physics
posted by mike .
The following wave function represents a travelling wave:
y = 3.45 / [6.35 + (6.35x−8.30 t )2]
where y and x are in cm, and t is in seconds.a) What is the maximum displacement of the wave at t = 7.50 s ?
b) what is the velocity.

Do you mean
y = 3.45 / [6.35 + (6.35x−8.30 t )^2] ??
if so for part a we want the shape when t = 7.5
y = 3.45/[ 6.35 + (6.35x  62.25)^2]
that is biggest when 6.35x =62.25
for part b, when is 6.35 x  8.30 t a constant? That is where if we hold that constant the wave looks the same.
y = f(6.35x8.30t)
constant when
6.35x8.30t = k
x = (8.3/6.35)t + k/6.35
dx/dt = 8.3/6.35 
The following wave function represents a travelling wave:
y = 3.45 / [6.35 + (6.35x−8.30 t )2]
where y and x are in cm, and t is in seconds. a). What is the maximum displacement of the wave at t = 7.50 s ?
b). what is the wave velocity?
please explain more 
If you move along with the wave, so that the wave always looks the same beside you, that is the phase velocity of the wave.
wave is a function of form:
y = f(axbt)
as long as axbt is constant, the function is constant
that happens when
a x  bt = constant
or
a dx/dt = b
dx/dt = b/a 
In part a, the function is big when the denominator is small.
That is when
6.35x−8.30 t = 0