# Math

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The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one four times as strong as the other, are placed 11 ft apart, how far away from the stronger light source should an object be placed on the line between the two sources so as to receive the least illumination?

• Math -

Let the object be placed x feet from the weaker source. Then

ks/x^2 = k(4s)/(11-x)^2
or
4x^2 = (11-x)^2
4x^2 = 121 - 22x + x^2
3x^2 + 22x -121 = 0
(x+11)(3x-11) = 0

BRIGHT_____x__WEAK
8'4" -- 3'8"

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