The loudness, L, of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d, from
the source of the sound.
A person 8 feet from a jetski, it is 60 decibels loud.
How loud is the jetski when the person is 41 feet away?

The jetski is 2.28 dB loud when the person is 41 feet away.

Step-by-step explanation:

Loudness (L) ∝ 1 / Distance² (d²)

Introduce a constant 'K'

L = K (1/d²)

L = K/d²

K = Ld²

Find the K from a previously known information: If a person 8 feet from a jetski hears 60 decibels loud

∴ d = 8 ft , L = 60 db

K = 60(8²) = 3840

How loud is the jetski when the person is 41 feet away?

Distance is now 41 ft

since: L = K/d²

∴ L = 3840 / 41²

L = 3840 / 1681

L = 2.28 db

Step-by-step explanation:

If two variables are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable. Also, a decrease in the value of one variable would cause a corresponding increase in the other variable.

Given that loudness, L varies inversely with the square of the distance, d², if we introduce a constant of proportionality, k, the expression becomes

L = k/d²

If L = 60 when d = 8, then

60 = k/8² = k/64

k = 60 × 64 = 3840

Therefore, the inverse variation equation is

L = 3840/d²

When d = 41, then

L = 3840/41²

L = 2.28 decibels

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b