Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To find the diver's depth in relation to the surface of the water, let's break down the problem step-by-step:
1. Convert the mixed numbers to improper fractions:
- The initial dive is [tex]\(17 \frac{2}{3}\)[/tex] yards.
[tex]\[ 17 \frac{2}{3} = 17 + \frac{2}{3} = \frac{17 \times 3 + 2}{3} = \frac{51 + 2}{3} = \frac{53}{3} \text{ yards} \][/tex]
- The deeper dive is [tex]\(9 \frac{3}{8}\)[/tex] yards.
[tex]\[ 9 \frac{3}{8} = 9 + \frac{3}{8} = \frac{9 \times 8 + 3}{8} = \frac{72 + 3}{8} = \frac{75}{8} \text{ yards} \][/tex]
2. Sum the depths to find the total depth:
- The total depth is the sum of the two improper fractions. To sum these, we need a common denominator. The least common multiple (LCM) of the denominators 3 and 8 is 24.
- Convert each fraction to have the common denominator:
[tex]\[ \frac{53}{3} = \frac{53 \times 8}{3 \times 8} = \frac{424}{24} \][/tex]
[tex]\[ \frac{75}{8} = \frac{75 \times 3}{8 \times 3} = \frac{225}{24} \][/tex]
- Add the two fractions:
[tex]\[ \frac{424}{24} + \frac{225}{24} = \frac{424 + 225}{24} = \frac{649}{24} \][/tex]
3. Convert the improper fraction to a mixed number:
- Divide 649 by 24 to get the mixed number.
[tex]\[ 649 \div 24 \approx 27.041666666666668 \][/tex]
- This means:
[tex]\[ 649 = 27 \times 24 + 1 \quad (\text{as } 27 \times 24 = 648, \text{ with a remainder of 1}) \][/tex]
[tex]\[ \text{Thus, } \frac{649}{24} = 27 \frac{1}{24} \][/tex]
4. Determine the diver's depth in relation to the surface:
- Since the diver is below the surface, the total depth will be negative.
[tex]\[ -27 \frac{1}{24} \][/tex]
Therefore, the diver's depth in relation to the surface of the water is:
[tex]\[ -27 \frac{1}{24} \text{ yards} \][/tex]
This is the correct depth in relation to the surface of the water. Thus, the correct answer is:
[tex]\[ \boxed{-27 \frac{1}{24}} \][/tex]
1. Convert the mixed numbers to improper fractions:
- The initial dive is [tex]\(17 \frac{2}{3}\)[/tex] yards.
[tex]\[ 17 \frac{2}{3} = 17 + \frac{2}{3} = \frac{17 \times 3 + 2}{3} = \frac{51 + 2}{3} = \frac{53}{3} \text{ yards} \][/tex]
- The deeper dive is [tex]\(9 \frac{3}{8}\)[/tex] yards.
[tex]\[ 9 \frac{3}{8} = 9 + \frac{3}{8} = \frac{9 \times 8 + 3}{8} = \frac{72 + 3}{8} = \frac{75}{8} \text{ yards} \][/tex]
2. Sum the depths to find the total depth:
- The total depth is the sum of the two improper fractions. To sum these, we need a common denominator. The least common multiple (LCM) of the denominators 3 and 8 is 24.
- Convert each fraction to have the common denominator:
[tex]\[ \frac{53}{3} = \frac{53 \times 8}{3 \times 8} = \frac{424}{24} \][/tex]
[tex]\[ \frac{75}{8} = \frac{75 \times 3}{8 \times 3} = \frac{225}{24} \][/tex]
- Add the two fractions:
[tex]\[ \frac{424}{24} + \frac{225}{24} = \frac{424 + 225}{24} = \frac{649}{24} \][/tex]
3. Convert the improper fraction to a mixed number:
- Divide 649 by 24 to get the mixed number.
[tex]\[ 649 \div 24 \approx 27.041666666666668 \][/tex]
- This means:
[tex]\[ 649 = 27 \times 24 + 1 \quad (\text{as } 27 \times 24 = 648, \text{ with a remainder of 1}) \][/tex]
[tex]\[ \text{Thus, } \frac{649}{24} = 27 \frac{1}{24} \][/tex]
4. Determine the diver's depth in relation to the surface:
- Since the diver is below the surface, the total depth will be negative.
[tex]\[ -27 \frac{1}{24} \][/tex]
Therefore, the diver's depth in relation to the surface of the water is:
[tex]\[ -27 \frac{1}{24} \text{ yards} \][/tex]
This is the correct depth in relation to the surface of the water. Thus, the correct answer is:
[tex]\[ \boxed{-27 \frac{1}{24}} \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
