Riley, a student, notices that the protractor tool does not measure the angle just as the ball leaves the surface. She sees that the ball must travel some distance before it crosses the protractor, so the direction of travel may have changed as the ball moves upwards. She says that this is the cause of the discrepancy between her predicted angle and the measured angle. Does this reasoning explain the discrepancy between your predicted angle and your measured angle. Use evidence to support your claim.

Riley's reasoning is correct

Explanation:

Her reasoning is correct because as the ball moves upwards, the acceleration due to gravity would be vertical and in downward position. Therefore at all points as the ball moves, the velocity of the ball is going to change in magnitude as well as in direction. given that the direction keeps changing at certain points, the angle made by the initial velocity just as the ball left the surface would also have to continuously change.

If Riley has to wait for this ball to move some inches before she uses the protractor to measure the angle, the angle of travel would have to change.

Therefore there is going to be discrepancies between the measured angle and the predicted angle. The predicted is the angle of velocity with the horizontal just as this ball moves from the surface.

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 .