# Algebra

Suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. Suppose also that a beam 6 inches wide, 2 inches high, and 12 feet long can support a maximum of 14 tons. What is the maximum weight that could be supported by a beam that is 4 inches wide, 3 inches high, and 14
feet long?

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1. w = k(1/l)(wh^2)
for the given:
14 = k(1/12)(6(2^2))
14 = k(2)
k = 7

so w = 7(wh^2/l)
= (7/14)(4(9))
= 18 tons

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2. Thank you!

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