In reactions involving oxides and water, carefully balance the equations and count the atoms to ensure accuracy in stoichiometry
The reactions of sodium oxide and dichlorine heptoxide with water are as follows:
\[ Na_2O + H_2O \rightarrow 2NaOH \]
\[ Cl_2O_7 + H_2O \rightarrow 2HClO_4 \]
Adding the coefficients from both equations: 1 +4=5
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: