Forensic specialists can estimate the height of a deceased person from the lengths of the person's bones. These lengths are substituted into mathematical inequalities. For instance, an inequality that relates the height h, in centimeters, of an adult female and the length f, in centimeters, of her femur is
|h − (2.47f + 54.10)| ¡Ü 3.72. Use this inequality to estimate the possible range of heights, rounded to the nearest 0.1 centimeter, for an adult female whose femur measures 45.39 centimeters.
The height, to the nearest 0.1 cm, is from ____ cm to ____ cm.
To estimate the possible range of heights for an adult female whose femur measures 45.39 centimeters, we can substitute the given length (45.39 cm) into the inequality equation and solve it.
The inequality equation is:
|h − (2.47f + 54.10)| ≤ 3.72
Substitute the value of f (femur length) with 45.39:
|h − (2.47 * 45.39 + 54.10)| ≤ 3.72
Simplify the equation:
|h − (112.1533 + 54.10)| ≤ 3.72
|h − 166.2533| ≤ 3.72
Now we have an absolute value inequality. To solve it, we have to consider two cases:
Case 1: h - 166.2533 ≤ 3.72
Solve for h:
h ≤ 3.72 + 166.2533
h ≤ 170.9733
Case 2: -(h - 166.2533) ≤ 3.72
Solve for h:
-h + 166.2533 ≤ 3.72
h - 166.2533 ≥ -3.72
h ≥ 162.5333
Therefore, the possible range of heights, rounded to the nearest 0.1 centimeter, for an adult female with a femur length of 45.39 centimeters is from 162.5 cm to 171.0 cm.
To estimate the possible range of heights for an adult female with a femur length of 45.39 centimeters, we will substitute this value into the inequality:
|h - (2.47f + 54.10)| ≤ 3.72
Substituting f = 45.39 into the inequality, we get:
|h - (2.47 * 45.39 + 54.10)| ≤ 3.72
|h - 112.2133| ≤ 3.72
Now, let's solve the inequality:
First, we will isolate the absolute value term:
-3.72 ≤ h - 112.2133 ≤ 3.72
Next, we will solve for the upper and lower bounds separately:
For the lower bound:
-3.72 + 112.2133 ≤ h
108.4933 ≤ h
For the upper bound:
112.2133 + 3.72 ≥ h
115.9333 ≥ h
Rounded to the nearest 0.1 centimeter, the estimated range of heights is from 108.5 cm to 115.9 cm.
well, you have
2.47f+54.1 = 166.21
So,
|h-166.21| <= 3.72
166.21-3.72 <= h <= 166.21+3.72
and so on