v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located at (-1,0): (1i) path 1: the triangle from (-1,0) to (2,0) to (0,2) and back to (-1,0). (ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise; (ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise; Which path would cause a rower to give more effort (i.e., produce a larger hindrance)? Is vector (velocity) field is conservative, I.e., is there a function f(x, y) such that Vƒ = v?

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.