From 914889e4fe2f726e428a6c3fefc945df78bcea1d Mon Sep 17 00:00:00 2001
From: Benjamin Chausse <benjamin@chausse.xyz>
Date: Tue, 3 Dec 2024 22:46:50 -0500
Subject: Ma baguette de pain est toute séchée!!!
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---
 annexe/main.tex | 22 ++++++++++++++++++----
 1 file changed, 18 insertions(+), 4 deletions(-)

(limited to 'annexe/main.tex')

diff --git a/annexe/main.tex b/annexe/main.tex
index 179ca97..bad3e6e 100644
--- a/annexe/main.tex
+++ b/annexe/main.tex
@@ -245,13 +245,27 @@
 	\end{gather*}
 	Il est maintenant trivial d'isoler $A_2$:
 	\begin{gather*}
-		\begin{array}{l@{\quad}cr@{}l}
-			                   &  & -176.4708 & {}=        \cancel{14.7059A_1}  + 14.7059A_2  \\
-			\text{\bfseries--} &  & 6\exp{7}  & {}= \cancel{14.7059 A_1} + 4'999'999.2941 A_2 \\ \cline{2-4}
-			                   &  & 0         & {}= -x-5
+		\begin{array}{l@{\quad}cr@{}ll}
+			                   &  & -176.4708 & {}=        \cancel{14.7059A_1} & + 14.7059A_2         \\
+			\text{\bfseries--} &  & 6\exp{7}  & {}= \cancel{14.7059 A_1}       & + 4'999'999.2941 A_2 \\ \cline{2-5}
+			\approx            &  & 6\exp{7}  & {}= 0                          & -4'999'999.2941 A_2
 		\end{array}
 	\end{gather*}
+	\begin{gather*}
+		\begin{align}
+			A_2 & \approx -\frac{6\exp{7}}{5\exp{6}} = -12 \\
+			-12 & = A_1 + A_2                              \\
+			A_1 & = 0
+		\end{align}
+	\end{gather*}
+	La solution de la décharge est donc:
 
+	\begin{gather*}
+		\begin{align}
+			\vlt & = \cancel{0e^{(\al-\rootd)t}} -12 e^{-5\exp{6}t} \\
+			\vlt & = -12 e^{-5\exp{6}t}
+		\end{align}
+	\end{gather*}
 
 
 \end{appendix}
-- 
cgit v1.2.3

