Question: Suppose that an observatory is to be built between cities A and B, which are 30 miles apart. For the best viewing, the observatory should

Suppose that an observatory is to be built between cities A and B, which are 30 miles apart. For the best viewing, the observatory should be located where the night brightness from these cities is minimum. If the night brightness of city A is 8 times that of city B, then the night brightness b between the two cities and x miles from A is given by

Where k is a constant. Find the best location for the observatory; that is, find x that minimizes b.

k 8k b = x2 (30 x)?

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