To solve the given problems step by step:
(a) Finding the Altitude of the Top of the Hill
1. We know that Checkpoint 2 has an altitude of [tex]\(-181\)[/tex] feet above sea level.
2. The question states that the top of the hill is 156 feet above Checkpoint 2.
3. To determine the altitude of the top of the hill, we add 156 feet to the altitude of Checkpoint 2:
[tex]\[
\text{Altitude of the top of the hill} = \text{Altitude of Checkpoint 2} + 156
\][/tex]
4. Plugging in the values:
[tex]\[
\text{Altitude of the top of the hill} = -181 + 156
\][/tex]
5. Calculating this gives:
[tex]\[
\text{Altitude of the top of the hill} = -25 \text{ feet}
\][/tex]
So, the altitude of the top of the hill is [tex]\(-25\)[/tex] feet.
(b) Finding How Much Lower Checkpoint 3 is Compared to Checkpoint 4
1. We know that Checkpoint 3 has an altitude of [tex]\(-128\)[/tex] feet above sea level.
2. Checkpoint 4 has an altitude of [tex]\(2,439\)[/tex] feet above sea level.
3. To determine how much lower Checkpoint 3 is compared to Checkpoint 4, we subtract the altitude of Checkpoint 3 from the altitude of Checkpoint 4:
[tex]\[
\text{Difference in altitude} = \text{Altitude of Checkpoint 4} - \text{Altitude of Checkpoint 3}
\][/tex]
4. Plugging in the values:
[tex]\[
\text{Difference in altitude} = 2439 - (-128)
\][/tex]
5. Simplifying this gives:
[tex]\[
\text{Difference in altitude} = 2439 + 128
\][/tex]
6. Calculating this gives:
[tex]\[
\text{Difference in altitude} = 2567 \text{ feet}
\][/tex]
So, Checkpoint 3 is [tex]\(2567\)[/tex] feet lower than Checkpoint 4.
In summary:
(a) The altitude of the top of the hill is [tex]\(-25\)[/tex] feet.
(b) Checkpoint 3 is [tex]\(2567\)[/tex] feet lower than Checkpoint 4.
