Lagrange's equations look funny at first, but they should make sense in ordinary cases. to see that this is so: (a) write down the lagrangian for a particle moving near the surface of the earth, in three dimensions, subject only to the force of gravity. (b) derive lagrange's equations of motion for this case, and show that they are the usual equations of motion you would expect.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

the force represented by vector a is normal force. if the hockey puck is moving to the right, when it is hit with a significant force by the hockey stick the puck will move off in a different direction. correct on edge.