SOLUTION: the stiffness 'S' of a rectangular beam varies jointly as the width and the cube of the depth. if the stiffness is 90 when the width is 2 and the depth is 3, find the stiffness for

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Question 200524: the stiffness 'S' of a rectangular beam varies jointly as the width and the cube of the depth. if the stiffness is 90 when the width is 2 and the depth is 3, find the stiffness for a beam with a width of 5 and a depth of 2
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given S+=+Kwd%5E3; where K is some constant. First thing we need to do is get enough info to solve for K. Lucky for you, the problem provides that.
90+=+K%2A2%2A3%5E3
90+=+K+%2A+54
90%2F54+=+K So we know K now
S+=%2890wd%5E3%29%2F54 Put K in the original equation
Now solve when w=5 and d=2
S+=%2890wd%5E3%29%2F54
S+=%2890%2A5%2A2%5E3%29%2F54
S+=+%2890%2A5%2A8%29%2F54
S+=+66.667