The intensity i of light bulb varies inversely as the square of the distance d from the light bulb. suppose i is 250 w/m^2 when the distance is 5 m. how much farther would it be to a point where the intensity is 40 w/m^2?

The answer is 7.5 m further.

Step 1. Calculate the constant k:
Step 2. Calculate d2.
Step 3. Subtract d2 and d1.

Step 1: Since The intensity I of light bulb varies inversely as the square of the distance d, using the constant k, this can be expressed as:
I = k/d²

We have:
k = ?
I1 = 250 w/m²
d1 = 5m

k = l1 * d1² = 250 * 5² = 250 * 25 = 6250 w

Step 2:
We have:
d2 = ?
l2 = 40 w/m²
k = 6250 w

l2 = k/d2²
d2² = k/l2
d2 = √( k/l2) = √(6250/40) = √156.25 = 12.5 m

Step 3: d2 - d1 = 12.5 - 5 = 7.5 m