1 Suppose youre relaxing one evening with a copy of Twelth N

1. Suppose you\'re relaxing one evening with a copy of Twelth Night, and the reading light is placed 5 ft. from the surface of the book. At what distance would the intensity of the light be twice as great?

2. Tamino\'s Aria is playing in the background, with the speakers 12 ft away. At what distance from the speakers would the intensity of sound be three times as great?

Solution

1. Suppose you\'re relaxing one evening with a copy of Twelth Night, and the reading light is placed 5 ft. from the surface of the book. At what distance would the intensity of the light be twice as great?
:
The inverse variation of the square of x: y = k/x^2 or k/x^2 = y
Let y = 1 (amt of light) and x = 5 ft; find k:
:
k/5^2 = 1
k = 25
:
Find x when y = 2 (twice as much light); k = 25
2 = 25/x^2
2x^2 = 25
x^2 = 25/2
x^2 = 12.5
x = sqrt(12.5)
x = 3.53 ft there will be twice as much light
:
:
2. Tamino\'s Aria is playing in the background, with the speakers 12 ft away. At what distance from the speakers would the intensity of sound be three times as great?
:
k/x^2 = y
x = 12 ft; y = 1 (sound level); find k
:
k/12^2 = 1
k/144 = 1
k = 144
:
Let the level of sound = 3
3 = 144/x^2
3x^2 = 144
x^2 = 48
x = sqrt(48)
x = 6.93 ft the sound is three times as much