Question

suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the square of its height. suppoalso that the beam is 3 inches wide, 4 inches high and 6 feet long can support a maximum of 28tons. what is the maximum weight that could be supported by a beam that is 5 inches wide, 4 inches high and 20 feet long

Answer 1

`\begin{gathered} \text{Let the maximum weight be represted by: W} \\ \text{Let the Length be represented by : L} \\ Let\text{ the width be represented by B} \\ Let\text{ the height be presented as : H} \\ W\text{ }\propto(1)/(L)^{} \\ W\text{ }\propto BH^2 \\ W\text{ }\propto(BH^2)/(L) \\ W\text{ = }(KBH^2)/(L) \\ \\ K=(WL)/(BH^2)\text{ } \\ B\text{ =3, H = 4, L = 6, W =28},\text{ K =?} \\ K=(WL)/(BH^2)\text{ }=\text{ }(28*6)/(3*4^2)\text{ = }(160)/(48)\text{ = }3.333 \\ W\text{ = ?, B = 5, H = 4, L = 20},\text{ K = 3.333} \\ \\ W\text{ = }(KBH^2)/(L)\text{ = }(3.333*5*4^2)/(20)\text{ =}(266.64)/(20)\text{ = 13.332} \\ \end{gathered}`