The light intensity of a light bulb varies inversely as the square of the distance from the light bulb. The function I(d) = k/d^2 models this situation, where I is the light intensity, d is the distance from a light source, and k is a constant. If the light intensity 6 feet away from a light bulb is 20 lumens, what is the light intensity 10 feet away from the same light bulb?

Question

The light intensity of a light bulb varies inversely as the square of the distance from the light bulb. The function I(d) = k/d^2 models this situation, where I is the light intensity, d is the distance from a light source, and k is a constant. If the light intensity 6 feet away from a light bulb is 20 lumens, what is the light intensity 10 feet away from the same light bulb?

Answer 1

I=k/d^2

20=k/6^2
k=20*36

I=(20*36)/10^2

Answer 2

To find the light intensity 10 feet away from the same light bulb, we can use the inversely proportional relationship between light intensity and the square of distance from the light bulb, given by the function I(d) = k/d^2.

First, let's use the given information to find the value of the constant k. We know that the light intensity 6 feet away from the light bulb is 20 lumens. So we have:

I(d) = k/d^2
20 = k/6^2
20 = k/36

To find k, we can multiply both sides of the equation by 36:

20 * 36 = k
720 = k

Now we have the value of the constant k, which is 720 lumens per foot squared (lm/ft^2).

We can substitute this value of k into the original function:

I(d) = 720/d^2

To find the light intensity 10 feet away from the light bulb, we plug in d = 10 into the function:

I(d) = 720/10^2
I(d) = 720/100
I(d) = 7.2 lumens

Therefore, the light intensity 10 feet away from the same light bulb is 7.2 lumens.

Answer 3

To find the light intensity 10 feet away from the light bulb, we can use the given information and the inverse square law relationship.

Let's start by determining the constant, k. We are given that the light intensity 6 feet away from the light bulb is 20 lumens. This can be represented as:

20 = k / 6^2

Simplifying:

20 = k / 36

To find the value of k, we can multiply both sides of the equation by 36:

20 * 36 = k

k = 720

Now that we have the value of k, we can substitute it into the inverse square law equation to find the light intensity 10 feet away. The equation becomes:

I(d) = 720 / d^2

Substituting d = 10 into the equation:

I(10) = 720 / 10^2

I(10) = 720 / 100

Simplifying:

I(10) = 7.2 lumens

Therefore, the light intensity 10 feet away from the same light bulb is 7.2 lumens.

Answer 4

I=k/d^2

To find the light intensity 10 feet away from the same light bulb, we can use the inversely proportional relationship between light intensity and the square of distance from the light bulb, given by the function I(d) = k/d^2.

To find the light intensity 10 feet away from the light bulb, we can use the given information and the inverse square law relationship.

Bobo ka sa math