From 30d3a125c39a13a6618fdeab0714a1496db4737a Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 24 Feb 2022 16:19:59 +0100 Subject: [PATCH] =?UTF-8?q?Feat:=20toutes=20les=20le=C3=A7ons=20pour=20l'i?= =?UTF-8?q?nformation=20chiffr=C3=A9e?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/14_Information_Chiffrée_2/exercises.tex | 91 +++++++++++++----- .../plan_de_travail.pdf | Bin 1902292 -> 1902505 bytes 2nd/14_Information_Chiffrée_2/solutions.pdf | Bin 35120 -> 38048 bytes 3 files changed, 69 insertions(+), 22 deletions(-) diff --git a/2nd/14_Information_Chiffrée_2/exercises.tex b/2nd/14_Information_Chiffrée_2/exercises.tex index debefe7..1c0b159 100644 --- a/2nd/14_Information_Chiffrée_2/exercises.tex +++ b/2nd/14_Information_Chiffrée_2/exercises.tex @@ -84,13 +84,14 @@ \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[->] (leftterme.north) edge [bend left] + \path[arrow] (leftterme.north) edge [bend left] node [pos=0.5, above] {+25\%} node [pos=0.5, below] {\times CM = ...} (centerterm.north) @@ -101,13 +102,14 @@ \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[->] (leftterme.north) edge [bend left] + \path[arrow] (leftterme.north) edge [bend left] node [pos=0.5, above] {+...} node [pos=0.5, below] {\times 0.12} (centerterm.north) @@ -118,13 +120,14 @@ \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[->] (leftterme.north) edge [bend left] + \path[arrow] (leftterme.north) edge [bend left] node [pos=0.5, above] {+...\%} node [pos=0.5, below] {\times ...} (centerterm.north) @@ -207,22 +210,23 @@ \begin{center} \begin{tikzpicture}[ 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 \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=of termD] {\makebox[0.5cm]{...}}; - \node[roundnode] (termF) [right=of termE] {\makebox[0.5cm]{}}; + \node (termE) [right=1cm of termD] {\makebox[0.5cm]{...}}; + \node[roundnode] (termF) [right=1cm of termE] {\makebox[0.5cm]{}}; %Lines - \path[->] (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[->] (termC.north) edge [bend left=50] node [above] {$+t_3$} node [below] {$\times CM_3$} (termD.north) ; + \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[->] (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{center} \end{propriete} @@ -233,24 +237,24 @@ \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[roundnode] (termE) [right=of termD] {\makebox[0.5cm]{}}; - \node[roundnode] (termF) [right=of termE] {\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[->] (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[->] (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[->] (termE.north) edge [bend left=50] node [above] {$+10\%$} node [below] {$\times ...$} (termF.north) ; + \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[->] (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{center} Le coefficient global est donc de $CM = ...$ @@ -282,3 +286,46 @@ \begin{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} diff --git a/2nd/14_Information_Chiffrée_2/plan_de_travail.pdf b/2nd/14_Information_Chiffrée_2/plan_de_travail.pdf index ac70667d0816a2ef7c0f42652bbcb92792495f46..e47c0d62b274997f43c45cc786c3912fb09f10b4 100644 GIT binary patch delta 8725 zcmajjWl-GSy9aQb7I$6T-5nNPSfKdgt}PUI-y+3Y910Y7cP(0^xKrHS-Tm_W%e^n} zeCLx%&UuoVyvWIu{Ec)ij&`jIM}p_)6iDJM0^r4GAt6Hf2|{k4@${4l)IB{JOz_4t zPWac-%}+&*gq)B9$S7Ba564s#^1z8D3MCctW@7;@2F&4&mzT~!b%BZJh47QZnK4B$+W$MQ6_6T`8c8 z0I4-X)5<0eAM(o|)WN=Cy1dpuh5d&G@ImBxQ60;8K!W@Av-Rae1(waSo0u+U^#)&t z>KRPQ@;(m_C}3c7#02a{(XsUBS@youb9!G=`V3mx;hK4}0{MlqUndzC*Z(Ik|J*3* zR|Q4M0V7(cLg{Qte{pBBI!LV>05`rS=Pbx9g-yx@#F?m3k~X?jB_m8+m6PoI z`%0PXFn!YsLQB`Muaex!VO-Xdv%$G#Vi3`Cw3T<^GZp_+<&xi^Das$9zV2NEUmZzi z2Zn|m29e=fqgE`32cjyb=W+@fE4--G4%on#P9zePlW1&zmN2wPh_hhN{x|8ev(jw0_i(h-Qgg=O(NzU`xelts6>gJMver>3rfDBUWKcD$c~4#QH?c&w 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