1. Firstly, we need to model this real-world situation with infinite series. Since the pendulum travels 8() inches in the first 3 4 1 pass, 8() inches in the second pass, and 4 2 8(2) inches in the third pass; develop a formula for the infinite series to model the distance travelled by the pendulum. (HINT: your formula should be written in the form E0, ar"-1 , and you should develop your formula based on the pattern you see above) 2. What type of series is represented by the formula you developed in step 1? (HINT: we covered this common type of series last week) 3. The series you created in step 1 converges, since |r| < 1. Using the formula s = a 1-r determine the series' sum s. This sum represents the total distance travelled by the pendulum, in inches!
1. Firstly, we need to model this real-world situation with infinite series. Since the pendulum travels 8() inches in the first 3 4 1 pass, 8() inches in the second pass, and 4 2 8(2) inches in the third pass; develop a formula for the infinite series to model the distance travelled by the pendulum. (HINT: your formula should be written in the form E0, ar"-1 , and you should develop your formula based on the pattern you see above) 2. What type of series is represented by the formula you developed in step 1? (HINT: we covered this common type of series last week) 3. The series you created in step 1 converges, since |r| < 1. Using the formula s = a 1-r determine the series' sum s. This sum represents the total distance travelled by the pendulum, in inches!
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A pendulum is released and swings until it stops. If it passes through an arc of 8 inches in the first pass, and if on each successive pass it travels 3434 the distance of the previous pass, how far will it travel before stopping?
Transcribed Image Text:1. Firstly, we need to model this real-world
situation with infinite series. Since the
pendulum travels 8( ) inches in the first
4
1
pass, 8() inches in the second pass,
3
and
4
8
4
3(2)* inches in the third pass; develop a
formula for the infinite series to model the
distance travelled by the pendulum. (HINT:
your formula should be written in the form
E, ar"-1 , and you should develop your
in=1
formula based on the pattern you see above)
2. What type of series is represented by the
formula you developed in step 1? (HINT: we
covered this common type of series last
week)
3. The series you created in step 1 converges,
since |r| < 1. Using the formula s =
a
determine the series' sum s. This sum
represents the total distance travelled by the
pendulum, in inches!
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