A student stands several meters in front of a smooth reflecting wall, holding a board on which a wire is fixed at each end. the wire, vibrating in its third harmonic, is 75.0cm long, has a mass of 2.25g, and is under a tension of 400 N. a second student, moving towards the wall, hears 8.30 beats per second. what is the speed of the student approaching the wall? (solve without calculus)

Explanation:

From the question we are told that

      The length of the wire is  

      The mass of the wire is  

      The tension is          

       The frequency of the beat heard by the second student is

The speed of the wave generated by the vibration of the wire is mathematically represented as

substituting values

         The wire is vibrating in its third harmonics so the wavelength is  

substituting values

The frequency of this vibration is mathematically represented as  

substituting values  

The speed of the second student (Observer) is mathematically represented as

substituting values    

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 .