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Answer :
Final answer:
The weight that the same type of beam can support can be determined using a proportional equation. By finding the value of the proportionality constant and plugging in the values for the second beam, we can calculate the weight it can support. The weight supported is 288 pounds.
Explanation:
To find the amount of weight that the beam can support, we can set up an equation using the given information. Let w be the weight that the beam can support, b be the width of the beam, d be the depth of the beam, and l be the length of the beam. According to the given information, the strength of the beam is directly proportional to its width and the square of its depth but inversely proportional to its length.
Using this information, we can set up the following equation:
w = k * (b * d^2) / l
where k is the proportionality constant.
Now, we can plug in the values from the first beam to find the value of k:
1800 = k * (6 * 10^2) / 3
Solving for k, we find k = 1800 * 3 / (6 * 10^2) = 9.
Now, we can use this value of k to find the amount of weight that the second beam can support:
w = 9 * (6 * 8^2) / 12
Simplifying, we get w = 9 * (6 * 64) / 12 = 288 pounds.
Therefore, the same type of beam that is 6 inches wide, 8 inches deep, and 12 feet long can support a weight of 288 pounds.
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