Answer:
The equation is:
[tex]L=3\,\,d^2\\[/tex]
and a beam with 10 in diagonal will support 300 lb
Step-by-step explanation:
The mathematical expression that represents the statement:
"The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. "
can be written as:
[tex]L=k\,\,d^2[/tex]
where k is the constant of proportionality
To find the constant we use the data they provide: "A beam with diagonal 6 in will support a maximum load of 108 lb.":
[tex]L=k\,\,d^2\\108 = k\,\,(6)^2\\k=\frac{108}{36} \,\,\frac{lb}{in^2}\\ k = 3\,\,\frac{lb}{in^2}[/tex]
Now we can use the proportionality found above to find the maximum load for a 10 in diagonal beam:
[tex]L=3\,\,d^2\\L=3\,\,(10)^2\\L=300 \,\,lb[/tex]
Answer:
L=3d^2 the beam will support 300 pounds
Step-by-step explanation:
108=k x 6^2
Dividing by 6^2=36 gives k=3, so an equation that relates L and d is
L=3d^2 d=10 yields
3(10)^2=300
So a beam with a 10in diagonal will support a 300lb load.
