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Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section: Chapter Questions

Problem 33CT

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Question

A grain elevator fills each railcar of a train with grain. The number of railcars filled after t hours is given by a differentiable function R for 0 ≤ t ≤ 15. Values of R(t) at various times t are given in the table above.
a) Use the data in the table to approximate the rate at which the number of filled railcars is changing at time t = 5. Show the computations that lead to your answer. Indicate units of measure.
b) Will the instantaneous rate at which the number of filled railcars is changing at some time t be equal to the approximation in part (a)? Justify your answer.
c) Use a trapezoidal sum with the four subintervals indicated in the table to estimate 1 ∫15 R(t)dt. 15 0
Using correct units, interpret the meaning of 1 ∫15 R(t)dt in the context of this problem. 15 0
d) Determine 1 ∫15 R'(t)dt. Using correct units, explain the meaning of the expression in the context 15 0
of this problem.

Please solve all four sub parts

1:28 PM Sun May 9
* 77%
3 of 3
FRQ 2
A graphing calculator is required for the following problem.
1
8
10
15
(hours)
R(t)
(railcars)
6
62
80
110
A grain elevator fills each railcar of a train with grain. The number of railcars filled after t hours is given by
a differentiable function R for 0 <t< 15. Values of R(t) at various times t are given in the table above.
a) Use the data in the table to approximate the rate at which the number of filled railcars is changing
at time t = 5. Show the computations that lead to your answer. Indicate units of measure.
b) Will the instantaneous rate at which the number of filled railcars is changing at some time t be
equal to the approximation in part (a)? Justify your answer.
15
c) Use a trapezoidal sum with the four subintervals indicated in the table to estimate R(t)dt.
15
15
Using correct units, interpret the meaning of S R(t)dt in the context of this problem.
15 Jo
15
d) Determine ° R'(t)dt. Using correct units, explain the meaning of the expression in the context
of this problem.
15 Jo

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