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Sagot :
Answer:
The ratio of the new distance to the old distance is (11/2) .
The intensity is inversely proportional to the square of the distance,
so the new intensity will be (2/11)² times the old intensity.
Intensity = 8,000 (2/11)² =
32,000 / 121 = 262.463 units
Rounded to the nearest whole unit: 262 units
Step-by-step explanation:
264 units of intensity came from a distance of 11 miles option (c) 264 units is correct.
It is given that the intensity is 8000 units at a distance of 2 miles.
It is required to find the intensity at a distance of 2 miles.
What is a fraction?
Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station.
Suppose the Intensity of the signal is I and the distance is d, then:
[tex]\rm I \propto\frac{1}{d^2}[/tex]
Intensity from the station [tex]\rm I_1=8000 \ units[/tex]
[tex]\rm I_1[/tex] intensity at distance [tex]\rm d_1=2 \ miles[/tex]
Intensity from the station [tex]=\rm I_2[/tex]
[tex]\rm I_1[/tex] intensity at distance [tex]\rm d_2=11 \ miles[/tex]
[tex]\rm \frac{I_2}{I_1} = \frac{d_1^2}{d_2^2}[/tex] (From the proportional relation)
[tex]\rm \frac{I_2}{8000} = \frac{2^2}{11^2}[/tex]
[tex]\rm I_2 =8000\times\frac{4}{121} \\\\\rm I_2 = 264.46 \ units[/tex] ≈ 264 units
Thus, the 264 units of intensity came from a distance of 11 miles.
Learn more about the fraction here:
brainly.com/question/1301963
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