DM de noel pour les 302
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3e/DM/DM noel/all_DM_noel.pdf
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3e/DM/DM noel/all_DM_noel.pdf
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3e/DM/DM noel/corr_DM_noel.pdf
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3e/DM/DM noel/corr_DM_noel.pdf
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3e/DM/DM noel/exo_calculs.tex
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3e/DM/DM noel/exo_calculs.tex
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\begin{enumerate}
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\item Compléter les pointillés pour qu'il y est bien égalité.
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\hspace{-1cm}
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\begin{center}
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\cdots}{\Var{c}} = \dfrac{\Var{a}}{\Var{b}}$
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\hfill
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\Block{set a,b,c = random_str("{a},{b},{a*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
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$\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{c}}{\cdots}$
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\end{center}
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\vfill
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\item Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible).
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\begin{multicols}{2}
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\begin{enumerate}
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\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1", "{a} > 0", "{c} > 0"])}
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\item $A = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "A")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1"])}
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\item $B = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "B")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{c} > 1", "{d} > 1"])}
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\item $C = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "C")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{d} > 1"])}
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\item $D = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "D")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} * {c}", ["{b} > 1", "{a} > 0", "{c} > 1", "{c} != {b}"])}
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\item $E = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "E")}
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\end{eqnarray*}
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\end{solution}
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\Block{set e = Expression.random("{a} / {b} * {c} / {d}", ["{b} > 1", "{a} > 0", "{c} > 0", "{d} > 1"])}
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\item $F = \Var{e}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{e.simplify().explain() | calculus(name = "F")}
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\end{eqnarray*}
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\end{solution}
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\end{enumerate}
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\end{multicols}
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\item Évaluer les expressions suivantes
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\begin{multicols}{2}
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\begin{enumerate}
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\Block{set P = Polynom.random(degree = 1)}
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\Block{set x = Expression.random("{a}")}
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\item $\Var{P}$ en $x = \Var{x}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{P(x).explain()| calculus()}
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\end{eqnarray*}
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\end{solution}
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\Block{set P = Polynom.random(degree = 2)}
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\Block{set x = Expression.random("{a}")}
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\item $\Var{P}$ en $x = \Var{x}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{P(x).explain()| calculus()}
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\end{eqnarray*}
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\end{solution}
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\Block{set P = Expression.random("{a} x * (x - {b})")}
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\Block{set x = Expression.random("{a}")}
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\item $\Var{P}$ en $x = \Var{x}$
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\Block{set P = Expression.random("({a}x + {b})({c} + {d}x)")}
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\Block{set x = Expression.random("{a}")}
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\item $\Var{P}$ en $x = \Var{x}$
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\end{enumerate}
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\end{multicols}
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\item Réduire les expressions suivantes
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\begin{multicols}{2}
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\begin{enumerate}
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\Block{set A = Expression.random("{a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
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\item A = $\Var{A}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{A.simplify().explain() | calculus()}
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\end{eqnarray*}
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\end{solution}
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\Block{set B = Expression.random("({b} - {a}) + {a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
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\item B = $\Var{B}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{B.simplify().explain() | calculus()}
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\end{eqnarray*}
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\end{solution}
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\Block{set C = Expression.random("{a}x^2 + {c} + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
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\item C = $\Var{C}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{C.simplify().explain() | calculus()}
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\end{eqnarray*}
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\end{solution}
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\Block{set D = Expression.random("{a}x^2 + {c}x^2 + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
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\item D = $\Var{D}$
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\begin{solution}
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\begin{eqnarray*}
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\Var{D.simplify().explain() | calculus()}
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\end{eqnarray*}
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\end{solution}
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\end{enumerate}
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\end{multicols}
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\end{enumerate}
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3e/DM/DM noel/exo_proba.tex
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3e/DM/DM noel/exo_proba.tex
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\Block{set a,b,c = random_str("{a*d},{b*d},{c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1", "{c} > 1", "{d}>1"]).split(',')}
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\Block{set total = int(a) + int(b) + int(c)}
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Dans un sac, il y a \Var{a} bonbons à la menthe, \Var{b} bonbons à la fraise et \Var{c} au chocolat. On choisit un bonbon au hasard dans ce sac.
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\begin{enumerate}
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\item Combien y a-t-il d'issues en tout?
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\begin{solution}
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Il y a \Var{total} bonbons.
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\end{solution}
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\item Calculer la probabilité de tirer un bonbon à la fraise.
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\begin{solution}
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$T($ tirer un bonbon à la fraise $) = \dfrac{\Var{a}}{\Var{total}}$
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\end{solution}
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\item Calculer la probabilité de tirer un bonbon qui n'est pas au chocolat.
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\begin{solution}
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\Block{set nonChoco = int(a) + int(b)}
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$T($ tirer un bonbon à la fraise $) = \dfrac{\Var{nonChoco}}{\Var{total}}$
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\end{solution}
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\item Calculer la probabilité de tirer un bonbon au réglisse.
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\begin{solution}
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$T($ tirer un bonbon au réglisse $) = \dfrac{0}{\Var{total}} = 0$
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\end{solution}
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\item Dans un autre sac, on place 25 bonbons à la menthe et 34 bonbons à la fraise. Lise préfère les bonbons à la menthe. Dans quel sac doit-elle tirer un bonbon pour avoir le plus de chance d'avoir un bonbon qu'elle préfère?
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\end{enumerate}
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3e/DM/DM noel/exo_tech_thales.tex
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3e/DM/DM noel/exo_tech_thales.tex
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\Block{set AO, OD, CD, OB = random_str("{a},{b},{c},{d}", ["{a} < {b}", "{c} != {d}"], 2, 20).split(',')}
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Dans la figure suivante, $(AB)$ et $(CD)$ sont parallèles, $AO = \Var{AO}$, $OD = \Var{OD}$, $CD = \Var{CD}$ et $OB = \Var{OB}$.
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\Block{set fig = random_str("{a}", [], 1, 2)}
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\begin{minipage}{0.5\textwidth}
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\includegraphics[scale=0.4]{./fig/thales\Var{fig}}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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Calculer les longueurs $AB$ et $BC$.
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\end{minipage}
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3e/DM/DM noel/fig/thales1.pdf
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3e/DM/DM noel/fig/thales1.pdf
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3e/DM/DM noel/fig/thales2.pdf
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3e/DM/DM noel/fig/thales2.pdf
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3e/DM/DM noel/tpl_DM_noel.tex
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3e/DM/DM noel/tpl_DM_noel.tex
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\documentclass[a4paper,12pt]{article}
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\usepackage{myXsim}
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\usepackage{wrapfig}
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\title{DM de noël}
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\tribe{302}
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\date{Mardi de ma rentrée}
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\sujet{\Var{infos.num}}
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\xsimsetup{
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solution/print = false
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}
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\begin{document}
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\maketitle
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Vous devez rendre le sujet avec la copie.
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\begin{exercise}[subtitle={Techniques de calculs \Cal}]
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\Block{include "./exo_calculs.tex"}
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\end{exercise}
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\begin{exercise}[subtitle={Thalès \Com \Rai}]
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\Block{include "./exo_tech_thales.tex"}
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\end{exercise}
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\begin{exercise}[subtitle={Mes bonbons préférés \Rep \Com}]
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\Block{include "./exo_proba.tex"}
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\end{exercise}
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\end{questions}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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