Find the Area of the Surface $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k }$

question 49

Multiple Choice

Find the area of the surface. The part of the paraboloid $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k }$ ; $0 \leq u \leq 7$ , $0 \leq v \leq 2 \pi$

• A) \(\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 12 }\)
• B) \(\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 3 }\)
• C) \(\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 6 }\)
• D) \(\frac { 5 \pi ( 197 \sqrt { 197 } - 1 ) } { 12 }\)

Grasp the challenges associated with forming and maintaining cartels, including the role of group size.

Identify the effects of output and price in firm decision-making within oligopolies.

Comprehend the role of free trade and competition in oligopolistic markets.

Analyze the strategic decisions of firms in game theory contexts, including dominant strategies and Nash equilibria.

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Definitions:

One Language

"One Language" typically refers to situations or policies where only a single language is promoted or used for communication in a community or country.

People

Human beings collectively or considered as members of a community, society, or culture.

Morphemes

The smallest meaningful units of language, such as prefixes, roots, and suffixes.

Zero

A numerical figure representing nothing or the absence of quantity or value.