Find the Polar Coordinates of the Point(s) of Intersection of the Given

question 30

Multiple Choice

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $$0 \leq \theta < 2 \pi$$
- $r = 4 + \cos \theta , r = 4 - \sin \theta$

• A) \(\left( 4 , \frac { 3 \pi } { 4 } \right) , \left( 4 , \frac { 7 \pi } { 4 } \right)\)
• B) \(\left( 4 - \frac { 1 } { \sqrt { 2 } } , \frac { 3 \pi } { 4 } \right) , \left( 4 + \frac { 1 } { \sqrt { 2 } } , \frac { 7 \pi } { 4 } \right)\)
• C) \(\left( 4 + \frac { 1 } { \sqrt { 2 } } , \frac { 3 \pi } { 4 } \right) , \left( 4 - \frac { 1 } { \sqrt { 2 } } , \frac { 7 \pi } { 4 } \right)\)
• D) \(\left( \frac { 7 } { 2 } , \frac { 3 \pi } { 4 } \right) , \left( \frac { 9 } { 2 } , \frac { 7 \pi } { 4 } \right)\)

---

Definitions:

Pareto Optimal

A state of allocation of resources from which it is impossible to make any one individual better off without making at least one individual worse off.

Public Goods

Goods that are non-excludable and non-rivalrous, meaning they are available to all members of a society, such as public parks and national defense.

Private Consumption

The total amount of goods and services consumed by individuals in a household.

Pareto Optimal

A situation where resources are distributed in such a way that improving one person's condition inevitably leads to the detriment of another individual.