Concept explainers
(a)
To calculate:The value of the water flow.
(a)
Answer to Problem 58RE
The volume of water in gallons that flowed through the pipe during the 24 hour period.
Explanation of Solution
Given information:
The given table is shown below,
Formula used:
Calculation:
In the trapezoidal rule, if [a, b] is partitioned into n subintervals of equal length
That is,
Where,
Now, apply the trapezoidal rule with
So,
Now, substitute values in equation,
This approximation gives volume of water in gallons that flowed through the pipe during the 24 hour period.
Conclusion:
The volume of water in gallons that flowed through the pipe during the 24 hour period.
(b)
To find:The value varies between 0 to 24.
(b)
Answer to Problem 58RE
The value is
Explanation of Solution
Given information:
The given table is shown below,
Formula used:
Calculation:
Yes, it is possible.
According to mean value theorem if a function is continuous on [a, b] then there is a point e in the interval satisfy this condition
Since,
Hence,
Conclusion:
The value is
(c)
To find:The average rate of water flow during 24 hr period.
(c)
Answer to Problem 58RE
The average rate of water flow during 24 hr period is
Explanation of Solution
Given information:
The given table is shown below,
Formula used:
Substitution method is used.
Calculation:
Since, water flow has been given by,
Since, average rate of water flow is required
Conclusion:
The average rate of water flow during 24 hr period is
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
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