Engine emits sound uniformly in all directions, radiating an acoustic power of 3.65 × 10 5 W. 3.65×105 W. Find the intensity of the sound at a distance of 52.7 m 52.7 m from

130.2dB

Explanation:

The formula for determining the intensity of a wave is expressed as

Where P is the power in watts, and A is the area of the sphere formed by the wave

Data given

Power,P=3.65*10^5W

distance,d=52.7

Hence since the distance represent the radius, we can determine the area of the sphere formed

The intensity can be computed as

we can convert to decibel

10.46W/m²

The intensity (I) of a sound is related to the power (P) radiated by the sound within an area (A) as follows;

I =              ----------------(i)

But;

A = 4 r²

Where;

r is the specified distance covered by the sound.

Substitute A = 4 r² into equation (i) to get;

I =               ------------------------(ii)

From the question;

P = acoustic power = 3.65 x 10⁵W

r = 52.7m

To calculate the intensity of the sound, take = 3.142 and substitute other values into equation (ii) as follows;

I =

I =

I = 10.46W/m²

Therefore, the intensity of the sound at that distance is 10.46W/m²

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 .