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Feat: toutes les leçons pour l'information chiffrée

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Bertrand Benjamin 2022-02-24 16:19:59 +01:00
parent f4b89a9133
commit 30d3a125c3
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2nd/14_Information_Chiffrée_2/exercises.tex
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@ -84,13 +84,14 @@
\begin{tikzpicture}[ \begin{tikzpicture}[
baseline, baseline,
roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
arrow/.style={->, shorten >=5pt, shorten <=5pt}
] ]
%Nodes %Nodes
\node[roundnode] (leftterme) {\makebox[0.5cm]{120}}; \node[roundnode] (leftterme) {\makebox[0.5cm]{120}};
\node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}}; \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}};
%Lines %Lines
\path[->] (leftterme.north) edge [bend left] \path[arrow] (leftterme.north) edge [bend left]
node [pos=0.5, above] {+25\%} node [pos=0.5, above] {+25\%}
node [pos=0.5, below] {\times CM = ...} node [pos=0.5, below] {\times CM = ...}
(centerterm.north) (centerterm.north)
@ -101,13 +102,14 @@
\begin{tikzpicture}[ \begin{tikzpicture}[
baseline, baseline,
roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
arrow/.style={->, shorten >=5pt, shorten <=5pt}
] ]
%Nodes %Nodes
\node[roundnode] (leftterme) {\makebox[0.5cm]{55}}; \node[roundnode] (leftterme) {\makebox[0.5cm]{55}};
\node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}}; \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}};
%Lines %Lines
\path[->] (leftterme.north) edge [bend left] \path[arrow] (leftterme.north) edge [bend left]
node [pos=0.5, above] {+...} node [pos=0.5, above] {+...}
node [pos=0.5, below] {\times 0.12} node [pos=0.5, below] {\times 0.12}
(centerterm.north) (centerterm.north)
@ -118,13 +120,14 @@
\begin{tikzpicture}[ \begin{tikzpicture}[
baseline, baseline,
roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
arrow/.style={->, shorten >=5pt, shorten <=5pt}
] ]
%Nodes %Nodes
\node[roundnode] (leftterme) {\makebox[0.5cm]{34}}; \node[roundnode] (leftterme) {\makebox[0.5cm]{34}};
\node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{123}}; \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{123}};
%Lines %Lines
\path[->] (leftterme.north) edge [bend left] \path[arrow] (leftterme.north) edge [bend left]
node [pos=0.5, above] {+...\%} node [pos=0.5, above] {+...\%}
node [pos=0.5, below] {\times ...} node [pos=0.5, below] {\times ...}
(centerterm.north) (centerterm.north)
@ -207,22 +210,23 @@
\begin{center} \begin{center}
\begin{tikzpicture}[ \begin{tikzpicture}[
roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
node distance=2cm and 2cm node distance=2cm and 2cm,
arrow/.style={->, shorten >=5pt, shorten <=5pt}
] ]
%Nodes %Nodes
\node[roundnode] (termA) {\makebox[0.5cm]{}}; \node[roundnode] (termA) {\makebox[0.5cm]{}};
\node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}}; \node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}};
\node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}}; \node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}};
\node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}}; \node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}};
\node (termE) [right=of termD] {\makebox[0.5cm]{...}}; \node (termE) [right=1cm of termD] {\makebox[0.5cm]{...}};
\node[roundnode] (termF) [right=of termE] {\makebox[0.5cm]{}}; \node[roundnode] (termF) [right=1cm of termE] {\makebox[0.5cm]{}};
%Lines %Lines
\path[->] (termA.north) edge [bend left=50] node [above] {$+t_1$} node [below] {$\times CM_1$} (termB.north) ; \path[arrow] (termA.north) edge [bend left=50] node [above] {$+t_1$} node [below] {$\times CM_1$} (termB.north) ;
\path[->] (termB.north) edge [bend left=50] node [above] {$+t_2$} node [below] {$\times CM_2$} (termC.north) ; \path[arrow] (termB.north) edge [bend left=50] node [above] {$+t_2$} node [below] {$\times CM_2$} (termC.north) ;
\path[->] (termC.north) edge [bend left=50] node [above] {$+t_3$} node [below] {$\times CM_3$} (termD.north) ; \path[arrow] (termC.north) edge [bend left=50] node [above] {$+t_3$} node [below] {$\times CM_3$} (termD.north) ;
\path[->] (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); \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);
\end{tikzpicture} \end{tikzpicture}
\end{center} \end{center}
\end{propriete} \end{propriete}
@ -233,24 +237,24 @@
\begin{center} \begin{center}
\begin{tikzpicture}[ \begin{tikzpicture}[
roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
node distance=2cm and 2cm arrow/.style={->, shorten >=5pt, shorten <=5pt}
] ]
%Nodes %Nodes
\node[roundnode] (termA) {\makebox[0.5cm]{}}; \node[roundnode] (termA) {\makebox[0.5cm]{}};
\node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}}; \node[roundnode] (termB) [right=2cm of termA] {\makebox[0.5cm]{}};
\node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}}; \node[roundnode] (termC) [right=2cm of termB] {\makebox[0.5cm]{}};
\node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}}; \node[roundnode] (termD) [right=2cm of termC] {\makebox[0.5cm]{}};
\node[roundnode] (termE) [right=of termD] {\makebox[0.5cm]{}}; \node[roundnode] (termE) [right=2cm of termD] {\makebox[0.5cm]{}};
\node[roundnode] (termF) [right=of termE] {\makebox[0.5cm]{}}; \node[roundnode] (termF) [right=2cm of termE] {\makebox[0.5cm]{}};
%Lines %Lines
\path[->] (termA.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termB.north) ; \path[arrow] (termA.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termB.north) ;
\path[->] (termB.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termC.north) ; \path[arrow] (termB.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termC.north) ;
\path[->] (termC.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termD.north) ; \path[arrow] (termC.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termD.north) ;
\path[->] (termD.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termE.north) ; \path[arrow] (termD.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termE.north) ;
\path[->] (termE.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termF.north) ; \path[arrow] (termE.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termF.north) ;
\path[->] (termA.south) edge [bend right=10] node [above] {Taux d'évolution global} node [below] {$\times ... \times ... \times ... \times ... \times ... = \times ...$} (termF.south); \path[arrow] (termA.south) edge [bend right=10] node [above] {Taux d'évolution global} node [below] {$\times ... \times ... \times ... \times ... \times ... = \times ...$} (termF.south);
\end{tikzpicture} \end{tikzpicture}
\end{center} \end{center}
Le coefficient global est donc de $CM = ...$ Le coefficient global est donc de $CM = ...$
@ -282,3 +286,46 @@
\begin{solution} \begin{solution}
<++> <++>
\end{solution} \end{solution}
\begin{exercise}[subtitle={Évolutions réciproques}, step={4}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\faIcon{users}}]
<++>
\end{exercise}
\begin{solution}
\section*{Taux d'évolution réciproque}
\begin{propriete}
Quand une quantité subit une évolution et que l'on souhaite revenir à la valeur initiale, elle subit une \textbf{évolution réciproque}.
\begin{center}
\begin{tikzpicture}[
roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
node distance=5cm and 5cm,
arrow/.style={->, shorten >=5pt, shorten <=5pt}
]
%Nodes
\node[roundnode] (termA) {\makebox[0.5cm]{$v_i$}};
\node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{$v_f$}};
%Lines
\path[arrow] (termA.north) edge [bend left] node [above] {$+t_1$} node [below] {$\times CM$} (termB.north) ;
\path[arrow] (termB.south) edge [bend left] node [above] {$\times \dfrac{1}{CM}$} node [below] {Taux d'évolution réciproque} (termA.south);
\end{tikzpicture}
\end{center}
Le coefficient multiplicateur de l'évolution réciproque est égal à $\dfrac{1}{CM}$.
Le taux d'évolution réciproque est égal à $\dfrac{1}{CM} - 1$
\end{propriete}
\paragraph{Exemples:}
\begin{itemize}
\item Un article coûte 50\euro hors taxe. Une diminution de 20\% fait passer le prix à 40\euro. Quelle devra être l'augmentation pour revenir au prix initial?
\vspace{1cm}
\item Une entreprise a augmenté ses emissions de CO2 de 14\% en un an. Quelle devra être l'évolution pour revenir aux émissions d'avant cette augmentation?
\vspace{1cm}
\end{itemize}
\afaire{Traiter les exemples}
\end{solution}

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2nd/14_Information_Chiffrée_2/plan_de_travail.pdf
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2nd/14_Information_Chiffrée_2/solutions.pdf
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