Ablock (mass 9.0 kg) is released from rest on a frictionless slope angled at 37° to the horizontal. draw a diagram with labelled vectors for forces/acceleration. what is the block's acceleration?

Force diagram is attached here.

Acceleration of the mass down the inclined plane is independent of its mass.

ma = mg sin 37

or Acceleration = a = g sin 37 = 5.9 m/s/s.

Explanation:

The object sliding down the inclined plane has several forces acting on it.

Forces are labelled here as 1, 2, 3, 4.

Force 1 = Normal force that acts at right angles to the inclined surface.

Force 2 : Parallel component of the gravitational force

                = mg sin 37.

Force 3: Mass x Acceleration due to gravity = Weight

This is the gravity force that acts perpendicular to the  

floor or ground.  

Force 4 : Perpendicular component of the gravitational force  = mg cos 37.  

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 .