`x(x,t)=(0.8)/([(4x+5t)^(2)+5])`, represents a moving pulse where x and y are in metre and t is in second. Find
(i) The direction of wave propagation.
(ii) The wave speed.
(iii) The maximum displacement from the mean position (i.e., the aplitude of the wave).
(iv). Whether the wave pulse is symmetric or not.

Explanation

To solve the given problem, we will analyze the function \( f(x, t) = \frac{0.8}{(4x + 5t)^2 + 5} \) step by step.

### Step 1: Determine the direction of wave propagation
The general form of a wave function can be expressed as \( f(x, t) = A \cdot g(kx - \omega t) \) or \( f(x, t) = A \cdot g(kx + \omega t) \). Here, \( g \) is some function, \( A \) is the amplitude, \( k \) is the wave number, and \( \omega \) is the angular frequency.

In our case, we can identify the argument of the function as \( 4x + 5t \). The coefficient of \( x \) is positive (4), and the coefficient of \( t \) is also positive (5). This indicates that the wave is propagating in the negative x-direction.

**Direction of wave propagation: Negative x-axis.**
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