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Q: Why does the air behave in this way in cartesian diver?
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What is a synonym for ordered pairs?

One such synonym would be coordinates, which is also the proper way of naming the ordered pairs on a Cartesian coordinate plane.


What is the implication and criticism of Cartesian dualism?

Cartesesian Dualism is seeing immaterial 'mind' as superior over body. It leads to accepting immaterial 'understanding' as possible, knowing what is 'good' without experience. That way the Pope can say: sex without condom is not cause of AIDS. Western Society is based on Cartesian Dualism. Quite opposed to 'neurology': "everything is physical"


What does origin mean in the MATH way?

The point in a Cartesian coordinate system where the axes intersect. On a 2-D graph, for example, this is where x and y equal zero. also the point (0,0) on a graph


Given three points in polar notation what are the polar coordinates of a point equidistant from the three given points and can this point be found without converting to Cartesian coordinates?

Technically, yes. But, the equations involved are complicated to the point that it would be a fraction of the difficulty of converting. Also, the equations are essentially the Cartesian equations with the conversions built in, so you might as well convert them to start with. However, if you insist on not converting, write out the entire process with all 4 points of interest in Cartesian coordinates. From beginning to end. Find the final equations needed and insert the conversion factors and simplify from there. To the best of my knowledge (and I did quite a bit of digging) there isn't a simply way of doing it. - Sorry.


What is your reflection on Cartesian coordinate system?

The reflection of a shape is defined with respect to some specified line. None is specified. If one were specified, the reflection of an object would be the set of points such that the line was exactly half-way between each point in the original shape and its reflection.