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Inversely proportional means:

Intensity=K/(Distance^2)

Substitute to calculate K:
8=K/36
K=288

Intensity=288/(Distance^2)
288=Intensity*(Distance^2)

It works when Intensity is 2 and Distance is 12

Distance=12
Intensity=2
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Intensity is inversely proportional to the square of the distance:
i*d^2 = fixed value

8*(6^2)= 288
fixed value = 288

i*d^2=288

if d=12 and i=2:
2*144=288

Distance=12 and Intensity=2
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Using the inverse square relationship.
Writing intensity I as inversely proportional to distance squared: I = k / d^2
We are given that when the distance is 6 meters, the intensity is 8 units.
So finding k: k = 8 × 6^2
k = 8 × 36 k = 288
Writing the general formula: I = 288 / d^2.

Checking the options:
Trying d = 12 meters:
I = 288 / (12^2)
I = 288 / 144
I = 2 units
Both values match the given options.
Selecting: Distance = 12 meters
Intensity = 2 units.
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A point light source shines equally in all directions. The light intensity measured at a sensor is inversely proportional to the square of the distance from the source.

When the distance is 6 meters, the intensity is 8 units.

Select for Distance a distance in meters and select for Intensity an intensity in units that would be jointly consistent with the given information, Make only two selections, one in each column.
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Intensity is proportional to 1/(distance^2)
8 = k * 1/(6^2)
k = 36*8 = 288

So, I = 288/(distance^2)

Using trial method
let distance = 2, intensity = 288/4 = 72 not available
let distance = 4, intensity = 288/16 = 72/4 = 18 not available
let distance = 12, intensity = 288/144 = 2 available
So distance = 12 m intensity = 2units
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A point light source shines equally in all directions. The light intensity measured at a sensor is inversely proportional to the square of the distance from the source.

When the distance is 6 meters, the intensity is 8 units.

Select for Distance a distance in meters and select for Intensity an intensity in units that would be jointly consistent with the given information, Make only two selections, one in each column.
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For this, we really need to properly understand that the relationship between the light intensity and the distance is.

At the most basic level, the farther the light source from the sensor, the lower the reading. The closer the light source, the higher. This is the "common sense part".

Then the math part: The light intensity measure is inversely proportional to the square of the distance from the source. What does this mean? The any increase or decrease in distance will an effect equivalent to the inversed-square of the distance change.

For instance, a decrease in the distance from 6 to 3, while being a decrease by 1/2, cutting it into two, will NOT increase the intensity (inversely speaking) by 2 times, but it will be 2^2 = 4 times. Thus, 8*4 = 32 will depict the units for a distance of metres.

Now, upon checking all the options, we can establish the below relationships:

Distance 2 | 72 Intensity
Distance 4 | 18 Intensity
Distance 12 | 2 Intensity

Anything further than this will just take the intensity to exponentially lower numbers, so we can close this by marking Distance 12 / 2 Intensity.





Quote:
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A point light source shines equally in all directions. The light intensity measured at a sensor is inversely proportional to the square of the distance from the source.

When the distance is 6 meters, the intensity is 8 units.

Select for Distance a distance in meters and select for Intensity an intensity in units that would be jointly consistent with the given information, Make only two selections, one in each column.
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Intensity (I) = k/(distance=d)^2

Given d= 6m
I = 8

8 = k/6^2 = k/36 = k = 288

Thus, I = 288/d^2

Check from tha available values: 2,4,12...32

d=12 => I = 288/12^2 = 288/144 = 2

Therefore, distance = 12m
Intensity = 2 units

Bunuel
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A point light source shines equally in all directions. The light intensity measured at a sensor is inversely proportional to the square of the distance from the source.

When the distance is 6 meters, the intensity is 8 units.

Select for Distance a distance in meters and select for Intensity an intensity in units that would be jointly consistent with the given information, Make only two selections, one in each column.
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I = K/D^2
K = 8* 36

I = 8 * 36 /D^2
Trying different combinations

D = 12, I = 2 will be satisfied
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