An enormous thunderstorm covers Dallas-Ft. Worth. Your best friend Clark is a storm chaser and heads to the center of the storm to take some readings while you stay dry at home. While Clark is at the center of the storm, he sees and hears lightning strike a tree that is 160 m from where he is standing. You are 137 km from the tree. How long does it take for the sound to reach Clark? Assume the speed of sound is 343 m/s.

The sound takes 0.47 seconds to reach Clark

Explanation:

We are analyzing the speed of the sound not the lightning. We need to ignore the irrelevant parameters in the question and make use of only those necessary to answer the question.

Speed of sound = 343m/s

Distance between Clark and the tree = 160m

recall, time of travel =

time =

∴ It takes the sound≈ 0.47 seconds to reach clark

wavelength variability is the right one

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 .