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\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 14393742693712--
%%--Etude d\'une fonction liée à une configuration plane--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


\begin{exercise}
$\vspace*{-0.35cm}$%

%TCIMACRO{\TeXButton{Partie A}{\section*{Partie A}}}%
%BeginExpansion
\section*{Partie A}%
%EndExpansion
On consid\`{e}re l'expression $A(x)=25-(x-5)^{2}$.

\begin{enumerate}
\item D\'{e}velopper, r\'{e}duire et ordonner $A(x)$.

\item Factoriser $A(x)$.

\item Utiliser la forme la plus adapt\'{e}e de $A(x)$ pour r\'{e}soudre les
(in)\'{e}quations suivantes:

\begin{multicols}{2}
\begin{enumerate}
\item $A(x)=25$
\item $A(x)\leqslant 0$
\end{enumerate}
\end{multicols}

\end{enumerate}%

%TCIMACRO{\TeXButton{Partie B}{\section*{Partie B}}}%
%BeginExpansion
\section*{Partie B}%
%EndExpansion
Soit $f$ la fonction d\'{e}finie sur $I=[0;10]$ par:
\[
f(x)=25-(x-5)^{2}%
\]


\begin{enumerate}
\item Compl\'{e}ter le tableau de valeurs \ref{0710021600} page
\pageref{0710021600}.

\item Tracer $\mathcal{C}_{f}$, la courbe repr\'{e}sentative de $f$ (figure
\ref{0710021610} page \pageref{0710021610}).

\begin{enumerate}
\item D\'{e}terminer graphiquement le maximum de $f$.

\item Retrouver alg\'{e}briquement ce r\'{e}sultat.
\end{enumerate}
\end{enumerate}

%

%TCIMACRO{\TeXButton{Partie C}{\section*{Partie C}}}%
%BeginExpansion
\section*{Partie C}%
%EndExpansion
Soit $S(x)$ l'aire gris\'{e}e de la figure \ref{0710021655} page
\pageref{0710021655}.

\begin{enumerate}
\item V\'{e}rifier que $S(x)=\frac{\pi}{4}f(x)$.

\item Pour quelle valeur de $x$ l'aire hachur\'{e}e est-elle maximale?

\item V\'{e}rifions g\'{e}om\'{e}triquement.

\begin{enumerate}
\item Montrer que $\widehat{MAH}=\widehat{MHB}$.

\item En utilisant la tangente de ces angles, montrer que:
\[
MH^{2}=\frac{4}{\pi}S(x)
\]


\item Conclure.%

%TCIMACRO{\FRAME{fpFU}{3.7459in}{2.2872in}{0pt}{\Qcb{$\quad$}}{\Qlb{0710021655}%
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%BeginExpansion
\begin{figure}
[p]
\begin{center}
\includegraphics[
height=2.2872in,
width=3.7459in
]%
{Include/figure.eps}%
\caption{$\quad$}%
\label{0710021655}%
\end{center}
\end{figure}
%EndExpansion

\end{enumerate}
\end{enumerate}

\begin{table}[p]
\begin{center}
$%
\begin{array}
[c]%
{|l||p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|p{1cm}|}%
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\\\hline
f(x) &
%---------------NE PAS TOUCHER A CES PARAMETRES------------------------------

{\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
%------------------------------------------------------------------------------------------------------------------

%

%----------------------PARAMETRE A MODIFIER-----------------------------------------------

%10mm est la hauteur de l'étai (en millimètres!)

\fbox{\rule[-4mm]{0pt}{10mm}}}
%-----------------------------------------------------------------------------------------------------------------
&  &  &  &  &  &  &  &  &  & \\\hline
\end{array}
$ \label{0710021600}
\end{center}
\caption{$\quad$}%
\end{table}

%% \begin{figure}[p]
%% \begin{center}
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%% \uput{.2}[270](10.5,0){$x$}
%% \uput{.2}[0](0,27){$y$}
%% \end{pspicture}
%% \label{0710021610}\caption{$\quad$}
%% \end{center}
%% \end{figure}%
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%BeginExpansion
\begin{figure}
[p]
\begin{center}
\includegraphics[
height=5.3889in,
width=4.2881in
]%
{Include/papier.eps}%
\caption{$\quad$}%
\label{0710021610}%
\end{center}
\end{figure}
%EndExpansion

\end{exercise}


\end{document}