The maximum weight M that can be supported by a beam is jointly proportional to its width w in inches and the square of its height h in inches and inversely proportional to its length L in feet.

(a) Write an equation that expresses this proportionality. (Use k as the constant of proportionality.)

(b) Determine the constant of proportionality if a beam 4 in. wide, 6 in. high, and 18 ft long can support a weight of 2400 lb.
k =

(c) If a 10-ft beam made of the same material is 2 in. wide and 10 in. high, what is the maximum weight it can support?

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