the intensity l of light from a light bulb, measured in watts per square meter (w/m^2), varies inversely as the square of the distance d from the light bulb. Suppose l is 70 w/m^2 when the distance is 5m. Find the intensity when the distance from the light bulb is 4 m away.

I = k (1/d^2)

given: when I = 70, d = 5
70 = k/25
k = 1750

so I = 1750/d^2

when d = 4
I = 1750/4^2 = 109.375

How did you get 25?

To find the intensity when the distance from the light bulb is 4 m away, we can use the inverse square law relationship.

The inverse square law states that the intensity is inversely proportional to the square of the distance. Mathematically, this can be represented as:

l ∝ 1/d^2

Given that the initial intensity is 70 w/m^2 when the distance is 5 m, we can write the equation as:

70 = k/5^2

where k is the constant of proportionality.

To find the value of k, we can rearrange the equation:

k = 70 * 5^2
k = 70 * 25
k = 1750

Now that we have the value of k, we can find the intensity when the distance is 4 m:

l = k/4^2
l = 1750/16
l = 109.375

Therefore, the intensity when the distance from the light bulb is 4 m away is approximately 109.375 watts per square meter (w/m^2).

To find the intensity when the distance from the light bulb is 4m, we can use the inverse square law. The inverse square law states that the intensity of light varies inversely with the square of the distance.

First, we need to set up the inverse variation equation using the given information. Let's denote the intensity as I and the distance as d. According to the problem, when the distance is 5m, the intensity is 70 w/m^2. This gives us the following equation:

I = k/d^2

where k is the constant of variation.

To find the value of k, we can substitute the given distance and intensity into the equation:

70 = k/5^2

Now, we solve for k:

k = 70 * 5^2

k = 70 * 25

k = 1750

Now that we have the value of k, we can use it to find the intensity when the distance is 4m.

I = 1750 / 4^2

I = 1750 / 16

I ≈ 109.4 w/m^2

Therefore, the intensity of light from the light bulb when the distance is 4m is approximately 109.4 w/m^2.