Find the euler–lagrange equation describing the brachistochrone curve for a particle moving inside a spherical earth of uniform mass density. obtain a first integral for this differential equation by analogy to the jacobi integral h. with the of this integral, show that the desired curve is a hypocycloid (the curve described by a point on a circle rolling on the inside of a larger circle). obtain an expression for the time of travel along the brachistochrone between two points on earth’s surface. how long would it take to go from new york to los angeles (assumed to be 4800 km apart on the surface) along a brachistochrone tunnel (assuming no friction) and how far below the surface would the deepest point of the tunnel be?

d) the number of neutrons plus the number of protons

b. lifting dumbbell weight at 20-degree angle from the body after a 45-degree angle

this is an example of "committed" time.

committed time, as contracted time, takes need over essential and available time since it is seen as profitable work. it alludes to the time allotted to keep up a home and family. at the point when a man is commuting using committed time this individual may feel that the drive is an obligation to family, for example, strolling youngsters to class or driving a mate to work. contracted and committed time clients may feel that their commute could really compare to the commute of important or leisure time clients on the grounds that their commute is profitable work. in this manner, they might be more disposed to pick a mechanized method of movement.