Question 190888This question is from textbook algebra and trigonometry structure and method book 2
: In problems 11 and 12, use the fact that the load a beam with a rectangular cross section can support is jointly proportional to the beams width and the square of its depth and inversely proportional to it's length.
11. A beam 3 cm wide and 5cm deep can support a load of 630kg. What load can it support when turned on its side?
please please please explain what you are doing if you answer this problem. it is so confusing i cant even think of what to do.
This question is from textbook algebra and trigonometry structure and method book 2
Answer by solver91311(24713)   (Show Source):
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If the load weight is jointly proportional to the width and the square of the depth and inversely proportional to the beam length, then you can write the relationship thus:
Where L is the load weight, w is the beam width, d is the beam depth, l is the beam length, and k is the constant of proportionality.
If something is proportional it goes in the numerator -- it is proportional to w and  , so both go in the numerator. If it is inversely proportional, it goes in the denominator, like our l. And finally, you have to put in a constant of proportionality. It doesn't matter where that goes except that it is generally computationally easier if you leave it in the numerator.
Since you didn't give the beam length, what we need to do is to calculate a value for  given that w = 3 cm, d = 5 cm, and L = 630 kg. So substitute the values:
(5)^2}{l} = \frac{75k}{l})
And then:
Now re-write your proportion:
And substitute the new values for w and d, namely 5 and 3 respectively.
(3)^2 = 8.4\,\cdot\,45 = 378\text{ kg})
John
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