Find the Curvature of the Curve R(t) $$r ( t ) = ( 2 t + 6 ) i - 4 j + \left( 8 - 1 t ^ { 2 } \right) \mathbf { k }$$

question 21

Multiple Choice

Find the curvature of the curve r(t) .
- $$r ( t ) = ( 2 t + 6 ) i - 4 j + \left( 8 - 1 t ^ { 2 } \right) \mathbf { k }$$

• A) \(k = \frac { 1 } { 2 \sqrt { 1 + t ^ { 2 } } }\)
• B) \(\kappa = 2 \sqrt { 1 + t ^ { 2 } }\)
• C) \(\kappa = 2 \left( 1 + t ^ { 2 } \right) ^ { 3 / 2 }\)
• D) \(\kappa = \frac { 1 } { 2 \left( 1 + t ^ { 2 } \right) ^ { 3 / 2 } }\)

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Definitions:

Extinction

In behavioral psychology, it refers to the gradual weakening and eventual disappearance of a conditioned response when the conditioned stimulus is no longer paired with the unconditioned stimulus.

Operant Conditioning

A learning process where behavior is controlled by consequences, such as rewards or punishments.

Respondent Conditioning

A learning process that involves creating an association between a naturally occurring stimulus and a previously neutral stimulus.

Shaping

A method of behavior training in which positive reinforcement is used to gradually guide an individual toward a desired behavior.