Respuesta :
Given:
Astronauts for NASA must measure between 62 and 75 inches tall.
To find:
The equation which best represents the minimum and maximum heights accepted for NASA astronauts.
Solution:
Let h be the height accepted for NASA astronauts.
Astronauts for NASA must measure between 62 and 75 inches tall.
[tex]62\leq h\leq 75[/tex]
Subtract both sides by midpoint of 62 and 75, i.e., 68.5.
[tex]62-68.5\leq h-68.5\leq 75-68.5[/tex]
[tex]-6.5\leq h-68.5\leq 6.5[/tex]
We know that, [tex]-a\leq x\leq a=|x|\leq a[/tex].
[tex]|h-68.5|\leq 6.5[/tex]
So, the absolute inequality for heights accepted for NASA astronauts is [tex]|h-68.5|\leq 6.5[/tex].
The equation of this inequality represents the minimum and maximum heights accepted for NASA astronauts.
[tex]|h-68.5|=6.5[/tex]
Using this equation we get [tex]h=62,75[/tex], which are minimum and maximum values respectively.
Therefore, the correct option is D.
