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:
The disintegration of unstable heavy atomic nuclei into lighter, more stable, atomic nuclei, accompanied in the process by the emission of ionizing radiation (alpha particles, beta particles or gamma rays). This is a random process at the atomic level but, given a large number of similar atoms, the decay rate on average is predictable, and is usually measured by the half-life of the substance.
The equation for finding out the decay rate is given below: