Analysis of Tetrahedral Geometry in Compounds
Step 1: Analyze Each Compound to Identify Tetrahedral Geometry
Step 2: Count the Species with Tetrahedral Geometry
Tetrahedral species: [Co(CN)₄]⁴⁻, [PCl₄]⁺, [Cu(CN)₄]³⁻, and P₄.
Step 3: Final Answer
The total number of tetrahedral species is 3.
To solve the problem, we need to determine the geometry of each species listed and count how many have tetrahedral geometry.
1. Analyze each species:
2. Count species with tetrahedral geometry:
- [PCl4]+
- [Cu(CN)4]3−
- P4
Total = 3 species.
Final Answer:
The total number of species with tetrahedral geometry is \(\boxed{3}\).
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.