Find Three Additional Polar Representations of the Point $\left( 5 , - \frac { \pi } { 3 } \right)$

question 21

Multiple Choice

Find three additional polar representations of the point $\left( 5 , - \frac { \pi } { 3 } \right)$ , given in polar coordinates, using $- 2 \pi < \theta < 2 \pi$ .

• A) \(\left( 5 , \frac { 5 \pi } { 3 } \right) , \left( 5 , \frac { 2 \pi } { 3 } \right) , \left( - 5 , - \frac { 4 \pi } { 3 } \right)\)
• B) \(\left( 5 , \frac { 5 \pi } { 3 } \right) , \left( 5 , \frac { 2 \pi } { 3 } \right) , \left( 5 , - \frac { 4 \pi } { 3 } \right)\)
• C) \(\left( 5 , \frac { 5 \pi } { 3 } \right) , \left( - 5 , \frac { 2 \pi } { 3 } \right) , \left( - 5 , - \frac { 4 \pi } { 3 } \right)\)
• D) \(\left( - 5 , \frac { 5 \pi } { 3 } \right) , \left( - 5 , \frac { 2 \pi } { 3 } \right) , \left( 5 , - \frac { 4 \pi } { 3 } \right)\)
• E) \(\left( - 5 , \frac { 5 \pi } { 3 } \right) , \left( 5 , \frac { 2 \pi } { 3 } \right) , \left( - 5 , - \frac { 4 \pi } { 3 } \right)\)

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Definitions:

Marginal Utility

The supplementary value or usefulness experienced from consuming one more unit of a good or service.

Consumer Surplus

The discrepancy between the amount consumers are prepared to pay for a product or service and the actual price they pay, symbolizing the advantage to consumers.

Marginal Utility

The increased contentment or value derived from the consumption of an extra unit of a good or service.

Total Utility

The aggregate level of satisfaction or fulfillment a consumer receives through the consumption of a specific quantity of goods and services.