Example 2
Completion requirements
| Example 2 |
The maximum distance between the Earth and the Sun is approximately \(152\thinspace 000\thinspace 000\thinspace \rm{ km}\), and the minimum distance between the Earth and the Sun is approximately \(147\thinspace 000\thinspace 000\thinspace \rm{ km}\). Write an absolute value equation, where \(d\) represents the distance between the Earth and the Sun in millions of kilometres.
The difference between the maximum and minimum is \(5\thinspace 000\thinspace 000\). The midpoint between the maximum and minimum is \(\left( \frac{152 \thinspace 000 \thinspace 000 + 147\thinspace 000\thinspace 000}{2} \right) = 149\thinspace 500 \thinspace 000\).
The maximum is \(2\thinspace 500\thinspace 000 \) greater than the midpoint, and the minimum is \(2\thinspace 500\thinspace 000 \) less than the midpoint. To write an absolute value equation, use \(149.5\) and \(2.5\) because \(d\) represents the maximum and minimum in millions of kilometres.
\(d_{\max } = 149.5 + 2.5\)
\(d_{\min } = 149.5 - 2.5\)
The absolute value equation is \(\left|d - 149.5 \right| = 2.5 \).
The maximum is \(2\thinspace 500\thinspace 000 \) greater than the midpoint, and the minimum is \(2\thinspace 500\thinspace 000 \) less than the midpoint. To write an absolute value equation, use \(149.5\) and \(2.5\) because \(d\) represents the maximum and minimum in millions of kilometres.
\(d_{\max } = 149.5 + 2.5\)
\(d_{\min } = 149.5 - 2.5\)
The absolute value equation is \(\left|d - 149.5 \right| = 2.5 \).
| For more information on absolute value equations, see pp. 380 – 388 of Pre-Calculus 11. |