The maximum force that a board of wood can support varies directly with its width and the square of its thickness, and inversely with the beam length.

A board that is 7 inches wide, 5 inches thick, and has a beam length of 14 feet supports 7200 pounds of force.

a. How much force could a board that is 10 inches wide, 5 inches thick, and has a beam length of 20 feet support?

The maximum force a board can support varies directly with its width and the square of its thickness, and inversely with the beam length. Using these relationships, we can find the maximum force a new board can support.

Explanation:

To solve this problem, we can use the concept of direct and inverse variation. Let's first find the constant of variation using the given information. The board that supports 7200 pounds has a width of 7 inches, thickness of 5 inches, and beam length of 14 feet. Using these values, we can set up the proportion:

7200 = k * 7 * (5^2) / 14

Solving for k, we find that the constant of variation is 7200 / (7 * 25 / 14) = 160. Now, let's use this constant to find the maximum force that the new board can support. The new board has a width of 10 inches, thickness of 5 inches, and beam length of 20 feet. Plugging these values into the equation, we get:

max force = 160 * 10 * (5^2) / 20

Calculating this, we find that the new board can support a maximum force of 2000 pounds.

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