Question

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

Answer 1

$W=\frac{k\cdot w\cdot h^2}{L}$

Where:

k = constant

w= width = 4

L = Length = 18

h = height = 3

W = weigth = 3 tons

Replacing:

$3=\frac{k\cdot4\cdot3^2}{18}$

Solve for k

$\begin{gathered} 3=2k \\ \frac{3}{2}=k \\ k=1.5 \end{gathered}$

So:

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