If R(t) Is the Position Vector of a Particle in the Plane

question 68

Multiple Choice

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.
-Find the velocity vector. r(t) = (cot t) i + (csc t) j

• A) \(\mathbf { v } = \left( - \sec ^ { 2 } t \right) \mathbf { i } - ( \tan t \sec t ) \mathbf { j }\)
• B) \(\mathbf { v } = \left( \csc ^ { 2 } \mathrm { t } \right) \mathbf { i } + ( \cot \mathrm { t } \csc \mathrm { t } ) \mathbf { j }\)
• C) \(\mathbf { v } = \left( - \csc ^ { 2 } \mathrm { t } \right) \mathbf { i } - ( \cot \mathrm { t } \csc \mathrm { t } ) \mathbf { j }\)
• D) \(\mathbf { v } = \left( \sec ^ { 2 } \mathrm { t } \right) \mathbf { i } + ( \tan \mathrm { t } \sec \mathrm { t } ) \mathbf { j }\)

---

Definitions:

Deskilling Thesis

A concept that suggests technological advancements in workplaces lead to the simplification of tasks, reducing the need for skilled labor.

Scientific Management

A management theory that analyzes and synthesizes workflows, aiming to improve economic efficiency and labor productivity.

Sociologist

A social scientist who studies the development, structure, and functioning of human society and the social problems it faces.

Free Markets

Economic systems in which prices for goods and services are determined by the open market and consumers, in the absence of government intervention.