I NEED HELP PLEASE! :) A train is moving at 23 m/s due east when it sounds a blast on its horn, frequency = 164 Hz. What frequency is heard by the driver of a car moving due east at 15 m/s along a road parallel to the tracks? Use 343 m/s for the speed of sound. Please show all work.

168 Hz

Explanation:

The Doppler equation describes how sound frequency depends on relative velocities:

fr = fs (c + vr) / (c + vs),

where fr is the frequency heard by the receiver,

fs is the frequency emitted at the source,

c is the speed of sound,

vr is the velocity of the receiver,

and vs is the velocity of the source.

Note: vr is positive if the receiver is moving towards the source, negative if away.

Conversely, vs is positive if the receiver is moving away from the source, and negative if towards.

Given:

fs = 164 Hz

c = 343 m/s

vr = -15 m/s

vs = -23 m/s

fr = fs (c + vr) / (c + vs)

fr = 164 Hz (343 m/s − 15 m/s) / (343 m/s − 23 m/s)

fr = 168 Hz

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 .