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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

Respuesta :

[tex]W=\frac{k\cdot w\cdot h^2}{L}[/tex]

Where:

k = constant

w= width = 4

L = Length = 18

h = height = 3

W = weigth = 3 tons

Replacing:

[tex]3=\frac{k\cdot4\cdot3^2}{18}[/tex]

Solve for k

[tex]\begin{gathered} 3=2k \\ \frac{3}{2}=k \\ k=1.5 \end{gathered}[/tex]

So:

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

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