the strength of a rectangular beam varies jointly with its width and the square of its thickness, If a beam 4 inches wide and 2 inches thick supports 320 pounds. how much can a beam of the same material that is 3 inches wide and 1 inch thick support?

60 pounds

Step-by-step explanation:

This is a joint variation question.

First, let us declare variables for the parameters. Let the strength of the beam, width of the beam and the thickness of the beam be s, w and t respectively.

Since it is a joint variation, let's call our constant of proportionality k, the joint variation equation we have will look like;

S = k * w * t^2

Now for our first set of parameters, we can calculate k.

Here, s = 320 pounds, w = 4 inches and t = 2 inches

We plug these values to get k;

320 = k * 4 * 2^2

320 = 16k

k = 320/16

K = 20

Now, we move to the second parameters set;

Here, s = ?, w = 3 inches and t = 1 inch

We plug these values into the original joint variation equation with k = 20

we have;

S = 20 * 3 * 1^2

S = 60 * 1 = 60 pounds