This is the question and what I have so far is under it.
"Given the length of a femur, f, in centimetres, a person’s height can be determined using the equation H=2.4f+61.4, where H is the height of the person in centimetres. Suppose this equation has a margin of error of ±3.4cm and that a femur is 43.2cm. Write an absolute value inequality that describes this person’s height and solve the inequality to find the range of possible heights."
I get that the person's height is that equation with H and they give the length of the femur but I do not know how to set the equation in terms that it stays within the ±3.4cm range. I also think I may have the wrong idea about what the question is asking.
To find the absolute value inequality that describes the person's height within the margin of error, you'll need to consider the upper and lower bounds of the range.
Let's start with the equation for the person's height:
H = 2.4f + 61.4
Given that the length of the femur, f, is 43.2 cm, you can substitute this value into the equation to find the person's height, H:
H = 2.4(43.2) + 61.4
= 103.68 + 61.4
= 165.08 cm
Now, let's consider the margin of error. The equation has a margin of error of ±3.4 cm, which means the height can be 3.4 cm higher or lower than the calculated value of 165.08 cm.
To find the upper bound, add the margin of error to the calculated height:
Upper Bound = 165.08 + 3.4
= 168.48 cm
To find the lower bound, subtract the margin of error from the calculated height:
Lower Bound = 165.08 - 3.4
= 161.68 cm
Therefore, the range of possible heights can be described by the following absolute value inequality:
|H - 165.08| ≤ 3.4
This inequality states that the absolute value of the difference between the person's height, H, and the calculated height of 165.08 cm should be less than or equal to 3.4 cm.
To solve the inequality, you will have two cases:
1. H - 165.08 ≤ 3.4:
H ≤ 168.48
2. -(H - 165.08) ≤ 3.4:
-H + 165.08 ≤ 3.4
-H ≤ 3.4 - 165.08
-H ≤ -161.68
Remember that multiplying or dividing by a negative number flips the inequality, so:
H ≥ 161.68
Therefore, the range of possible heights is 161.68 cm ≤ H ≤ 168.48 cm.