How does matter around us make sound move?

Sound travels through the air as waves. When we speak, for example, the vibration of our vocal cords compresses the air around them. The compressed air moves the air around it, which carries the sound waves. Eventually, these compressions reach the ears of a listener, whose brain interprets that activity as sound.

Explanation:

no. dot product   =0 when vecs at right angles

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 .