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) \(\mathbf { v } = \left( \sec ^ { 2 } \mathrm { t } \right) \mathbf { i } + ( \tan \mathrm { t } \sec \mathrm { t } ) \mathbf { j }\)

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Definitions:

Constant-cost Industries

Industries where the costs of production do not change significantly with an increase or decrease in the quantity produced.

Economic Efficiency

A condition where resources are allocated in a way that maximizes the production of goods and services, and minimizes waste and inefficiency.

Economic Profit

The difference between total revenues and total costs, including both explicit and implicit costs, representing the financial gain in undertaking a particular business activity.

MR = MC

An economic condition where a firm's marginal revenue equals its marginal cost, often used to determine the profit-maximizing level of production.