Math Applications: Optimization, Differential Eq, Trajectory

Which area of mathematics is most directly concerned with finding the optimal route for a delivery truck visiting multiple locations?

If a physical system's behavior is modeled by a differential equation, which branch of mathematics is most likely used to analyze and predict its future states?

Consider a scenario where you need to determine the trajectory of a projectile, accounting for both its initial velocity and the angle of launch. Which mathematical area would be most applicable?

Which of the following statements accurately describes the relationship between rational and irrational numbers within the set of real numbers?

In computer graphics, transformations like rotations, scaling, and translations are applied to 3D models. Which branch of mathematics provides the foundation for these transformations?

Which mathematical concept is most crucial for developing secure encryption algorithms in cryptography?

Which theorem links differentiation and integration, providing a method to calculate definite integrals using antiderivatives?

A study finds that as the sample size increases, the distribution of sample means approaches a normal distribution. Which theorem is being demonstrated?

In economics, mathematical models are used to analyze markets and consumer behavior. Which area of mathematics is most often applied in optimization problems, such as maximizing profit or minimizing cost?

Considering the broad applications of mathematics, in which field would the study of continuity, limits, and series be most essential?