Question

The strength of a beam varies inversely with the square of its length. If a 10-foot beam can support 500 pounds how many pounds can a 13 foot beam support? Round the answer to the nearest pound.

Answer 1

The beam varies inversely with the square of it's length. Let's call S the strength and L the length.

Then we can write:

`S=(k)/(L^2)`

For a constant k.

Then, we know that if L = 10ft then S = 500 pounds

We write:

`\begin{gathered} 500=(k)/((10)^2) \\ \end{gathered}`

And solve for k:

`k=500\cdot10^2=500\cdot100=50,000`

Then the inverse relation equation is:

`S=(50,000)/(L^2)`

Then, for L = 13ft, the strength is:

`S=(50,000)/(13^2)=(50,000)/(169)=295.857`

To the nearest pound, a beam of 13ft can support 296 pounds.