Calculate the Arc Length of the Indicated Portion of the Curve

question 124

Multiple Choice

Calculate the arc length of the indicated portion of the curve r(t) .
- $$\mathbf { r } ( \mathrm { t } ) = 4 \mathrm { ti } + \left( 6 \cos \frac { 1 } { 2 } \mathrm { t } \right) \mathbf { j } + \left( 6 \sin \frac { 1 } { 2 } \mathrm { t } \right) \mathbf { k } ; - 8 \leq \mathrm { t } \leq 1$$

• A) -35
• B) 45
• C) -175
• D) 225

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Definitions:

Groupthink

A psychological phenomenon where the desire for harmony or conformity within a group leads to an irrational or dysfunctional decision-making outcome.

Harmony

A state of agreement, peacefulness, or concord between individuals or groups; also refers to a pleasing combination of musical notes.

Cognitive Dissonance

A psychological state that occurs when an individual holds two or more contradictory beliefs, ideas, or values at the same time, often leading to discomfort and a drive to reduce the inconsistency.

Social Pressure

The influence that is exerted by society or a social group on an individual, encouraging conformity to social norms or expectations.