In shops with lots of ice-cream flavors there are many different flavor combinations, even with only a 2-scoop cone. With 1 ice-cream flavor there is 1 kind of 2-scoop ice cream, but with 2 flavors there are 3 possible combinations (eg vanilla/vanilla, chocolate/chocolate, and vanilla/chocolate).

How many kinds of 2-scoop cones are there with 10 flavors?

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)