Topic
Q:
Simplify:
\[ \frac{2^{x}-2^{-x}}{4^{x}-1} \]
Q:
\begin{tabular}{l} Find the third proportion of each \\ \( \begin{array}{ll}{[1] 6,12} & {[2] \mathrm{x}^{2},-5 \mathrm{x}}\end{array} \) \\ \hline\end{tabular}
Q:
If \( 2 \mathrm{a}-\frac{1}{2 \mathrm{a}}=3 \) then \( 16 \mathrm{a}^{4}+\frac{1}{16 \mathrm{a}^{4}} \) is?
Q:
\( \left( \begin{array} { l l } { 2 } & { 0 } \\ { 3 } & { 1 } \end{array} \right) \left( \begin{array} { l l } { 2 } & { 0 } \\ { 3 } & { 1 } \end{array} \right) + 2 \left( \begin{array} { l l } { 20 } \\ { 31 } \end{array} \right) + 3 \)
Q:
What does the exponent in an expression indicate?
Q:
\( \left. \begin{array} { l } { a , b \in N } \\ { ( \frac { 2 a + 1 } { b - 3 } ) \in Z } \\ { ( \frac { b - 3 } { 2 a + 1 } ) \in Z } \\ { \Rightarrow \min ( a + b ) = ? } \end{array} \right. \)
Q:
Calculate the value of \( a^{-2}b^{4} \) when \( a = 2 \) and \( b = 3 \).
Q:
\( \frac { a } { 10 } + \frac { a } { 100 } + \frac { a } { 1000 } + \frac { a } { 10000 } + \ldots = \frac { 4 } { 9 } \)
Q:
Олон гишүүнтүүдийг үржигдэхүун болгон задал.
\( \begin{array}{ll}\text { а) } a^{2}+2 a b+b^{2} & \text { г) } 2 c d+d^{2}+c^{2} \\ \text { б) } a^{2}-6 a+9 & \text { д) } x^{2}-2 x+1 \\ \text { в) } m^{2}+n^{2}-2 m n & \text { е) } 4 a^{2}+4 a+1\end{array} \)
Q:
\( x+y=8.64 \)
\( x^{2}+y^{2}=24.6496 \)
Find the exact value of \( x y \)
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