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

Question

a) write an equation that expresses the proportionality.
b) determine the constant of proportionality if a beam is 4 in. wide, 6 in. high, and 12 ft long can support a weight of 4800 lb.
c) if a 10-ft beam, made of the same material is 3 in. wide and 10 in.high, what is the max. weight it can support?

Answer 1

M = k(w)h^2/l

b)4800 = k(4)(36)/12
solve for k

c) now that you have the full equation, just sub in the values given to find M

Answer 2

a)M=k(w)h^2/l
b)4800=k(4)(6)^2/144
k=4800 first change the unit of the length from feet to inch and use the expression that i used above.Unit conversion between in and feet is 1ft=30.48cm and 1in=2.54cm
c)since u have the equation all u have to do is plug in the values to the equation