The brightness of a light bulb varies inversely as the square of the distance from the source. If a light bulb has a brightness of 300 lumens at 2 ft, what will its brightness be at 10 ft?
To solve this problem, we can use the formula for inverse variation:
brightness = k / distance^2
where k is the constant of variation.
We are given that the brightness of the light bulb is 300 lumens when the distance is 2 ft. Let's use this information to find the value of k:
300 = k / 2^2
300 = k / 4
To find k, we can multiply both sides of the equation by 4:
4 * 300 = k
1200 = k
Now that we have the value of k, we can use it to find the brightness at a distance of 10 ft:
brightness = k / distance^2
brightness = 1200 / 10^2
brightness = 1200 / 100
brightness = 12 lumens
Therefore, the brightness of the light bulb at 10 ft will be 12 lumens.
To find the brightness at 10 ft, we can use the inverse square law formula:
Brightness = k/distance^2
where k is the constant of variation.
Given that the brightness is 300 lumens at 2 ft, we can substitute these values into the formula to find the value of k:
300 = k/(2^2)
300 = k/4
k = 1200
Now that we know the value of k, we can substitute it into the formula to find the brightness at 10 ft:
Brightness = 1200/(10^2)
Brightness = 1200/100
Brightness = 12 lumens
Therefore, the brightness of the light bulb at 10 ft will be 12 lumens.