Parameterize the Curve Which Lies on the Plane 5x - $x ^ { 2 } + y ^ { 2 } = 25$

question 44

Multiple Choice

Parameterize the curve which lies on the plane 5x - 10y + z = 6 above the circle $x ^ { 2 } + y ^ { 2 } = 25$

• A) \(\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 - 5 \sin t + 10 \cos t ) \vec { k }\)
• B) \(\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 - 25 \sin t - 50 \cos t ) \vec { k }\)
• C) \(\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 + 25 \sin t + 25 \cos t ) \vec { k }\)
• D) \(\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 - 25 \sin t + 50 \cos t ) \vec { k }\)
• E) \(\vec { r } ( t ) = 5 \sin t \vec { i } + 5 \cos t \vec { j } + ( 6 - 5 \sin t + 25 \cos t ) \vec { k }\)

Apply strategies for crafting messages with positive emphasis to enhance reader engagement and response.

Recognize the importance of tone and politeness levels in professional communication.

Understand the role of positive emphasis in organizational success and employee motivation.

Distinguish between direct and indirect requests and the appropriate contexts for each.

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Comparative Advantage

The ability of an entity to produce a good or service at a lower opportunity cost than others.

Lowest Opportunity Cost

The situation where the choice made uses the least possible sacrifice of alternatives, having the minimal foregone benefits among all options.

Produce More

The act of increasing the output or quantity of goods or services produced by a company, entity, or individual.

Trade Restrictions

Government-imposed limitations on the free exchange of goods and services between countries.