Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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.

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.