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September 19th, 2011, 01:10 PM   #1
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direct variation problem

OK, on one of the last three problems. Here goes:

The sum of the distances of an object and its image in a mirror from a point vary as do their product.

If the image distance is 120 mm and the object distance is 300 mm, calculate the image distance when the object distance is 540 mm.

To find the law here I figured I'd set it up thus: 120 + 300 = (120)(300)k, 420 = 36000k, 420/36000 = k, .01166 = k.

IF that is correct (and I know that is a big "if"!), then I would suppose that to find the image distance I'd set it up as a variable + 540 = 540x(.0116). But I'm sure that's not right.

Then I thought that it could be proportional (120:300 = x:540) but that can't be right since this is in variation to the product which a simple ratio does not show.

Anyone have a better approach? Thanks in advance!
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