Respuesta :
The intensity of soundwave at a distance of 12 miles is 222.22 miles.
What is Directly proportional and inversely proportional?
The link between two variables whose ratio is equal to a constant number is known as a direct proportional, while the multiplication of two variables whose ratio is equal to a constant number is known as an inversely proportional.
It is given that the intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. therefore, the relation between the intensity of the radio wave(I) and distance(r) can be written as,
[tex]I\propto \dfrac{1}{r^2}\\\\\\I=k \dfrac{1}{r^2}[/tex]
Now, it is stated that the intensity of the radio wave at a distance of 2 miles is 8000 units, therefore, substituting the value in the above equation to get the value of the constant,
[tex]I=k\dfrac{1}{r^2}\\\\8000=k\dfrac{1}{2^2}\\\\8000=k\dfrac{1}{4}\\\\k = 8000 \times 4 = 32,000\rm\ units[/tex]
Thus, the value of the constant k is 32,000 units, and the equation of the intensity of the radio signal can be written as,
[tex]I=\dfrac{32,000 }{r^2}[/tex]
Further, the intensity of soundwave at a distance of 12 miles will be equal to,
[tex]I=\dfrac{32,000 }{r^2}\\\\I=\dfrac{32,000 }{12^2}\\\\I=\dfrac{32,000 }{144}\\\\I = 222.22\rm\ units[/tex]
Hence, the intensity of soundwave at a distance of 12 miles is 222.22 miles.
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