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

question 29

Essay

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

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Definitions:

Expectancy Theory

A motivation theory suggesting that individuals are more likely to act in a certain way based on the expectation that the act will be followed by a given outcome and the attractiveness of that outcome.

Pay Systems

Structures within an organization that determine how employees are compensated for their work, including wages, salaries, benefits, and incentives.

Escalator Clauses

Clauses in collective agreements that provide for quarterly cost-of-living adjustments in wages, basing the adjustments on changes in the consumer price index.

Cost of Living Adjustment

An increase in income or salary to counteract inflation, helping maintain employees' purchasing power.