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kirill [66]
3 years ago
11

The illuminance of a surface varies inversely with the square of its distance from the light source.If the illuminance of a surf

ace is 120 lumens per square meter when its distance from a certain light source is 6 meters, by how many meters should the distance of the surface from the source be increased to reduce its illuminance to 30 lumens per square meter?
Mathematics
1 answer:
VashaNatasha [74]3 years ago
6 0

Answer:

Distance between the surface and source of light will be increased by 6 meters.

Step-by-step explanation:

The illuminance of a surface varies inversely with the square of ts distance from the light source.

Let illuminance of the surface = x lumens per square meter

and distance from a light source = y meter.

Now x ∝ \frac{1}{y^{2} }

Or x=\frac{k}{y^{2} } [k = proportionality constant]

Now we will find the value of k.

k = xy²

k = 120×(6)²

k = 4320

We have to calculate the distance of the source if illuminance of the surface is 30 lumens per square meter.

30=\frac{4320}{y^{2}}

y² = \frac{4320}{30}

y² = 144

y = √144 = 12 meters

So the source of the light will be shifted away from the surface = 12 - 6 = 6 meters.

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Answer:

Biff's tree is 14 m off the ground and Rocco's tree is 7 m off the ground.

Step-by-step explanation:

Let the height of Biff's tree be represented by x, so that the height of Rocco's tree is \frac{x}{2}.

Draw a straight line from Rocco's point of view to a point t to the middle of Biff's tree. This line divides x into two equal parts, and the angle is divided into 35^{0} each.

By alternate angle property,

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