# Math

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The strength S of a rectangular beam varies jointly as its width w and the square of its thickness t. If a wood beam 3 inches wide and 5 inches thick supports 300 pounds, how much can a similar beam 3 inches wide and 8 inches thick support?
S=? pounds

• Math -

S(w,t) = kwt^2
Find k:
300 = k*3*25
k=4

So, S(w,t)=4wt^2

S(3,8) = 4*3*64 = 768

• Math -

The strength of a rectangular beam varies jointly with its width and the square of its depth. If the strength of a beam 2 inches wide by 10 inches deep is 1200 pounds per square inch, what is the strength of a beam 8 inches wide and 12 inches deep?

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