Question 927454
s = k*b*d/l^2

s = stiffness of a beam.
b = breadth
d = depth
l = length
k = constant of variation.


if b and d and l are each increased 10%, then the resulting equation becomes:


s = (k * 1.10*b*1.10*d)/(1.10*l)^2


this becomes:


s = k * 1.10^2*b*d/(1.10^2*l^2)


it appears that the 1.10^2 in the numerator and the 1.10^2 in the denominator cancel each other out and you are left with:


s = k*b*d/l^2


this looks a lot like your original equation.


in other words, if you increase each of the 3 dimensions by 10%, the net change in the stiffness of the beam is 0.


let's give some values to b and d and l and see if that works the way it looks like it's working.


assume:
b = 5
d = 10
l = 15


assume the constant of variation is equal to 45.


you get:


s = 45 * 5 * 10 / 15^2 which becomes:


s = 2250 / 225 which becomes:


s = 10


now we'll increase each of the dimensions by 10%.


5 becomes 5.5
10 becomes 11
15 becomes 16.5


formula becomes:


s = 45 * 5.5 * 11 / 16.5^2 which becomes:


s = 2722.5 / 272.25 which becomes:


s = 10


s remained the same.


looks like the formula works and there is no net change if all of the dimensions are each increased by 10%.


this is because the 1.10^2 in the numerator and the 1.10^2 in the denominator cancel out.


here's a reference that talks about joint inverse combined variation type word problems.


<a href = "http://www.shelovesmath.com/algebra/beginning-algebra/direct-inverse-and-joint-variation/#JointVariationWordProblem" target = "_blank">http://www.shelovesmath.com/algebra/beginning-algebra/direct-inverse-and-joint-variation/#JointVariationWordProblem</a>