### (a) The top of a hill rises 252 feet above Checkpoint 1. What is the altitude of the top of the hill?
1. Identify the altitude of Checkpoint 1:
The altitude of Checkpoint 1 is -183 feet.
2. Determine how much higher the top of the hill is compared to Checkpoint 1:
The top of the hill is 252 feet above Checkpoint 1.
3. Calculate the altitude of the top of the hill:
To find the altitude, add the height difference to the altitude of Checkpoint 1.
[tex]\[
\text{Hill Top Altitude} = \text{Altitude of Checkpoint 1} + 252
\][/tex]
Plugging in the values:
[tex]\[
\text{Hill Top Altitude} = -183 + 252 = 69 \text{ feet}
\][/tex]
Thus, the altitude of the top of the hill is [tex]\( \boxed{69} \)[/tex] feet.
### (b) How much higher is Checkpoint 5 than Checkpoint 4?
1. Identify the altitudes of Checkpoints 5 and 4:
- The altitude of Checkpoint 5 is 3,146 feet.
- The altitude of Checkpoint 4 is -69 feet.
2. Calculate the altitude difference between Checkpoint 5 and Checkpoint 4:
[tex]\[
\text{Altitude Difference} = \text{Altitude of Checkpoint 5} - \text{Altitude of Checkpoint 4}
\][/tex]
Plugging in the values:
[tex]\[
\text{Altitude Difference} = 3,146 - (-69) = 3,146 + 69 = 3,215 \text{ feet}
\][/tex]
Thus, Checkpoint 5 is [tex]\( \boxed{3,215} \)[/tex] feet higher than Checkpoint 4.
