After a movie has ended, an elderly man falls when walking down the steps of the crowded theater. there is an extremely long pause before anyone moves to the man. this is an example of
a) aggression.
b) egoism.
c) altruism.
d) the bystander effects.

It would be D. The bystander effect. It takes some time before anyone helps because they might assume he will get up on his own ok, that someone else will help, or maybe didn't see what happen and are waiting for someone else to take control. The more people their are, the more likely this is to happen. It's not really our fault, it's just something we do in a unexpected situation. :)

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .