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rénovation de sa chambre pour changer son radiateur électrique. Dans le magasin de bricolage trois puissances de radiateurs sont disponibles : + + \begin{minipage}{0.5\linewidth} + \begin{tabular}{|*{3}{c|}} + \hline + Modèle & Puissance & Prix \\ + \hline + Modèle 1 & 500W & 220\euro \\ + \hline + Modèle 2 & 1000W & 250\euro \\ + \hline + Modèle 3 & 1 500W & 295\euro \\ + \hline + \end{tabular} + + \end{minipage} + \begin{minipage}{0.5\linewidth} + \includegraphics[scale=0.7]{./fig/chambre} + \end{minipage} + + Le vendeur leur conseille de prévoir $40W$ pour $1m^3$ chauffé. + \begin{enumerate} + \item Les parents de Juliette ont mesuré la hauteur de la chambre: $h=2,50m$. + + A l'aide du plan ci-dessus, calculer le volume de la chambre. + + \item On considère que le volume de la chambre de Juliette est de $24m^3$. + + Les parents de Juliette souhaitent minimiser les dépenses. Quel modèle de radiateur doivent-ils acheter pour bien chauffer la chambre? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Cuve de stockage}] + \begin{tikzpicture} + \node (a) [cylinder, shape border rotate=90, draw, minimum height=20mm, minimum width=7.5mm] {}; + \draw [<->] ([xshift=5pt]a.before bottom) -- ([xshift=5pt]a.after top) node [midway, right] {$100cm$}; + \draw [<->] ([yshift=-5pt]a.bottom) -- ([yshift=-5pt]a.bottom -| a.before bottom) node [midway, below] {$10cm$}; + \end{tikzpicture} + \hfill + \begin{tikzpicture} + \node (a) [cylinder, shape border rotate=90, draw, minimum height=15mm, minimum width=15mm] {}; + \draw [<->] ([xshift=5pt]a.before bottom) -- ([xshift=5pt]a.after top) node [midway, right] {$50cm$}; + \draw [<->] ([yshift=-5pt]a.bottom) -- ([yshift=-5pt]a.bottom -| a.before bottom) node [midway, below] {$50cm$}; + \end{tikzpicture} + \hfill + \begin{tikzpicture} + \node (a) [cylinder, shape border rotate=90, draw, minimum height=15mm, minimum width=20mm] {}; + \draw [<->] ([xshift=5pt]a.before bottom) -- ([xshift=5pt]a.after top) node [midway, right] {$40cm$}; + \draw [<->] ([yshift=-5pt]a.bottom) -- ([yshift=-5pt]a.bottom -| a.before bottom) node [midway, below] {$60cm$}; + \end{tikzpicture} + \hfill + Volume du cylindre: $V = \pi \times r^2 \times h + + \begin{enumerate} + \item Calculer le volume de ses 3 cuves de stockage. + \item On veut remplir la première cuve avec un tuyau qui a un débit de 15 litre par heure. Combien de temps devra-t-on attendre avant que la cuve soit entièrement remplie? + \end{enumerate} + +\end{exercise} + +\begin{exercise}[subtitle={Extraction}] + La structure d’un bâtiment est représentée ci-dessous (ce schéma n’est pas à l’échelle). + + Un dispositif permet de renouveler l’air du bâtiment, on note Q son débit volumique. + + \includegraphics[scale=0.9]{./fig/batiment} + + \begin{enumerate} + \item Montrer que le volume $V$du bâtiment est d’environ $\np{300000}m^3$ + \item Le débit volumique $Q$ vaut $10^6 m^3/h$ + + Calculer, à l’unité près, le taux de brassage noté $T$ (il s’exprime sans unité) qui s’obtient en utilisant la + \[ T = \frac{Q}{V} \] + \item Pour être en conformité, le taux de brassage $T$ de l’air doit être inférieur à 5. + + Déduire de la réponse à la question 2, si la structure du bâtiment respecte cette norme. + \end{enumerate} + +\end{exercise} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff 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