Bijay is a student of class VIII. He writes his monthly fee in the expanded form as: \( 3 \times 5^{4}+3 \times 5^{3}+1 \times 5^{2}+0 \times 5^{1}+0 \times 5^{0} \) Write the short form of his fee in quinary numbers. Convert his monthly fee into a binary number system. Convert his yearly fee in scientific notation.

12. Si: \( \begin{aligned} x & =\frac{m n}{m+n} \cdot \text { Calcular: } \\ A & =\frac{x+2 m}{2 n-x}-\frac{2 m-x}{x+2 n}+\frac{4 m n}{x^{2}-4 n^{2}}\end{aligned} \)

\( \left. \begin{array} { l }{ f ( x ) = 11 x ^ { 4 } } \\ { f ^ { \prime } ( 1 ) = \square } \end{array} \right. \)

olve for \( x \) : \[ 2 \log _{9}(x)+2 \log _{x}(9)=5 \]

Exercice 3: « 5 points» \( \overrightarrow{A B C} \) est un triangle, \( I ; J \) et \( K \) sont des points tel que : \( \overrightarrow{A I}=2 / 3 \overrightarrow{A B}, \overrightarrow{B J}=1 / 2 \overrightarrow{B C} \) et \( \overrightarrow{A K}=2 \overrightarrow{A C} \) 1. Construire une figure convenable. 2. Ecrire chacun des deux vecteurs \( \overrightarrow{I J e t} \overrightarrow{J K} \) en fonction de \( \overrightarrow{A B} \) et \( \overrightarrow{B C} \). 3. Montrer que : \( \overrightarrow{3 I J}=\overrightarrow{A B}+3 / 2 \overrightarrow{B C} \). 4. Déduire que les points \( I, J \) et \( K \) sont alignés.

h. If \( g(4)=3 \), what is the minimum value of \( g \) on the interval \( [0,8] \) ?