# Thread: joint and inverse variation

1. ## joint and inverse variation

21. The amount that a beam bends downward when it is supported at each end and centrally loaded varies jointly as the mass of the load and the cube of the length, and varies inversely as the cube of the depth of the beam. A beam 4 meters long that has a depth of 15 centemeters bends 0.7 centimeters downwardwhen loaded with a mass of 1,000 kilograms. To the nearest tenth, what is the maximum load that a beam 5 meters long and with a depth of 10 centimeters can carry at its center without bending more than 3.2 centimeters?

Seems that I need to use joint and direct variation in one problem. I'm not sure what to do.

2. Let b=amount of bend
Let m=mass
Let l=length
Let d=depth

$b=\frac{kml^3}{d^3}$

k is your constant of proportionality.

3. can you help me figure out the rest of the problem?

4. Originally Posted by masters
Let b=amount of bend
Let m=mass
Let l=length
Let d=depth

$b=\frac{kml^3}{d^3}$

k is your constant of proportionality.
$0.7=\frac{k\cdot1000\cdot4^3}{15^3}$

Solve for k.

Then substitute k back into:

$3.2=\frac{km5^3}{10^3}$

and solve for m.