Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine the total distance fallen by the bungee jumper after five falls, we need to analyze the given pattern in the distances of each fall, recognize it, and then use this pattern to find the distances for the fourth and fifth falls. Finally, we will sum all these distances.
1. Observe the pattern in the fall distances:
- First fall: 97.2 feet
- Second fall: 64.8 feet
- Third fall: 43.2 feet
2. Recognize that the sequence of distances is decreasing in a specific pattern. We can see that this is a geometric sequence where each distance is reduced by a common ratio from the previous distance.
To find the common ratio \( r \):
[tex]\[ r = \dfrac{\text{Distance of 2nd fall}}{\text{Distance of 1st fall}} = \dfrac{64.8}{97.2} \][/tex]
3. Calculate the common ratio \( r \):
[tex]\[ r = \dfrac{64.8}{97.2} = 0.6667 \][/tex]
4. Using this common ratio, find the fourth and fifth falls:
- Fourth fall:
[tex]\[ \text{Fourth fall} = 43.2 \times 0.6667 = 28.8 \, \text{feet} \][/tex]
- Fifth fall:
[tex]\[ \text{Fifth fall} = 28.8 \times 0.6667 = 19.2 \, \text{feet} \][/tex]
5. List all the fall distances:
- First fall: 97.2 feet
- Second fall: 64.8 feet
- Third fall: 43.2 feet
- Fourth fall: 28.8 feet
- Fifth fall: 19.2 feet
6. Sum the total distance fallen:
[tex]\[ \text{Total distance} = 97.2 + 64.8 + 43.2 + 28.8 + 19.2 \][/tex]
7. Calculate the total:
[tex]\[ \text{Total distance} = 97.2 + 64.8 + 43.2 + 28.8 + 19.2 = 253.2 \, \text{feet} \][/tex]
Therefore, the total distance the bungee jumper drops after five falls is \( 253.2 \, \text{feet} \).
Among the given options, the correct answer is:
[tex]\[ \boxed{253.2 \, \text{ft}} \][/tex]
1. Observe the pattern in the fall distances:
- First fall: 97.2 feet
- Second fall: 64.8 feet
- Third fall: 43.2 feet
2. Recognize that the sequence of distances is decreasing in a specific pattern. We can see that this is a geometric sequence where each distance is reduced by a common ratio from the previous distance.
To find the common ratio \( r \):
[tex]\[ r = \dfrac{\text{Distance of 2nd fall}}{\text{Distance of 1st fall}} = \dfrac{64.8}{97.2} \][/tex]
3. Calculate the common ratio \( r \):
[tex]\[ r = \dfrac{64.8}{97.2} = 0.6667 \][/tex]
4. Using this common ratio, find the fourth and fifth falls:
- Fourth fall:
[tex]\[ \text{Fourth fall} = 43.2 \times 0.6667 = 28.8 \, \text{feet} \][/tex]
- Fifth fall:
[tex]\[ \text{Fifth fall} = 28.8 \times 0.6667 = 19.2 \, \text{feet} \][/tex]
5. List all the fall distances:
- First fall: 97.2 feet
- Second fall: 64.8 feet
- Third fall: 43.2 feet
- Fourth fall: 28.8 feet
- Fifth fall: 19.2 feet
6. Sum the total distance fallen:
[tex]\[ \text{Total distance} = 97.2 + 64.8 + 43.2 + 28.8 + 19.2 \][/tex]
7. Calculate the total:
[tex]\[ \text{Total distance} = 97.2 + 64.8 + 43.2 + 28.8 + 19.2 = 253.2 \, \text{feet} \][/tex]
Therefore, the total distance the bungee jumper drops after five falls is \( 253.2 \, \text{feet} \).
Among the given options, the correct answer is:
[tex]\[ \boxed{253.2 \, \text{ft}} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.