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values of the rate at three-hour time intervals are shown in the table. t (hr) r(t) (L/hr) lower estimate = a) Find lower and upper estimates for the total amount of liquid that leaked out. upper estimate = 0 3 6 9 12 15 More accurate estimate = liters liters 7.4 7.1 6.8 6.5 6.2 5.9 b) Using the lower and upper estimate above, determine a more accurate estimate by averaging the values. liters

values of the rate at three-hour time intervals are shown in the table. t (hr) r(t) (L/hr) lower estimate = a) Find lower and upper estimates for the total amount of liquid that leaked out. upper estimate = 0 3 6 9 12 15 More accurate estimate = liters liters 7.4 7.1 6.8 6.5 6.2 5.9 b) Using the lower and upper estimate above, determine a more accurate estimate by averaging the values. liters

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Title: Estimating Liquid Leakage from a Damaged Tank** **Introduction** Liquid leaked from a damaged tank at a rate of \( r(t) \) liters per hour. The rate decreased as time passed, and values of the rate at three-hour time intervals are shown in the table below. **Data Table** | \( t \) (hr) | \( r(t) \) (L/hr) | |--------------|------------------| | 0 | 7.4 | | 3 | 7.1 | | 6 | 6.8 | | 9 | 6.5 | | 12 | 6.2 | | 15 | 5.9 | **Exercises** 1. **Find lower and upper estimates for the total amount of liquid that leaked out.** - **Lower Estimate:** \(\text{lower estimate} = \underline{\phantom{--------}}\) liters - **Upper Estimate:** \(\text{upper estimate} = \underline{\phantom{--------}}\) liters 2. **Using the lower and upper estimate above, determine a more accurate estimate by averaging the values.** - **More Accurate Estimate:** \(\text{more accurate estimate} = \underline{\phantom{--------}}\) liters **Conclusion** By calculating both a lower and upper estimate based on the rates provided at discrete intervals and subsequently averaging these estimates, a more precise approximation of the total liquid leakage can be obtained. This method is a practical application of numerical integration techniques such as the trapezoidal rule and can assist in real-world scenarios involving fluid loss or similar processes.
Transcribed Image Text:**Title: Estimating Liquid Leakage from a Damaged Tank** **Introduction** Liquid leaked from a damaged tank at a rate of \( r(t) \) liters per hour. The rate decreased as time passed, and values of the rate at three-hour time intervals are shown in the table below. **Data Table** | \( t \) (hr) | \( r(t) \) (L/hr) | |--------------|------------------| | 0 | 7.4 | | 3 | 7.1 | | 6 | 6.8 | | 9 | 6.5 | | 12 | 6.2 | | 15 | 5.9 | **Exercises** 1. **Find lower and upper estimates for the total amount of liquid that leaked out.** - **Lower Estimate:** \(\text{lower estimate} = \underline{\phantom{--------}}\) liters - **Upper Estimate:** \(\text{upper estimate} = \underline{\phantom{--------}}\) liters 2. **Using the lower and upper estimate above, determine a more accurate estimate by averaging the values.** - **More Accurate Estimate:** \(\text{more accurate estimate} = \underline{\phantom{--------}}\) liters **Conclusion** By calculating both a lower and upper estimate based on the rates provided at discrete intervals and subsequently averaging these estimates, a more precise approximation of the total liquid leakage can be obtained. This method is a practical application of numerical integration techniques such as the trapezoidal rule and can assist in real-world scenarios involving fluid loss or similar processes.
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