A carpenter is cutting a 2 by 4 for the framing of a roof. The length needs to be 5 feet. He allows 0.1-foot possible variation for the length of the cut. What values of l represent the acceptable lengths for the board, in feet?
Could this be correct?
L≤5.1
almost.
4.9 ≤ L ≤ 5.1
Would 4.9 not be equally acceptable?
Seems to me it would be 4.95 </ = L </= 5.05
No, that is incorrect. The correct inequality is:
L ≥ 4.9
This represents that the board length (L) needs to be greater than or equal to 4.9 feet in order to be an acceptable length.
To determine the acceptable lengths for the board, given a 0.1-foot possible variation, you need to consider both the upper and lower limits.
Let's start with the lower limit. Since the length of the cut should be 5 feet, and the carpenter allows for a 0.1-foot variation, the minimum acceptable length would be 5 feet minus 0.1 feet. Therefore, the lower limit would be 4.9 feet.
Now let's move on to the upper limit. The maximum acceptable length would be equal to the desired length (5 feet) plus the allowed variation (0.1 feet). Therefore, the upper limit would be 5.1 feet.
So, to answer your question, the acceptable lengths for the board, in feet, would be any value less than or equal to 5.1 feet (L ≤ 5.1), and greater than or equal to 4.9 feet (L ≥ 4.9).