Question

The strength s of the rectangular beam varies jointly as its width w and the square of its depth d. If s = 1200 pounds per square inch and w = 3 inches and d = 10 inches, what is the strength of a beam four inches wide and 6 inches deep?

Answer 1

The strength of a rectangular beam varies jointly as its width and the square of its depth. The proportional relationship can be found using the given values. Then, the strength of a beam with specific dimensions can be calculated using the proportionality constant.

Step-by-step explanation:

The strength of a rectangular beam varies jointly as its width and the square of its depth. This means that the strength (s) is directly proportional to the product of the width (w) and the square of the depth (d).

We are given that s = 1200 pounds per square inch, w = 3 inches, and d = 10 inches. Now we can use these values to find the proportionality constant.

s = k * w * d^2, where k is the proportionality constant.

Plugging in the known values, we have 1200 = k * 3 * 10^2.

Solving for k, we get k = 1200 / (3 * 100) = 4.

Now we can use this value of k to find the strength of a beam with a width of 4 inches and a depth of 6 inches.

s = 4 * 4 * 6^2 = 576 pounds per square inch.