Question
Use a variation model to solve for the unknown value. Round your answer to the nearest whole number.
The strength of a wooden beam varies jointly as the width of the beam and the square of the thickness of the beam, and inversely as the length of the beam. A beam that is 60 in. long, 5 in. wide, and 2 in. thick can support a load of 441 lb.
The strength of a wooden beam varies jointly as the width of the beam and the square of the thickness of the beam, and inversely as the length of the beam. A beam that is 60 in. long, 5 in. wide, and 2 in. thick can support a load of 441 lb.
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GPT 3.5
Let the strength of the beam be represented as S, the width as w, the thickness as t, and the length as l.
The strength of the beam can be written as:
S = k * (w * t^2) / l
where k is the constant of variation.
Plugging in the given values:
441 = k * (5 * 2^2) / 60
441 = k * (5 * 4) / 60
441 = k * 20 / 60
441 = k * 1/3
k = 1323
Now, we can find the strength of a beam that is 10 in. wide, 3 in. thick, and 50 in. long:
S = 1323 * (10 * 3^2) / 50
S = 1323 * (10 * 9) / 50
S = 1323 * 90 / 50
S = 2381
Therefore, a beam that is 10 in. wide, 3 in. thick, and 50 in. long can support a load of 2381 lb.
The strength of the beam can be written as:
S = k * (w * t^2) / l
where k is the constant of variation.
Plugging in the given values:
441 = k * (5 * 2^2) / 60
441 = k * (5 * 4) / 60
441 = k * 20 / 60
441 = k * 1/3
k = 1323
Now, we can find the strength of a beam that is 10 in. wide, 3 in. thick, and 50 in. long:
S = 1323 * (10 * 3^2) / 50
S = 1323 * (10 * 9) / 50
S = 1323 * 90 / 50
S = 2381
Therefore, a beam that is 10 in. wide, 3 in. thick, and 50 in. long can support a load of 2381 lb.
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