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.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the...
Related questions
Question
Look at picture please!
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2389f032-88c0-4991-a0a6-99e56a1fefa3%2Fbdd788c3-346d-4c10-bcdf-f0f32adfa9a3%2Fj2vfbb_processed.png&w=3840&q=75)
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.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
![Big Ideas Math A Bridge To Success Algebra 1: Stu…](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage