Write the dual of the statement \( p \wedge [\neg q \vee (p \wedge q) \vee \neg r] \).

Find the area of a triangle with vertices \( A(1, 2, 3) \), \( B(2, 3, 4) \), and \( C(3, 4, 5) \).

Differentiate \( \cos^{-1} \left( \frac{1-x^2}{1+x^2} \right) \) with respect to \( x \).

Find the principal value of \( \sin^{-1} \left( -\frac{1}{2} \right) \).

Write the converse, inverse, and contrapositive of: "If voltage increases, then current decreases".

Evaluate \( \int \frac{x + 2}{2x^2 + 6x + 5} \, dx \) using the substitution or partial fraction method.

A die is tossed twice. If a “success” is getting a number greater than 4, find the probability distribution of the number of successes.

The population of a town grows at a rate proportional to its size. If it grows from 40,000 to 60,000 in 40 years, what will it be in another 20 years?

Prove that \( \int \sqrt{a^2 - x^2} \, dx = \frac{x}{2}\sqrt{a^2 - x^2} + \frac{a^2}{2}\sin^{-1} \left( \frac{x}{a} \right) + C \).

Prove the Section Formula for internal division in vectors.