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 sof its height. suppose also that a beam 6 inches wide, 2 inches high, and 12 feet long can support a maximum of 14 tons. what is the maximum weight that could be supported by a beam that is 4 inches wide, 3 inches high and 14 feet long

Answer 1

Step 1

Write the formula connecting all variables.

Weight = w

Length = L

Width = b

Height = H

k = constant

`w\text{ = }(kbH^2)/(L)`

Step 2

Use the values below to find the constant k.

b = 6

H = 2

L = 12

W = 14

`\begin{gathered} 12\text{ = }\frac{k\text{ }*\text{ 6 }*2^2}{12} \\ 14\text{ = }(24k)/(12) \\ \text{Cross multiply} \\ 24k\text{ = 14 x 12} \\ 24k\text{ = 1}68 \\ k\text{ = }(168)/(24) \\ k\text{ = }7 \end{gathered}`

Step 3

Find the unknow

W = ?

b = 4

H = 3

L = 14

`\begin{gathered} W\text{ = }(kbH^2)/(L) \\ W\text{ = }\frac{7\text{ }*\text{ 4 }*3^2}{14} \\ W\text{ = }\frac{7\text{ }*\text{ 4 }*\text{ 9}}{14} \\ W\text{ = }(252)/(14) \\ W=\text{ 18 tons} \end{gathered}`

The maximum weight = 18 tons