Find all polar coordinates of point p where p = ordered pair 1 comma pi divided by 3.

  (1, π/3 +2kπ), (-1, 4π/3 +2kπ) . . . where k is any integer

Step-by-step explanation:

Adding any multiple of 2π to the angle results in the same point in polar coordinates.

Adding 180° (π radians) to the point effectively negates the magnitude. As above, adding any multiple of 2π to this representation is also the same point in polar coordinates.

There are an infinite number of ways the coordinates can be written.

All the polar coordinates of point P are and , where n is an integer.

Step-by-step explanation:

The given point is

           .... (1)

If a point is defined as

         .... (2)

then the polar coordinates of point P is defined as

where, n is an integer and θ is in radian.

From (1) and (2) we get

So, the polar coordinates of point P are

Therefore all the polar coordinates of point P are and , where n is an integer.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950