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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.

The Strength Of A Beam Varies Inversely With The Square Of Its Length If A 10foot Beam Can Support 500 Pounds How Many Pounds Can A 13 Foot Beam Support Round T class=

Sagot :

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:

[tex]S=\frac{k}{L^2}[/tex]

For a constant k.

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

We write:

[tex]\begin{gathered} 500=\frac{k}{(10)^2} \\ \end{gathered}[/tex]

And solve for k:

[tex]k=500\cdot10^2=500\cdot100=50,000[/tex]

Then the inverse relation equation is:

[tex]S=\frac{50,000}{L^2}[/tex]

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

[tex]S=\frac{50,000}{13^2}=\frac{50,000}{169}=295.857[/tex]

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

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