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a 20ft cantilever beam is shown in the figure below. A__10ft__B__10ft__C Load w1 = 200lb, w2 = 500lb, or both may be appled at the mid point B or at the end of the beam C. The bending moment incuded at the fixed support A(mA), will depend on the maginutes of the loads at B and C. Determine the sample space of A?

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The solution is {0,5000,10000,2000,7000,12000,4000,9000,14000} I think I might need to calculate the magnitudes of the loads at B and C, but how do I do that?
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I think i figured it out. Load at B is times 10, and at C times 20.

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