The rate at which water flows into a tank, in gallons per hour, is given by a differentiable function R of time t. The table below gives the rate as measured at various times in an 8-hour time period. t (hours) R(t) (gallons per hour) 0 2. Is there some time t, 0 < t < 8, such that R'(t) = 0? Justify your answer. 1.95 2 2.5 3 2.8 7 4 8 4.26 1. Use a trapezoidal sum with the four sub-intervals indicated by the data in the table to estimate JR(t) dt. Using correct units, explain the meaning of your answer in terms of water flow. Give 3 decimal places in your answer. 3. The rate of water flow R(t) can be estimated by W(t) = In(t² + 7). Use W(t) to approximate the average rate of water flow during the 8-hour time period. Indicate units of measure.
The rate at which water flows into a tank, in gallons per hour, is given by a differentiable function R of time t. The table below gives the rate as measured at various times in an 8-hour time period. t (hours) R(t) (gallons per hour) 0 2. Is there some time t, 0 < t < 8, such that R'(t) = 0? Justify your answer. 1.95 2 2.5 3 2.8 7 4 8 4.26 1. Use a trapezoidal sum with the four sub-intervals indicated by the data in the table to estimate JR(t) dt. Using correct units, explain the meaning of your answer in terms of water flow. Give 3 decimal places in your answer. 3. The rate of water flow R(t) can be estimated by W(t) = In(t² + 7). Use W(t) to approximate the average rate of water flow during the 8-hour time period. Indicate units of measure.
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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Transcribed Image Text:The rate at which water flows into a tank, in gallons per hour, is given by a differentiable function R of time t. The table below gives the rate as measured at
various times in an 8-hour time period.
t (hours)
R(t) (gallons per hour)
0
2. Is there some time t, 0 < t < 8, such that R'(t) = 0? Justify your answer.
1.95
2
2.5
3
2.8
7
4
8
4.26
1. Use a trapezoidal sum with the four sub-intervals indicated by the data in the table to estimate JR(t) dt. Using correct units, explain the meaning of your
answer in terms of water flow. Give 3 decimal places in your answer.
0
3. The rate of water flow R(t) can be estimated by W(t) = In(t2 + 7). Use W(t) to approximate the average rate of water flow during the 8-hour time period.
Indicate units of measure.
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