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19 votes
19 votes
suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as it's length and jointly as its width and the square of its height. suppose also got a beam 4 inches wide, 3 inches wide and 18 ft long can support a maximum of 3 tons. what is the maximum weight that could be supported by a beam that is 7 inches wide, 4 inches high, and 6 ft long?_Tons

User Ildiko
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2.7k points

1 Answer

16 votes
16 votes


W=(k\cdot w\cdot h^2)/(L)

Where:

k = constant

w= width = 4

L = Length = 18

h = height = 3

W = weigth = 3 tons

Replacing:


3=(k\cdot4\cdot3^2)/(18)

Solve for k


\begin{gathered} 3=2k \\ (3)/(2)=k \\ k=1.5 \end{gathered}

So:

W = (1.5 * 7 * 4^2 )/6 = 28 tons

User Gary Davies
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3.2k points