Gypsum (CaSO$_4\cdot$2H$_2$O) is added to cement to regulate the setting time. Without gypsum, cement would set immediately upon mixing with water, leaving no time for concrete placement.
Gypsum reacts with tricalcium aluminate (C$_3$A) in cement to form insoluble calcium sulfoaluminates, which slows down the hydration reaction.
This delay ensures sufficient time for the mixing, transportation, and placement of concrete before it hardens.
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: