Answer:
62 kg.
Step-by-step explanation:
Let w be the weight of beam and l be the length of beam.
We have been given that the weight that a horizontal beam can support varies inversely as the length of the beam.
We know that inversely proportion quantities are in form:
, where k is constant of proportionality.
![w=\frac{k}{l}](https://tex.z-dn.net/?f=w%3D%5Cfrac%7Bk%7D%7Bl%7D)
First of all, we will find the value of k using the
and
in inversely proportion equation as:
![310=\frac{k}{2}](https://tex.z-dn.net/?f=310%3D%5Cfrac%7Bk%7D%7B2%7D)
![310*2=\frac{k}{2}*2](https://tex.z-dn.net/?f=310%2A2%3D%5Cfrac%7Bk%7D%7B2%7D%2A2)
![620=k](https://tex.z-dn.net/?f=620%3Dk)
Now we will substitute
and
, in our given equation as:
![w=\frac{620}{10}](https://tex.z-dn.net/?f=w%3D%5Cfrac%7B620%7D%7B10%7D)
![w=62](https://tex.z-dn.net/?f=w%3D62)
Therefore, a 10-m beam can support 62 kilograms.