The weight P in pounds that a beam can safely carry is inversely proportional to the distance D in feet between the supports of the beam. For a certain type of wooden beam, Upper P equals StartFraction 8 comma 000 Over Upper D EndFraction
. What distance between supports is needed to carry 2000 lb?
For the beam to support a weight of 2000 lb, the distance between the supports needs to be no more than
enter your response here feet.
(Simplify your answer. Round to two decimal places as needed.)
The weight P is inversely proportional to the distance D, so we can set up the equation:
P = k/D
where k is the constant of proportionality.
Given that P = 8000/D, we can plug in P = 2000 and solve for D:
2000 = 8000/D
D = 8000/2000
D = 4 feet
Therefore, the distance between the supports needed to carry 2000 lb is 4 feet.