Suppose that an observatory is to be built between cities a, Engineering Mathematics

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Suppose that an observatory is to be built between cities a

Night brightness

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

b= (8k/x2) + [k/(30-x²)

where k is a constant.

Find the best location for the observatory; that is, find x that minimizes b.

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