Chapter A.5, Problem 96E

To determine

Verify that the femur belongs to the missing man.

Answer to Problem 96E

  $\boxed{74inches}$ , $\boxed{Yes,itbelongstothemissingman}$

Explanation of Solution

Given information:

The relationship between the length of an adult’s femur (thigh bone) and the height of the adult can be approximated by the linear equations

  $\begin{array}{l}y=0.432x-10.44\\ y=0.449x-12.15\end{array}$

Where $y$ is the length of the femur in inches and $x$ is the height of the adult in inches(see figure).

  

Officials search a forest for a missing man who is $6$ feet $2$ inches tall. They find an adult male femur that is $21$ inches long. Is it possible that the femur belongs to the missing man?

Calculation:

Here, we will consider the following information:

The relationship between the lengths of a male femur (thigh bone) and the height of the adult can be approximated by the linear equation:

  $y=0.449x-12.15$

Thus, $y$ is the length of the femur in inches and $x$ is the height of the male in inches.

As, height of the man is equal to $6$ feet $2$ inches,

  $1feet=12in.$

Thus, the height of the man in inches will be:

  $6feet2inches=6feet+2inches$

  $=6\left(12in.\right)+2in.$

  $=72in.+2in.$

  $=74inches$

Hence, the height of the man is $\boxed{74inches}$ .

Now, as the length of the adult male femur is $21$ inches long,

So, to estimate the height we will substitute $y=21$ in equation $y=0.449x-12.15$ for the value of $x$ :

  $21=0.449x-12.15$

Now, add $12.15$ to both the sides of the equation:

  $21+12.15-0.449x$

  $33.15=0.449x$

Now, divide both sides by $0.432$ :

  $\frac{33.15}{0.449}=\frac{0.449x}{0.449}$

Thus, value of $x$ is given by:

  $x=73.9$

  $x\approx 74$

As, the exact height is almost same as the estimated height.

Hence, the femur belongs to the missing man.