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

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d

part a: 1.08

part b: 27.59