Question

the strength of a beam varies inversely with the square of its length. if a 10 -foot beam can support 400 pounds, how many pounds can a15 -foot beam support? round the answer to the nearest pound.

Answer 1

≈ 178 pounds

Explanation:

let S be strength and l be length

given S varies inversely with l² then the equation relating them is

S =
`(k)/(l^2)` ← k is the constant of variation

to find k use the condition l = 10, S = 400

400 =
`(k)/(10^2)` =
`(k)/(100)` ( multiply both sides by 100 )

40000 = k

S =
`(40000)/(l^2)` ← equation of variation

when l = 15 , then

S =
`(40000)/(15^2)` =
`(40000)/(225)` ≈ 178 pounds ( to the nearest pound )