Question

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)| ≤ 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 32.25 centimeters.

Answer 1

Answer:

$130.2845\leq h\leq 137.7245$

Step-by-step explanation:

Given an inequality that relates the height h, in centimeters, of an adult female and the length f, in centimeters, of her femur by the equation

$|h - (2.47f + 54.10)| \leq 3.72$

If an adult female measures her femur as 32.25 centimeters, we can determine the possible range of her height by plugging f = 32.25cm into the modelled equation as shown:

$|h - (2.47(32.25) + 54.10)| \leq 3.72\\|h - (79.9045 + 54.10)| \leq 3.72\\|h - (134.0045)| \leq 3.72$

If the modulus function is positive then:

$h - 134.0045 \leq 3.72\\h \leq 3.71+134.0045\\h\leq 137.7245$

If the modulus function is negative then:

$-(h - 134.0045) \leq 3.72\\-h+134.0045 \leq 3.72\\-h\leq 3.72-134.0045\\-h\leq -130.2845$

multiply through by -1

$-(-h)\geq -(-130.2845)\\h\geq 130.2845\\130.2845\leq h$

combining the resulting inequalities, the estimate of the possible range of heights will be $130.2845\leq h\leq 137.7245$