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Question 937504: The intensity of light on the plane surface varies inversely as the square of the distance from the source of light. you're reading the book 5 feet from an electric light. if you move one foot closer how many times greater is the intensity of light in the book?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! inverse ratio equation is:
y = k/x
that tells you that the intensity of the light varies inversely as the distance from the source of light.
in order to derive the intensity of the light varies inversely as the square of the distance from the source of light, you have to square x to get:
y = k/x^2
if you are reading a book 5 feet away from the light , then the equation becomes:
y1 = k / 5^2 = k / 25
solve for k and you get k = 25 * y1
that's your constant of variation.
now you move 1 foot closer, so you are 4 feet away.
the equation becomes:
y2 = k / 16 = 25 * y1 / 16 = 1.5625 * y1
the light will be 1.5625 times more intense at 4 feet than it was at 5 feet.
let's put some numbers into it so you can see how it works.
assume the light intensity at 5 feet is 1000 lumens.
you get 1000 = k / 5^2 = k / 25
solve for k to get k = 1000 * 25 = 25000
that's your constant of variation and it always stays the same.
now assume you are 4 feet away.
the equation becomes y = 25000 / x^2 = 25000 / 16 = 1562.5
when you are 4 feet away, the intensity of the light will be 1562.5 lumens.
1562.5 / 1000 = 1.5625 which means that 1562.5 lumens is 1.5625 as intense as 1000 lumens.
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