Question

The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h, and inversely proportional to its length L.

a. Write an equation that expresses this prportionality
b. Determine the constant of proportionality if a beam 4 in. wide, 6 in. high, and 12 ft long can support a weight of 4800 lb.
c. If a 10-ft beam made of the same material is 3 in. wide and 10 in. high, what is the maximum weight it can support?
So far, I've got the equation. It's M=k^2wh^2/L. I need help working out the problem.

Answer 1

Answer:

Step-by-step explanation:

a) The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h, and inversely proportional to its length L. If k represent the constant of proportionality, the expression would be

M = kwh²/L

b) if w = 4 inches, h = 6 inches, length = 12 ft

1 foot = 12 inches

12 ft = 12 × 12 = 144 inches. Therefore

L = 144 inches

M = 4800lb

Substituting these values into

M = kwh²/L, it becomes

4800 = (k × 4 × 6²)/144

4800 = k

The equation becomes

M = 4800wh²/L

c) if L = 10ft(10 × 12 = 120 inches),

h = 10 inches

w = 3 inches, then

M = 4800 × 3 × 10²/120

M = 12000 lbs