From 1b429865180527e89d7775dc569a4863b5bf50f1 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 28 Feb 2022 16:00:37 +0100 Subject: [PATCH] =?UTF-8?q?Feat:=20mises=20=C3=A0=20jour=20en=20fonction?= =?UTF-8?q?=20des=20remarques=20de=20Camille?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../2B_coef_mult.tex | 95 ++++++++ .../3B_successive.pdf | Bin 0 -> 27425 bytes .../3B_successive.tex | 82 +++++++ .../4B_reciproque.pdf | Bin 0 -> 25957 bytes .../4B_reciproque.tex | 49 ++++ 2nd/14_Information_Chiffrée_2/exercises.tex | 218 ++---------------- 2nd/14_Information_Chiffrée_2/index.rst | 17 +- .../plan_de_travail.pdf | Bin 1906013 -> 1905911 bytes .../plan_de_travail.tex | 8 +- 2nd/14_Information_Chiffrée_2/solutions.pdf | Bin 50294 -> 37672 bytes 10 files changed, 268 insertions(+), 201 deletions(-) create mode 100644 2nd/14_Information_Chiffrée_2/2B_coef_mult.tex create mode 100644 2nd/14_Information_Chiffrée_2/3B_successive.pdf create mode 100644 2nd/14_Information_Chiffrée_2/3B_successive.tex create mode 100644 2nd/14_Information_Chiffrée_2/4B_reciproque.pdf create mode 100644 2nd/14_Information_Chiffrée_2/4B_reciproque.tex diff --git a/2nd/14_Information_Chiffrée_2/2B_coef_mult.tex b/2nd/14_Information_Chiffrée_2/2B_coef_mult.tex new file mode 100644 index 0000000..e14d762 --- /dev/null +++ b/2nd/14_Information_Chiffrée_2/2B_coef_mult.tex @@ -0,0 +1,95 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Information chiffrée 2 - Cours} +\date{2022-01-13} + +\pagestyle{empty} + +\begin{document} + +\maketitle + + +\section*{Lien entre taux d'évolution et coefficient multiplicateur} + +\begin{propriete} + Soit $t$ le taux d'évolution qui fait évolution $v_i$ vers $v_f$ alors + \[ + v_f = (1+t)v_i + \] +\end{propriete} +\begin{definition} + $1+t$ est appelé \textbf{coefficient multiplicateur}, noté $CM$, associé au taux d'évolution $t$. + + \noindent + On a ainsi + \[ + CM = 1+t \qquad \mbox{ou encore} \qquad t = CM - 1 + \] + et + \[ + v_f = CM \times v_i \qquad \mbox{ ou encore } \qquad CM = \frac{v_f}{v_i} + \] +\end{definition} +\paragraph{Exemples} +\begin{itemize} + \item + \begin{tikzpicture}[ + baseline, + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + arrow/.style={->, shorten >=5pt, shorten <=5pt} + ] + %Nodes + \node[roundnode] (leftterme) {\makebox[0.5cm]{120}}; + \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}}; + + %Lines + \path[arrow] (leftterme.north) edge [bend left] + node [pos=0.5, above] {+25\%} + node [pos=0.5, below] {\times CM = ...} + (centerterm.north) + ; + \end{tikzpicture} + Coefficient multiplicateur: \hfill Valeur finale: \hfill. + \item + \begin{tikzpicture}[ + baseline, + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + arrow/.style={->, shorten >=5pt, shorten <=5pt} + ] + %Nodes + \node[roundnode] (leftterme) {\makebox[0.5cm]{55}}; + \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}}; + + %Lines + \path[arrow] (leftterme.north) edge [bend left] + node [pos=0.5, above] {+...} + node [pos=0.5, below] {\times 0.12} + (centerterm.north) + ; + \end{tikzpicture} + Taux d'évolution: \hfill Valeur finale: \hfill. + \item + \begin{tikzpicture}[ + baseline, + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + arrow/.style={->, shorten >=5pt, shorten <=5pt} + ] + %Nodes + \node[roundnode] (leftterme) {\makebox[0.5cm]{34}}; + \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{123}}; + + %Lines + \path[arrow] (leftterme.north) edge [bend left] + node [pos=0.5, above] {+...\%} + node [pos=0.5, below] {\times ...} + (centerterm.north) + ; + \end{tikzpicture} + Taux d'évolution: \hfill Valeur finale: \hfill. +\end{itemize} + +\afaire{Compléter les calculs} +\end{document diff --git 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, shorten >=5pt, shorten <=5pt} + ] + %Nodes + \node[roundnode] (termA) {\makebox[0.5cm]{}}; + \node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}}; + \node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}}; + \node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}}; + \node (termE) [right=1cm of termD] {\makebox[0.5cm]{...}}; + \node[roundnode] (termF) [right=1cm of termE] {\makebox[0.5cm]{}}; + + %Lines + \path[arrow] (termA.north) edge [bend left=50] node [above] {$+t_1$} node [below] {$\times CM_1$} (termB.north) ; + \path[arrow] (termB.north) edge [bend left=50] node [above] {$+t_2$} node [below] {$\times CM_2$} (termC.north) ; + \path[arrow] (termC.north) edge [bend left=50] node [above] {$+t_3$} node [below] {$\times CM_3$} (termD.north) ; + + \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{center} +\end{propriete} + +\paragraph{Exemples:} +\begin{itemize} + \item Une quantité a subit 5 augmentations de 10\%. + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + arrow/.style={->, shorten >=5pt, shorten <=5pt} + ] + %Nodes + \node[roundnode] (termA) {\makebox[0.5cm]{}}; + \node[roundnode] (termB) [right=2cm of termA] {\makebox[0.5cm]{}}; + \node[roundnode] (termC) [right=2cm of termB] {\makebox[0.5cm]{}}; + \node[roundnode] (termD) [right=2cm of termC] {\makebox[0.5cm]{}}; + \node[roundnode] (termE) [right=2cm of termD] {\makebox[0.5cm]{}}; + \node[roundnode] (termF) [right=2cm of termE] {\makebox[0.5cm]{}}; + + %Lines + \path[arrow] (termA.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termB.north) ; + \path[arrow] (termB.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termC.north) ; + \path[arrow] (termC.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termD.north) ; + \path[arrow] (termD.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termE.north) ; + \path[arrow] (termE.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termF.north) ; + + \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{center} + Le coefficient global est donc de $CM = ...$ + + On en déduit le \textbf{taux d'évolution global} $t = ...$ + \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. +\end{itemize} +\afaire{Compléter les exemples} + +\end{document} diff --git a/2nd/14_Information_Chiffrée_2/4B_reciproque.pdf b/2nd/14_Information_Chiffrée_2/4B_reciproque.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5186bb58240510d862669d90ca8b4d638ac351e1 GIT binary patch literal 25957 zcmce;1CT7;((gUCZQHhO+qP|UkFm$L%{{ic$F^0nAguOV+_ zWoqm~K(Fj-i z{_j2iwf!@$Wa@11>SS!{Ou+hQNa@d^ENxs&o&LPq7`m8>m>S!g{5h|Tshzot1py-~ z0Usa1e?Op{U7Sn}ZJ|8Ye#1{IP)zRt0f2u3-awh!nf!ly{=EC^`q}>+`9Eg|$G^=E z&i|+#jDLCX-{TO*zk=XD=MhGxf1f4)+1O(I_XQWzU+(_T`Go1O5cu~*7ZdY;){?)L z$$yh2Z2wtH{tD)Qk0s21O~L<;u79<}GqEr;|6`H=#}a?3C2dd4j?{gw{(x^mmn({d z05Y1uBVf12SQjoRx0MYG#NB(4*wdqbyIGyW+k$*Shd`2%QV})eRj=2S^~F1O`dh9h zS7?=DiX^mAZWpo1(d-S@zIFTK^Y_)2;d86Ed{Rq4IQ{0sjVn0FM=2R@NIlCdMu@wg zmq$+bMe%|-ZB;2w^cys~M83C+bmezZKsOBnAz`eF?OLQRF?wfwB7MhfZ*~)$k4T`9%iGq!$mmcuu&iTWKl^>+1aL%N)UHjiFBqE>~=hinuC--=FGSAonH00khgj5e2v5435-9izn;G0IVl@%=(zx?A};_ 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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] {$+t$} 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{document} diff --git a/2nd/14_Information_Chiffrée_2/exercises.tex b/2nd/14_Information_Chiffrée_2/exercises.tex index d1ad212..f5f2876 100644 --- a/2nd/14_Information_Chiffrée_2/exercises.tex +++ b/2nd/14_Information_Chiffrée_2/exercises.tex @@ -14,14 +14,10 @@ \end{enumerate} \end{exercise} -\begin{exercise}[subtitle={Contre-intuitions}, step={2}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\faIcon{users}}] +\begin{exercise}[subtitle={Contre-intuitions}, step={1}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\faIcon{users}}] Au regard des deux situations étudiées dans l'exercice précédent, quelles sont les deux erreurs que l'on aurait envie de faire avec les pourcentages d'évolutions mais qu'il va falloir éviter? \end{exercise} -\begin{solution} - -\end{solution} - % ---- % 2E: Taux d'évolution et coefficient multiplicateur @@ -58,89 +54,6 @@ \end{enumerate} \end{exercise} -\begin{solution} - \section*{Lien entre taux d'évolution et coefficient multiplicateur} - - \begin{propriete} - Soit $t$ le taux d'évolution qui fait évolution $v_i$ vers $v_f$ alors - \[ - v_f = (1+t)v_i - \] - \end{propriete} - \begin{definition} - $1+t$ est appelé \textbf{coefficient multiplicateur}, noté $CM$, associé au taux d'évolution $t$. - - \noindent - On a ainsi - \[ - CM = 1+t \qquad \mbox{ou encore} \qquad t = CM - 1 - \] - et - \[ - v_f = CM \times v_i \qquad \mbox{ ou encore } \qquad CM = \frac{v_f}{v_i} - \] - \end{definition} - \paragraph{Exemples} - \begin{itemize} - \item - \begin{tikzpicture}[ - baseline, - roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, - arrow/.style={->, shorten >=5pt, shorten <=5pt} - ] - %Nodes - \node[roundnode] (leftterme) {\makebox[0.5cm]{120}}; - \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}}; - - %Lines - \path[arrow] (leftterme.north) edge [bend left] - node [pos=0.5, above] {+25\%} - node [pos=0.5, below] {\times CM = ...} - (centerterm.north) - ; - \end{tikzpicture} - Coefficient multiplicateur: \hfill Valeur finale: \hfill. - \item - \begin{tikzpicture}[ - baseline, - roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, - arrow/.style={->, shorten >=5pt, shorten <=5pt} - ] - %Nodes - \node[roundnode] (leftterme) {\makebox[0.5cm]{55}}; - \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{...}}; - - %Lines - \path[arrow] (leftterme.north) edge [bend left] - node [pos=0.5, above] {+...} - node [pos=0.5, below] {\times 0.12} - (centerterm.north) - ; - \end{tikzpicture} - Taux d'évolution: \hfill Valeur finale: \hfill. - \item - \begin{tikzpicture}[ - baseline, - roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, - arrow/.style={->, shorten >=5pt, shorten <=5pt} - ] - %Nodes - \node[roundnode] (leftterme) {\makebox[0.5cm]{34}}; - \node[roundnode] (centerterm) [right=2cm of leftterme] {\makebox[0.5cm]{123}}; - - %Lines - \path[arrow] (leftterme.north) edge [bend left] - node [pos=0.5, above] {+...\%} - node [pos=0.5, below] {\times ...} - (centerterm.north) - ; - \end{tikzpicture} - Taux d'évolution: \hfill Valeur finale: \hfill. - \end{itemize} - - \afaire{Compléter les calculs} -\end{solution} - \begin{exercise}[subtitle={Questions divers}, step={2}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\faIcon{tools}}] Répondre aux questions suivantes en détaillant les calculs \begin{enumerate} @@ -201,76 +114,6 @@ \end{enumerate} \end{exercise} -\begin{solution} - \section*{Taux d'évolution successifs} - - \begin{propriete} - Quand une quantité subit des \textbf{évolution successives} $t_1, t_2, ...$, elle subit alors une \textbf{évolution globale}. - - Les taux d'évolution \textbf{ne peuvent pas} s'ajouter. - - \bigskip - - Il faut multiplier les \textbf{coefficient multiplicateur} entre eux. - - \begin{center} - \begin{tikzpicture}[ - 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 - \node[roundnode] (termA) {\makebox[0.5cm]{}}; - \node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}}; - \node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}}; - \node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}}; - \node (termE) [right=1cm of termD] {\makebox[0.5cm]{...}}; - \node[roundnode] (termF) [right=1cm of termE] {\makebox[0.5cm]{}}; - - %Lines - \path[arrow] (termA.north) edge [bend left=50] node [above] {$+t_1$} node [below] {$\times CM_1$} (termB.north) ; - \path[arrow] (termB.north) edge [bend left=50] node [above] {$+t_2$} node [below] {$\times CM_2$} (termC.north) ; - \path[arrow] (termC.north) edge [bend left=50] node [above] {$+t_3$} node [below] {$\times CM_3$} (termD.north) ; - - \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{center} - \end{propriete} - - \paragraph{Exemples:} - \begin{itemize} - \item Une quantité a subit 5 augmentations de 10\%. - \begin{center} - \begin{tikzpicture}[ - roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, - arrow/.style={->, shorten >=5pt, shorten <=5pt} - ] - %Nodes - \node[roundnode] (termA) {\makebox[0.5cm]{}}; - \node[roundnode] (termB) [right=2cm of termA] {\makebox[0.5cm]{}}; - \node[roundnode] (termC) [right=2cm of termB] {\makebox[0.5cm]{}}; - \node[roundnode] (termD) [right=2cm of termC] {\makebox[0.5cm]{}}; - \node[roundnode] (termE) [right=2cm of termD] {\makebox[0.5cm]{}}; - \node[roundnode] (termF) [right=2cm of termE] {\makebox[0.5cm]{}}; - - %Lines - \path[arrow] (termA.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termB.north) ; - \path[arrow] (termB.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termC.north) ; - \path[arrow] (termC.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termD.north) ; - \path[arrow] (termD.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termE.north) ; - \path[arrow] (termE.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termF.north) ; - - \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{center} - Le coefficient global est donc de $CM = ...$ - - On en déduit le \textbf{taux d'évolution global} $t = ...$ - \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. - \end{itemize} - \afaire{Compléter les exemples} -\end{solution} - \begin{exercise}[subtitle={Techniques}, step={3}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\faIcon{tools}}] \begin{enumerate} \item Calculer le taux d'évolution global d'une évolution constituée de 3 augmentations de 30\%. @@ -387,43 +230,6 @@ Détailler toutes les méthodes développée dans le groupe pour trouver le taux d'évolution "réciproque" de la baisse de 60\% dans l'exercice précédent. \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} - \begin{exercise}[subtitle={Techniques}, step={4}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\trainMode}] \begin{enumerate} \item Une robe, soldée à -15\%, peut être achetée à 40\euro. Quel était son prix avant les soldes? @@ -443,3 +249,25 @@ \item Pour cela, il faut contrer la différence de 15\% donc la multiplication par $1+\frac{15}{100} = 1.15$. Il faut diviser les prix par 1.15 ou encore les multiplier par $1\div 1.15 = 0.87$. Le taux d'évolution est donc de $t = 0.87 - 1 = -0.13 = -13\%$. \end{enumerate} \end{solution} + +\begin{exercise}[subtitle={Tableau}, step={4}, origin={Création}, topics={ Information Chiffrée 2 }, tags={ Information chiffrée }, mode={\trainMode}] + Compléter le tableau suivant + + \begin{center} + \begin{tabular}{|*{4}{p{4cm}|}} + \hline + Valeur initiale & Valeur finale & Taux d'évolution & Coefficient multiplicateur \\ + \hline + & 45 & +20\% & \\ + \hline + & 87 & -15\% & \\ + \hline + & 4.3 & & 0.8\\ + \hline + & 345 & & 1.5\\ + \hline + & 0.34 & +150\% & \\ + \hline + \end{tabular} + \end{center} +\end{exercise} diff --git a/2nd/14_Information_Chiffrée_2/index.rst b/2nd/14_Information_Chiffrée_2/index.rst index 172994b..c1ec5db 100644 --- a/2nd/14_Information_Chiffrée_2/index.rst +++ b/2nd/14_Information_Chiffrée_2/index.rst @@ -2,7 +2,7 @@ Information Chiffrée 2 ###################### :date: 2022-02-07 -:modified: 2022-02-22 +:modified: 2022-02-28 :authors: Benjamin Bertrand :tags: Information chiffrée :category: 2nd @@ -55,6 +55,10 @@ On travaillera aussi cette transformation en sens inverse c'est à dire du coeff Bilan: Passage de l'un à l'autre (on l'a déjà fait dans le premier chapitre mais on le refait ici!) +.. image:: ./2B_coef_mult.pdf + :height: 200px + :alt: Bilan sur le coefficient multiplicateur + Étape 3: Évolutions successives ------------------------------- @@ -62,8 +66,19 @@ On a vu que l'on ne pouvait pas ajouter des taux d'évolutions. La répétition Bilan: Taux d'évolution successif +.. image:: ./3B_successive.pdf + :height: 200px + :alt: Bilan sur les évolutions successives + + Étape 4: Évolutions réciproques ------------------------------- Calcul du taux d'évolution réciproque avec la formule du taux d'évolution. Recherche d'un lien (pas facile à voir!) puis calcul du coefficient multiplicateur lié aux deux taux d'évolutions et le lien peut être plus simple. +Bilan: + +.. image:: ./4B_reciproque.pdf + :height: 200px + :alt: Bilan sur les évolutions réciproque + diff --git a/2nd/14_Information_Chiffrée_2/plan_de_travail.pdf b/2nd/14_Information_Chiffrée_2/plan_de_travail.pdf index d29c9e04ab3cc0401b20f1463361b558d2d52f7e..d68540541bb1ea173dd13447ac6bbef20551af0d 100644 GIT binary patch delta 28984 zcmZshV{j)yySF#CZQHhOb7R{ZC;yFYCmY+gZQHi(@=s;2M$ z-J4}D&!sLk2H-%935MX50A^NpLVkY2|Gl7{U7Sn}ZK2)QE;D5k)?1KakCt3IA>5m&+9_Pl@EmK9%`yIs4tJ1d>g#w-I!lM?C4 zD1@g1k~GU?5u$nsn`)Uh0GckH%_79Mt&KcNc7~?MiDQLd z^;%>#emy6UYNA2FshT;pooJ4edPRHdq^lc2Z)_YLX424gE@ZR5_MsRR_P_cq+^4 zjG=ue-{uio-8%G3Z8l1F=ks zYNU^l$2H`loV4n$g%WuWQz_J_l#<-4mJXTeRhu5`LNrP*%FAfkxwMxL_FfRH#ll>a zjz#90MlGtGtE-n^?2RRT&}6T;>5oWi)67y^maB`V?(m>ol7H@;jGBCx7r!ke(mes>E`cpca z0@`+{P2;7P+!W1}_f|ig;SN6*8UE1BGFFwOc@PZ>6Cp95IP43NgL5lX`kRoS>bmKY~ 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