Vanillin is an organic compound with the molecular formula \( C_8H_8O_3 \). It is a phenolic aldehyde with functional groups including an aldehyde, hydroxyl, and ether, and is the primary component of vanilla bean extract.
Structure of Vanillin:
\[\text{HO-C}_6H_3(\text{OCH}_3)\text{CHO}\]
Counting oxygen atoms and \(\pi\) electrons:
Total number of oxygen atoms = 3.
Total number of \(\pi\)-bonds = 4 (one in the carbonyl group and three in the benzene ring).
Since each \(\pi\)-bond has two \(\pi\)-electrons:
\[\text{Total number of \(\pi\)-electrons} = 4 \times 2 = 8\]
Therefore, the sum of oxygen atoms and \(\pi\)-electrons is:
\[3 + 8 = 11\]
Find the equivalent capacitance between A and B, where \( C = 16 \, \mu F \).
If the equation of the parabola with vertex \( \left( \frac{3}{2}, 3 \right) \) and the directrix \( x + 2y = 0 \) is \[ ax^2 + b y^2 - cxy - 30x - 60y + 225 = 0, \text{ then } \alpha + \beta + \gamma \text{ is equal to:} \]