96 lines
3.0 KiB
TeX
96 lines
3.0 KiB
TeX
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\documentclass[a4paper,12pt]{article}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\title{Information chiffrée 2 - Cours}
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\date{Mars 2023}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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\section*{Lien entre taux d'évolution et coefficient multiplicateur}
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\begin{propriete}
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Soit $t$ le taux d'évolution qui fait évolution $v_i$ vers $v_f$ alors
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\[
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v_f = (1+t)v_i
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\]
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\end{propriete}
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\begin{definition}
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$1+t$ est appelé \textbf{coefficient multiplicateur}, noté $CM$, associé au taux d'évolution $t$.
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\noindent
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On a ainsi
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\[
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CM = 1+t \qquad \mbox{ou encore} \qquad t = CM - 1
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\]
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et
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\[
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v_f = CM \times v_i \qquad \mbox{ ou encore } \qquad CM = \frac{v_f}{v_i}
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\]
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\end{definition}
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\paragraph{Exemples}
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\begin{itemize}
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\item
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\begin{tikzpicture}[
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baseline,
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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arrow/.style={->, shorten >=5pt, shorten <=5pt}
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]
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%Nodes
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\node[roundnode] (leftterme) {\makebox[0.5cm]{120}};
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\node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}};
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%Lines
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\path[arrow] (leftterme.north) edge [bend left]
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node [pos=0.5, above] {+25\%}
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node [pos=0.5, below] {\times CM = ...}
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(centerterm.north)
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;
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\end{tikzpicture}
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Coefficient multiplicateur: \hfill Valeur finale: \hfill.
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\item
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\begin{tikzpicture}[
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baseline,
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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arrow/.style={->, shorten >=5pt, shorten <=5pt}
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]
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%Nodes
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\node[roundnode] (leftterme) {\makebox[0.5cm]{55}};
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\node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}};
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%Lines
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\path[arrow] (leftterme.north) edge [bend left]
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node [pos=0.5, above] {+...}
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node [pos=0.5, below] {\times 0.12}
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(centerterm.north)
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;
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\end{tikzpicture}
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Taux d'évolution: \hfill Valeur finale: \hfill.
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\item
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\begin{tikzpicture}[
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baseline,
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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arrow/.style={->, shorten >=5pt, shorten <=5pt}
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]
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%Nodes
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\node[roundnode] (leftterme) {\makebox[0.5cm]{34}};
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\node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{123}};
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%Lines
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\path[arrow] (leftterme.north) edge [bend left]
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node [pos=0.5, above] {+...\%}
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node [pos=0.5, below] {\times ...}
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(centerterm.north)
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;
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\end{tikzpicture}
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Taux d'évolution: \hfill Valeur finale: \hfill.
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\end{itemize}
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\afaire{Compléter les calculs}
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\end{document}
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