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zvAUt0vFZL8%U19sHUlWJaz0`A)=>Uz4HKAdh=sQ;bo|Eh&^g@$V=pad>Or~dtEaP>ISex_CmRzp3^}>Df&|R}0whjGNB{r; diff --git a/Tstmg/05_Suites_et_moyennes/1B_moyennes.tex b/Tstmg/05_Suites_et_moyennes/1B_moyennes.tex index b425fcc..ae5409f 100644 --- a/Tstmg/05_Suites_et_moyennes/1B_moyennes.tex +++ b/Tstmg/05_Suites_et_moyennes/1B_moyennes.tex @@ -22,21 +22,21 @@ m = \frac{a + b}{2} = (a + b) \times \frac{1}{2} \] - \vspace{1em} - - \begin{center} - \begin{tikzpicture}[scale=1.5] - \draw[thick,->] (0,0) -- (4,0); - \draw[thick] (0.5,-0.1) -- (0.5,0.1) node[below=3pt] {$a$}; - \draw[thick] (3.5,-0.1) -- (3.5,0.1) node[below=3pt] {$b$}; - \draw[thick,red] (2,-0.15) -- (2,0.15) node[below=5pt] {$m$}; - - \draw[<->] (0.5,0.3) -- (2,0.3) node[midway,above] {\small $\frac{b-a}{2}$}; - \draw[<->] (2,0.3) -- (3.5,0.3) node[midway,above] {\small $\frac{b-a}{2}$}; - \end{tikzpicture} - \end{center} - - La moyenne arithmétique est au \textbf{milieu} de $a$ et $b$. + % \vspace{1em} + % + % \begin{center} + % \begin{tikzpicture}[scale=1.5] + % \draw[thick,->] (0,0) -- (4,0); + % \draw[thick] (0.5,-0.1) -- (0.5,0.1) node[below=3pt] {$a$}; + % \draw[thick] (3.5,-0.1) -- (3.5,0.1) node[below=3pt] {$b$}; + % \draw[thick,red] (2,-0.15) -- (2,0.15) node[below=5pt] {$m$}; + % + % \draw[<->] (0.5,0.3) -- (2,0.3) node[midway,above] {\small $\frac{b-a}{2}$}; + % \draw[<->] (2,0.3) -- (3.5,0.3) node[midway,above] {\small $\frac{b-a}{2}$}; + % \end{tikzpicture} + % \end{center} + % + % La moyenne arithmétique est au \textbf{milieu} de $a$ et $b$. \end{definition} @@ -51,27 +51,27 @@ m = \sqrt{a \times b} = (a \times b)^{\frac{1}{2}} \] - \vspace{1em} - - \begin{center} - \begin{tikzpicture}[scale=0.8] - \draw[thick] (0,0) rectangle (4,2); - \draw[dashed] (0,0) -- (4,2); - \node at (2,-0.5) {$a$}; - \node at (-0.5,1) {$b$}; - - \draw[thick,red] (0,0) -- (2.828,2.828); - \node[red] at (1.2,1.8) {$m$}; - - \draw[thick,red] (2.828,0) -- (2.828,2.828); - \node[red] at (3.3,1.4) {$m$}; - - \draw[thick] (2.828,-0.1) -- (2.828,0.1); - \draw[thick] (4.1,2.828) -- (3.9,2.828); - \end{tikzpicture} - \end{center} - - La moyenne géométrique est le côté d'un \textbf{carré} d'aire $a \times b$. + % \vspace{1em} + % + % \begin{center} + % \begin{tikzpicture}[scale=0.8] + % \draw[thick] (0,0) rectangle (4,2); + % \draw[dashed] (0,0) -- (4,2); + % \node at (2,-0.5) {$a$}; + % \node at (-0.5,1) {$b$}; + % + % \draw[thick,red] (0,0) -- (2.828,2.828); + % \node[red] at (1.2,1.8) {$m$}; + % + % \draw[thick,red] (2.828,0) -- (2.828,2.828); + % \node[red] at (3.3,1.4) {$m$}; + % + % \draw[thick] (2.828,-0.1) -- (2.828,0.1); + % \draw[thick] (4.1,2.828) -- (3.9,2.828); + % \end{tikzpicture} + % \end{center} + % + % La moyenne géométrique est le côté d'un \textbf{carré} d'aire $a \times b$. \end{definition} @@ -87,6 +87,35 @@ \end{itemize} - \afaire{} +\afaire{} +\begin{methode}[Taux d'évolution moyen] + \begin{minipage}{0.65\textwidth} + Un quantité subit une transformation global d'un taux d'évolution $t_{global}$. + + On souhaite découper cette évolution en deux évolutions identiques alors le taux d'évolution de chacune de ces évolutions se calcule avec + $$ t_{moyen} = \sqrt{(1 + t_{global})} - 1 $$ + \end{minipage} + \hfill + \begin{minipage}{0.3\textwidth} + \begin{tikzpicture}[scale=0.8, + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + \node[roundnode] (a) {}; + \node[roundnode, fill=green!30] (b) [right=1.5cm of a] {}; + \node[roundnode] (c) [right=1.5cm of b] {}; + + \path[->] (a.north) edge [bend left] node [above] {$t_{global}$} (c.north); + \path[->] (a.south) edge [bend right] node [below] {$t_{moyen}$} (b.south); + \path[->] (b.south) edge [bend right] node [below] {$t_{moyen}$} (c.south); + \end{tikzpicture} + \end{minipage} +\end{methode} + +\paragraph{Exemple}:~ +Le chiffre d'affaire d'une entreprise est passé de 1 million d'euro à 1,5 millions d'euros en 2ans. 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