What is the significance of path independence in relation to how it affects limits for functions of several variables?

Amuffin recipe, which yields 12 muffins, calls for cup of milk for every 1 cups of flour. the same recipe calls for cup of coconut for every cup of chopped apple. to yield a batch of 30 muffins, how much flour will be needed in the mix?

The lengths of all sides of a triangle are integers when measured in decimeters. one of the sides has length of 1 dm and another of 3 dm. find the perimeter of the triangle.'

Angle xyz is formed by segments xy and yz on the coordinate grid below: a coordinate plane is shown. angle xyz has endpoints at 3 comma negative 1 and 6 negative 2 and 3 comma negative 3 and measures 36.87 degrees. angle xyz is rotated 270 degrees counterclockwise about the origin to form angle x′y′z′. which statement shows the measure of angle x′y′z′?