83 lines
4.1 KiB
TeX
83 lines
4.1 KiB
TeX
\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*{Taux d'évolution successifs}
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\begin{propriete}
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Quand une quantité subit des \textbf{évolution successives} $t_1, t_2, ...$, elle subit alors une \textbf{évolution globale}.
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Les taux d'évolution \textbf{ne peuvent pas} s'ajouter.
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\bigskip
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Il faut multiplier les \textbf{coefficient multiplicateur} entre eux.
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\begin{center}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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node distance=2cm and 2cm,
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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] (termA) {\makebox[0.5cm]{}};
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\node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}};
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\node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}};
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\node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}};
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\node (termE) [right=1cm of termD] {\makebox[0.5cm]{...}};
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\node[roundnode] (termF) [right=1cm of termE] {\makebox[0.5cm]{}};
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%Lines
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\path[arrow] (termA.north) edge [bend left=50] node [above] {$+t_1$} node [below] {$\times CM_1$} (termB.north) ;
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\path[arrow] (termB.north) edge [bend left=50] node [above] {$+t_2$} node [below] {$\times CM_2$} (termC.north) ;
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\path[arrow] (termC.north) edge [bend left=50] node [above] {$+t_3$} node [below] {$\times CM_3$} (termD.north) ;
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\path[arrow] (termA.south) edge [bend right=10] node [above] {Taux d'évolution global} node [below] {$\times CM_1 \times CM_2 \times CM_3 \times ...$} (termF.south);
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\end{tikzpicture}
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\end{center}
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\end{propriete}
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\paragraph{Exemples:}
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\begin{itemize}
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\item Une quantité a subit 5 augmentations de 10\%.
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\begin{center}
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\begin{tikzpicture}[
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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] (termA) {\makebox[0.5cm]{}};
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\node[roundnode] (termB) [right=2cm of termA] {\makebox[0.5cm]{}};
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\node[roundnode] (termC) [right=2cm of termB] {\makebox[0.5cm]{}};
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\node[roundnode] (termD) [right=2cm of termC] {\makebox[0.5cm]{}};
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\node[roundnode] (termE) [right=2cm of termD] {\makebox[0.5cm]{}};
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\node[roundnode] (termF) [right=2cm of termE] {\makebox[0.5cm]{}};
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%Lines
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\path[arrow] (termA.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termB.north) ;
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\path[arrow] (termB.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termC.north) ;
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\path[arrow] (termC.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termD.north) ;
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\path[arrow] (termD.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termE.north) ;
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\path[arrow] (termE.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termF.north) ;
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\path[arrow] (termA.south) edge [bend right=10] node [above] {Taux d'évolution global} node [below] {$\times ... \times ... \times ... \times ... \times ... = \times ...$} (termF.south);
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\end{tikzpicture}
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\end{center}
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Le coefficient global est donc de $CM = ...$
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On en déduit le \textbf{taux d'évolution global} $t = ...$
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\item Une quantité a subit une augmentation de 5\% puis un diminution de 10\% et enfin une autre augmentation de 5\%. Calculons le taux d'évolution global.
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\end{itemize}
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\afaire{Compléter les exemples}
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\end{document}
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