicture} + \hspace{2cm} + 2h25 + \hspace{2.5cm} + \begin{tikzpicture}[cap=round, transform canvas={scale=0.9}] + \clockB + \end{tikzpicture} + \hspace{2cm} + 6h04 + \hspace{2.5cm} + \begin{tikzpicture}[cap=round, transform canvas={scale=0.9}] + \clockB + \end{tikzpicture} + \hspace{2cm} + 11h44 + + \vspace{2cm} + \end{enumerate} +\end{exercise} + + +\begin{exercise}[subtitle={Longueur d'un pas}] + \begin{enumerate} + \item Mariam a mesuré la longueur d'un de ses pas, 1 pas mesure 70cm. + \begin{enumerate} + \item Complète le tableau avec la mesure que vient de faire Abdou. + + \begin{tabular}{|c|*{5}{p{2cm}|}} + \hline + Nombre de pas & & & & & \\ + \hline + Distance (en cm) & & & & & \\ + \hline + \end{tabular} + \item Elle a mesuré que pour sortir de la salle d'histoire, elle devrait faire 6pas. Quelle distance parcourt elle pour sortir? + \\[0.2cm] .\dotfill + \item Elle a mesuré que pour aller du cours de français au cours de math, elle faisait 20pas. Cela fait combien de cm? + \\[0.2cm] .\dotfill + \item Quand elle est rentré chez elle, elle a compté 554 pas. Combien de km a-t-elle parcouru? + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \end{enumerate} + \end{enumerate} +\end{exercise} + +\clearpage +\begin{exercise}[subtitle={Tailles des élèves}] + Dans le tableau ci-dessous, on a reporté les tailles des élèves d'une classe de 6e. + + \begin{tabular}{|c|*{5}{p{2cm}|}} + \hline + Élève & Mariam & Abdou & Roubouanti & Ikram & Faiz \\ + \hline + Taille & 1,5m & 1,45m & 1,63m & 1,4m & 1,53m \\ + \hline + \end{tabular} + \begin{enumerate} + \item Qui est la plus grande, Mariam ou Ikram? + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \item Ranger en ordre croissant la taille des élèves. + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \\[0.2cm] .\dotfill + \item Convertir la taille de Faiz en cm. + \\[0.2cm] .\dotfill + \item Convertir la taille de Mariam en km. + \\[0.2cm] .\dotfill + \end{enumerate} + + \vspace{3cm} + + \begin{tikzpicture}[scale=8] + \draw (0,0) -> (2.2, 0); + \foreach \x in {0,...,2} {% + \draw (\x,0) -- (\x, -0.1); + } + \foreach \x in {0,...,21} {% + \draw ({0.1*\x},0) -- ({0.1*\x}, -0.07); + } + \foreach \x in {0,...,210} {% + \draw ({0.01*\x},0) -- ({0.01*\x}, -0.03); + } + \end{tikzpicture} +\end{exercise} + +\begin{exercise}[subtitle={Angle et mesures}] + \begin{enumerate} + \item \textbf{Mesurer} les angles de la figure. + + \includegraphics[scale=0.9]{./fig/mes_angles-2} + + \begin{center} + $\widehat{ABC} = ....$ \hfill + $\widehat{BCD} = ....$ \hfill + $\widehat{CDE} = ....$ + \end{center} + \item Tracer la droite (d) parallèle à la droite $(AB)$ passant par le point $C$ + + \includegraphics[scale=0.9]{./fig/paral-2} + \end{enumerate} +\end{exercise} + + +\end{document} + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: +