2. The rate at which sand is excavated from a pit, in gallons per hour, is given by differentiable function R(t). The table at the right gives values of R(t) measured once every 6 hours over a 24-hour period. t (hours) R(t) (gallons per hour) 0 6 12 18 24 400 420 510 320 400 a) Use a Right Riemann sum with 4 equal subdivisions to approximate 5* R(t)dt. Using correct units, explain the meaning of the answer in the context of the problem. b) Must there be a time t, 0 < t < 24, such that R'(t) = 0? Justify your answer. c) Values for R(t) can be estimated by using the continuous function S(x) =((25650 +375x – 20x²). Use S(x) to find the average rate of flow over the 24-hour period. Give units for your answer.
2. The rate at which sand is excavated from a pit, in gallons per hour, is given by differentiable function R(t). The table at the right gives values of R(t) measured once every 6 hours over a 24-hour period. t (hours) R(t) (gallons per hour) 0 6 12 18 24 400 420 510 320 400 a) Use a Right Riemann sum with 4 equal subdivisions to approximate 5* R(t)dt. Using correct units, explain the meaning of the answer in the context of the problem. b) Must there be a time t, 0 < t < 24, such that R'(t) = 0? Justify your answer. c) Values for R(t) can be estimated by using the continuous function S(x) =((25650 +375x – 20x²). Use S(x) to find the average rate of flow over the 24-hour period. Give units for your answer.
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:2. The rate at which sand is excavated from a pit, in gallons
per hour, is given by differentiable function R(t). The table
at the right gives values of R(t) measured once every 6
hours over a 24-hour period.
|t (hours) | R(t) (gallons per hour)
400
420
12
510
18
320
24
400
a) Use a Right Riemann sum with 4 equal subdivisions to approximate *R(t)dt. Using correct
units, explain the meaning of the answer in the context of the problem.
b) Must there be a time t, 0 < t < 24, such that R'(t) = 0? Justify your answer.
c) Values for R(t) can be estimated by using the continuous function
= (25650 + 375x – 20x²). Use S(x) to find the average rate of flow over the
24-hour period. Give units for your answer.
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