person's adult height can be guessed from knowing his/her shoe size by the equation H= 1.6s + 4.3 where H is the person's adult height in feet and s is the persons shoe size. this equation has a margin of error of ±3.5 inches.
for the problems below, the example of the shoe size used will be size 13.
write answers rounded to 3 decimal places.
A) write an absolute value inequality (tolerance) that describes the person's possible heights. (height is in feet; error is in inches - convert inches. into feet)
b) solve the inequality and find the range of heights possible
please explain thoroughly thank you!
A) To write an absolute value inequality that describes the person's possible heights, we need to consider the margin of error of ±3.5 inches. Since the equation H = 1.6s + 4.3 represents the person's adult height, we need to account for the possible range of heights within that margin of error.
First, we need to convert the ±3.5 inches into feet. Since there are 12 inches in a foot, ±3.5 inches is ±3.5/12 = ±0.2917 feet.
Therefore, the absolute value inequality can be written as:
|H - (1.6s + 4.3)| ≤ 0.2917
B) To solve the absolute value inequality and find the range of heights possible, we need to consider two cases - one where the expression inside the absolute value is positive and one where it is negative.
Case 1: H - (1.6s + 4.3) ≥ 0
In this case, we can rewrite the inequality as:
H ≥ 1.6s + 4.3
Substituting s = 13 (from the given example shoe size), we get:
H ≥ 1.6(13) + 4.3
H ≥ 20.8 + 4.3
H ≥ 25.1
Therefore, the range of heights for this case is H ≥ 25.1 feet.
Case 2: -H + (1.6s + 4.3) ≥ 0
In this case, we need to reverse the sign of the inequality when we remove the absolute value:
H - 1.6s - 4.3 ≥ 0
Substituting s = 13, we get:
H - 1.6(13) - 4.3 ≥ 0
H - 20.8 - 4.3 ≥ 0
H - 25.1 ≥ 0
Therefore, the range of heights for this case is H ≤ 25.1 feet.
Combining both cases, we find that the range of heights possible is 25.1 feet ≥ H ≥ 25.1 feet. However, since this is a redundant statement, the actual range of heights possible is:
H = 25.1 feet
Please note that the range of heights I've provided is specific to the example shoe size of 13. For other shoe sizes, the range of heights will vary accordingly.