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Answer :
To determine the scuba diver's position in relation to sea level after both descents, follow these steps:
1. Start with the First Descent:
The scuba diver descended [tex]\(19 \frac{5}{12}\)[/tex] feet below sea level. This mixed number can be converted to a decimal for easier addition. [tex]\(19 \frac{5}{12}\)[/tex] is equivalent to:
[tex]\[
19 + \frac{5}{12} = 19.4167 \text{ feet} \quad (\text{approximately})
\][/tex]
2. Consider the Second Descent:
The scuba diver then descended an additional [tex]\(3 \frac{3}{5}\)[/tex] feet. Convert this mixed number to a decimal as well:
[tex]\[
3 + \frac{3}{5} = 3.6 \text{ feet}
\][/tex]
3. Calculate the Total Descent:
Add the two decimal values from the descents to find the total distance the scuba diver has descended from sea level:
[tex]\[
19.4167 + 3.6 = 23.0167 \text{ feet} \quad (\text{approximately})
\][/tex]
4. Determine the Diver's Location in Relation to Sea Level:
Since the diver descended below sea level, the position relative to sea level is negative. Therefore, the diver's location is:
[tex]\[
-23.0167 \text{ feet}
\][/tex]
Given the options:
- A. [tex]\(15 \frac{49}{60}\)[/tex] feet
- B. [tex]\(23 \frac{1}{60}\)[/tex] feet
- C. [tex]\(-15 \frac{49}{60}\)[/tex] feet
- D. [tex]\(-23 \frac{1}{60}\)[/tex] feet
The correct answer is D. The location of the scuba diver in relation to sea level was [tex]\(-23 \frac{1}{60}\)[/tex] feet.
1. Start with the First Descent:
The scuba diver descended [tex]\(19 \frac{5}{12}\)[/tex] feet below sea level. This mixed number can be converted to a decimal for easier addition. [tex]\(19 \frac{5}{12}\)[/tex] is equivalent to:
[tex]\[
19 + \frac{5}{12} = 19.4167 \text{ feet} \quad (\text{approximately})
\][/tex]
2. Consider the Second Descent:
The scuba diver then descended an additional [tex]\(3 \frac{3}{5}\)[/tex] feet. Convert this mixed number to a decimal as well:
[tex]\[
3 + \frac{3}{5} = 3.6 \text{ feet}
\][/tex]
3. Calculate the Total Descent:
Add the two decimal values from the descents to find the total distance the scuba diver has descended from sea level:
[tex]\[
19.4167 + 3.6 = 23.0167 \text{ feet} \quad (\text{approximately})
\][/tex]
4. Determine the Diver's Location in Relation to Sea Level:
Since the diver descended below sea level, the position relative to sea level is negative. Therefore, the diver's location is:
[tex]\[
-23.0167 \text{ feet}
\][/tex]
Given the options:
- A. [tex]\(15 \frac{49}{60}\)[/tex] feet
- B. [tex]\(23 \frac{1}{60}\)[/tex] feet
- C. [tex]\(-15 \frac{49}{60}\)[/tex] feet
- D. [tex]\(-23 \frac{1}{60}\)[/tex] feet
The correct answer is D. The location of the scuba diver in relation to sea level was [tex]\(-23 \frac{1}{60}\)[/tex] feet.
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