# Math

The intensity of Illumination on a surface varies inversely as the square of the distance from the light source. A surface is 12 meters from a light source and has an intensity of 2. How far must the surface be from the light source to receive twice as much intensity of illumination? Approximate to the nearest tenth of meter. When I solved it, I got 2, is it right?

1. 👍
2. 👎
3. 👁
1. no

2 is 1/6 of 12 , so the intensity would be 36 times 2

I * d^2 = k ... 2 * 12^2 = 288

for twice the intensity ... (2 * 2) * d^2 = 288 ... d^2 = 72

1. 👍
2. 👎
2. L1 = intensity of Illumination 1

L2 = intensity of Illumination 2

d1 = distance 1

d2 = distance 2

The inverse-square law:

L2 / L 1 = ( d1 / d2 )²

You know L2 / L1 = 2 and d1 = 12

so:

2 = (12 / d2 )²

Take square root of both sides

√2 = 12 / d2

Multiply both sides by d2

√2 ∙ d2 = 12

Divide both sides by √2

d2 = 12 / √2 = 6 ∙ 2 / √2 =

6 ∙ √2 ∙ √2 / √2 = 6 ∙ √2 =

6 ∙ 1.41421 = 8.48526 m

d2 = 8.5 m rounded to the nearest tenth of meter

1. 👍
2. 👎

## Similar Questions

1. ### Pre-Algebra

If y varies directly with x, find the constant of variation with x = 4 and y = -24 If y varies inversely with x, find the constant of variation with x=5 and y = 10 If y varies directly with x, and y = 35 when x = 5 , find x when y

2. ### algebra

The intensity I of 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 I is 45 w/m^2 when the distance is 5 m . find the intensity when the

3. ### math

the cube root of r varies inversely with the square of s. which two equations model this relationship?

4. ### Inverse Variation

Help me please.. Explain also :( 1. E is inversely proportional to Z and Z = 4 when E = 6. 2. P varies inversely as Q and Q = 2/3 when P = 1/2. 3.R is inversely proportional to the square of I and I = 25 when R = 100. 4. F varies

1. ### Algebra!!!! HELP

Find a mathematical model for the verbal statement. (Use k for the constant of proportionality.) V varies inversely as the square of t. V=

2. ### MATH

if p varies inversely as the square of q and p=8 when q=4.find q when p=32

3. ### Algebra II

The weight of a body varies inversely as the square of its distance from the center of the earth. If the radius of the earth is 4000 mi, how much would a 200 lb man weigh 1000 mi above the surface of the earth?

4. ### Math-Algebra

1. The surface area of a cube varies directly as the square of its edge. Find its surface are. 2. A certain object traveling at 24 meters per second has a kinetic energy of 72 joules. If the kinetic energy of that object varies

1. ### algebra

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

2. ### College Algebra

Intensity of Light. The intensity I of light from a light bulb varies inversely as the square of the distance d from the bulb. Suppose that I is 90 W / m 2 90W/m2 (watts per square meter) when the distance is 5 m. How much farther

3. ### Calculus

A light is suspended at a height h above the floor. The illumination at the point P is inversely proportional to the square of the distance from the point P to the light and directly proportional to the cosine of the angle θ. How

4. ### variation

Can you please check my answers? Thanxs! Write an equation that expresses the relationship. Use k as the constant of variation. 20. f varies jointly as b and the square of c. -I got: f=kbc^2 22. r varies jointly as the square of s