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Find the Eccentricity and Directrix of the Conic r=31cosθ/2r = \frac { 3 } { 1 - \cos \theta / 2 }

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Essay

Find the eccentricity and directrix of the conic r=31cosθ/2r = \frac { 3 } { 1 - \cos \theta / 2 } and graph the conic. Find an equation for the conic rotated counterclockwise about the origin through an angle π/6\pi / 6 , and graph it.

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Definitions:

Classical Conditioning

A learning process that occurs when two stimuli are repeatedly paired; a response that is at first elicited by the second stimulus is eventually elicited by the first stimulus alone.

Conditioned Stimulus

A previously neutral stimulus that, after being paired with an unconditioned stimulus, elicits a conditioned response in classical conditioning.

Unconditioned Stimulus

In classical conditioning, a stimulus that naturally and automatically triggers a response without any prior learning.

Extinction

The weakening and eventual disappearance of a learned response; in classical conditioning, it occurs when the conditioned stimulus is no longer paired with the unconditioned stimulus; in operant conditioning, it occurs when a response is no longer followed by a reinforcer.

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