The load L a horizontal beam can safely support varies jointly as the width w and the square of the depth d and inversely as the length l. If a 12-foot beam with width 6 inches and depth 8 inches safely supports 600 pounds, how many pounds can a 14-foot beam that has width 5.5 inches and depth 4 inches be expected to support? Round to the nearest pound. Assume the two beams are made of the same material.

Answer 1

"The load L a horizontal beam can safely support varies jointly as the width w and the square of the depth d and inversely as the length l"

---- >Load = k(wd^2/L)
given :
L = 12, w = 6inches or 1/2 , d = 8 inches or 2/3, load = 600
600 = k(1/2)(4/9) /12
(1/54)k = 600
k = 32400

Load = 32400(wd^2/L)
for the case L = 14 , w = 11/24 , d = 1/3

Load = 32400(11/24)(1/9)/14 = 117.857 or 118 to the nearest pound

check my arithmetic, easy to make a mistake on this one.

Answer 2

Show me the steps in doing this problem

30ax-15ay+42x-21y