Louie made 8.1 liters of fruit punch using only grape juice and carbonated water. He used 4.2 liters of grape juice. The equation 4.2 + c = 8.1 can be used to represent this situation, where c is the number of liters of carbonated water used. How many liters of carbonated water did Louie use?

Find a parametrization for the curve「and determine the work done on a particle moving along γ in r3 through the force field f: r^3--r^3'where f(x,y,z) = (1,-x,z) and (a) im (γ) is the line segment from (0,0,0) to (1,2,1) (b) im (γ) is the polygonal curve with successive vertices (1,0,0), (0,1,1), and (2,2,2) (c) im (γ) is the unit circle in the plane z = 1 with center (0,0,1) beginning and ending at (1,0,1), and starting towards (0,1,1)