Début du chapitre sur l'utilisation des formules
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\documentclass[a5paper,12pt]{article}
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\usepackage{myXsim}
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\title{Distance d'arrêt}
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\date{Janvier 2018}
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\tribe{Troisième}
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\renewcommand{\lexo}{%
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\setcounter{exo}{0}
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\begin{Exo}
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\begin{center}
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{\Large\textbf{Distance d'arrêt}}
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\end{center}
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La distance d’arrêt pour un automobiliste est la distance qu'il parcourt entre le moment où il voit un obstacle et le moment où il s’arrête après avoir freiné.
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La distance d'arrêt, notée $D$, depend de la vitesse du conducteur $V$ et de son état:
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\begin{itemize}
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\item Pour un conducteur lucide:
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\[D = V\div 6 + 0,007\times V^2\]
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\item Pour un conducteur peu lucide:
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\[D = V\div 2 + 0,007\times V^2\]
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\end{itemize}
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\begin{enumerate}
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\item Complète le tableau suivant en écrivant les calculs sur ton cahier.
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\hspace{-0.7cm}
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\begin{tabular}{|m{3.5cm}|*{5}{p{1.3cm}|}}
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\hline
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Vitesse $V$ en km/h & 50 & 90 & 100 & 110 & 130 \\
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\hline
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Distance $D$ d'arrêt pour le conducteur lucide & & & & & \\
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\hline
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Distance $D$ d'arrêt pour le conducteur peu lucide & & & & & \\
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\hline
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\end{tabular}
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\item Un conducteur roule à 100 km/h. Un obstacle surgit à 100 m de lui. Pourra-t-il s’arrêter à temps ?
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\item Un conducteur lucide veut pouvoir s’arrêter en 10 mètres au maximum. Détermine la vitesse qu’il ne doit pas dépasser.
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\end{enumerate}
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\end{Exo}
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}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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La distance d’arrêt pour un automobiliste est la distance qu'il parcourt entre le moment où il voit un obstacle et le moment où il s’arrête après avoir freiné.
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La distance d'arrêt, notée $D$, depend de la vitesse du conducteur $V$ et de son état:
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\begin{itemize}
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\item Pour un conducteur lucide:
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\[D = \frac{V}{6} + 0,007\; V^2\]
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\item Pour un conducteur peu lucide:
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\[D = \frac{V}{2} + 0,007\; V^2\]
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\end{itemize}
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\begin{enumerate}
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\item Complète le tableau suivant en écrivant les calculs sur ton cahier.
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\hspace{-1cm}
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\begin{tabular}{|m{3.5cm}|*{5}{p{1.3cm}|}}
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\hline
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Vitesse $V$ en km/h & 50 & 90 & 100 & 110 & 130 \\
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\hline
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Distance $D$ d'arrêt pour le conducteur lucide & & & & & \\
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\hline
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Distance $D$ d'arrêt pour le conducteur peu lucide & & & & & \\
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\hline
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\end{tabular}
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\item Un conducteur roule à 100 km/h. Un obstacle surgit à 100 m de lui. Pourra-t-il s’arrêter à temps ?
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\item Un conducteur lucide veut pouvoir s’arrêter en 10 mètres au maximum. Détermine la vitesse qu’il ne doit pas dépasser.
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\end{enumerate}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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\documentclass[landscape, a5paper,12pt]{article}
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\usepackage{myXsim}
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\title{Réceptions}
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\date{Janvier 2018}
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\tribe{Troisième}
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\pagestyle{empty}
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\begin{document}
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%\maketitle
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\noindent
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Lors d'une réception, le serveur doit choisir le verre le plus adapté pour servir 15cL ($=150cm^3$).
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Pour cela il doit choisir parmi tous les verres à sa disposition:
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\begin{multicols}{3}
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\includegraphics[scale=0.1]{./fig/V_pave} \textbf{Verres pavé}
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\begin{itemize}
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\item $a = 2cm$, $b = 2cm$ et $c = 5cm$
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\item $a = 3cm$, $b = 3cm$ et $c = 2cm$
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\end{itemize}
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\includegraphics[scale=0.1]{./fig/V_cylindre} \textbf{Verres cylindre }
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\begin{itemize}
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\item $h = 3cm$ et $r = 2cm$
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\item $h = 1cm$ et $r = 4cm$
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\item $h = 12cm$ et $r = 1cm$
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\end{itemize}
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\includegraphics[scale=0.1]{./fig/V_cone} \textbf{Verres cône}
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\begin{itemize}
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\item $h = 5cm$ et $r = 1cm$
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\item $h = 1cm$ et $r = 2cm$
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\item $h = 6cm$ et $r = 1cm$
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\end{itemize}
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\end{multicols}
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Pour vous aider à choisir, voici les formules qui permettent de calculer le volume de ces verres:
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\begin{multicols}{3}
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\textbf{Verres pavé}\\
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\includegraphics[scale=0.4]{./fig/V_pave} $V = a\times b \times c
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\textbf{Verres cylindre }\\
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\includegraphics[scale=0.4]{./fig/V_cylindre} $V = \pi \times r^3 \times h$
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\textbf{Verres cône}\\
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\includegraphics[scale=0.4]{./fig/V_cone} $V = \dfrac{\pi \times r^3 \times h}{3}$
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\end{multicols}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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29
3ePasserelles/Nombres_Calculs/Formules_litterales/index.rst
Normal file
29
3ePasserelles/Nombres_Calculs/Formules_litterales/index.rst
Normal file
@ -0,0 +1,29 @@
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Utilisation de formules avec les 3e passerelles pour l'année 2017-2018
|
||||
###########################################################################
|
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|
||||
:date: 2018-01-08
|
||||
:modified: 2018-01-08
|
||||
:tags: Calcul littéral, Volumes
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Évaluation des formules dans divers contextes avec les 3ePasserelles pour l'année 2017-2018.
|
||||
|
||||
|
||||
|
||||
Étape 1
|
||||
=======
|
||||
|
||||
Évaluation de formules pour calculer `distance d'arrêt <./E1_distance_arret.pdf>`_
|
||||
|
||||
Cette activité sera ensuite continuée en salle informatique. On reproduira le tableau sur le tableur et on commencera à voir le calcul avec les formules.
|
||||
|
||||
Étape 2
|
||||
=======
|
||||
|
||||
On dispose de plusieurs verres pour servir un cocktail avec plusieurs calculs de volumes, les élèves doivent trouver le verre le plus adapté.
|
||||
|
||||
`Choix d'un verre <./E2_volumes_verres.pdf>`_
|
||||
|
||||
Étape 3
|
||||
=======
|
||||
|
||||
Loading…
Reference in New Issue
Block a user