To determine the location of the dolphin relative to the surface of the water, we proceed step-by-step as follows:
1. Convert the Mixed Fractions to Improper Fractions:
- The initial depth is [tex]\(4 \frac{1}{2}\)[/tex] feet, which can be converted to an improper fraction:
[tex]\[
4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}
\][/tex]
Since the depth is below the surface, it is a negative value:
[tex]\[
-\frac{9}{2}
\][/tex]
- The second descent is [tex]\(2 \frac{3}{4}\)[/tex] feet, which can be converted to an improper fraction:
[tex]\[
2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}
\][/tex]
Since this is also below the surface:
[tex]\[
-\frac{11}{4}
\][/tex]
2. Find a Common Denominator to Add the Fractions:
- Convert [tex]\(-\frac{9}{2}\)[/tex] to a fraction with a denominator of 4:
[tex]\[
-\frac{9}{2} = -\frac{9 \times 2}{2 \times 2} = -\frac{18}{4}
\][/tex]
- Now, add the two fractions:
[tex]\[
-\frac{18}{4} + (-\frac{11}{4}) = -\frac{18 + 11}{4} = -\frac{29}{4}
\][/tex]
3. Convert the Resulting Fraction to a Mixed Number:
- To convert [tex]\(-\frac{29}{4}\)[/tex] to a mixed number, divide 29 by 4:
[tex]\[
29 \div 4 = 7 \text{, remainder }1
\][/tex]
Therefore:
[tex]\[
-\frac{29}{4} = -7 \frac{1}{4}
\][/tex]
So, the dolphin's location relative to the surface of the water is [tex]\(-7 \frac{1}{4}\)[/tex] feet or [tex]\(-7.25\)[/tex] feet.
