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

Respuesta :

[tex]\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\frac{1}{L}^{} \\ W\text{ }\propto BH^2 \\ W\text{ }\propto\frac{BH^2}{L} \\ W\text{ = }\frac{KBH^2}{L} \\ \\ K=\frac{WL}{BH^2}\text{ } \\ B\text{ =3, H = 4, L = 6, W =28},\text{ K =?} \\ K=\frac{WL}{BH^2}\text{ }=\text{ }\frac{28\times6}{3\times4^2}\text{ = }\frac{160}{48}\text{ = }3.333 \\ W\text{ = ?, B = 5, H = 4, L = 20},\text{ K = 3.333} \\ \\ W\text{ = }\frac{KBH^2}{L}\text{ = }\frac{3.333\times5\times4^2}{20}\text{ =}\frac{266.64}{20}\text{ = 13.332} \\ \end{gathered}[/tex]

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