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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

Sagot :

Step 1

Write the formula connecting all variables.

Weight = w

Length = L

Width = b

Height = H

k = constant

[tex]w\text{ = }\frac{kbH^2}{L}[/tex]

Step 2

Use the values below to find the constant k.

b = 6

H = 2

L = 12

W = 14

[tex]\begin{gathered} 12\text{ = }\frac{k\text{ }\times\text{ 6 }\times2^2}{12} \\ 14\text{ = }\frac{24k}{12} \\ \text{Cross multiply} \\ 24k\text{ = 14 x 12} \\ 24k\text{ = 1}68 \\ k\text{ = }\frac{168}{24} \\ k\text{ = }7 \end{gathered}[/tex]

Step 3

Find the unknow

W = ?

b = 4

H = 3

L = 14

[tex]\begin{gathered} W\text{ = }\frac{kbH^2}{L} \\ W\text{ = }\frac{7\text{ }\times\text{ 4 }\times3^2}{14} \\ W\text{ = }\frac{7\text{ }\times\text{ 4 }\times\text{ 9}}{14} \\ W\text{ = }\frac{252}{14} \\ W=\text{ 18 tons} \end{gathered}[/tex]

The maximum weight = 18 tons