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 14 -foot beam support? Round the answer t o the nearest pound.
REmember that
the relationship between two variables x and y is inversely proportional, when the equation is of the form
yx=k
where
k is the constant of proportionality
so
In this problem we have
yx^2=k
where
y is the strength
x is is the length
we have
x=10 ft
y=500 pounds
Find the value of k
500*(10^2)=k
k=50,000
therefore
yx^2=50,000
For x=14 ft
substitute
y*(14^2)=50,000
solve for y
y=50,000/14^2
y=255 pounds
answer is 255 pounds