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Ch. 3 - Derivatives
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 3 - Derivatives문제 52a
3장, 문제 52a

An angler hooks a trout and begins turning her circular reel at 1.5 rev/s. Assume the radius of the reel (and the fishing line on it) is 2 inches.
a. Let R equal the number of revolutions the angler has turned her reel and suppose L is the amount of line that she has reeled in. Find an equation for L as a function of R.

검증된 단계별 안내
1
Understand that the problem involves a circular motion where the reel is turning, and we need to relate the number of revolutions (R) to the length of the line reeled in (L).
Recognize that each complete revolution of the reel corresponds to the circumference of the circle formed by the reel. The circumference C of a circle is given by the formula: C = 2πr, where r is the radius.
Substitute the given radius of the reel into the circumference formula. Here, the radius r is 2 inches, so the circumference C = 2π(2) = 4π inches.
Since each revolution reels in a length of line equal to the circumference of the reel, the amount of line L reeled in after R revolutions is L = R * C.
Substitute the expression for the circumference into the equation for L: L = R * 4π. Therefore, the equation for L as a function of R is L(R) = 4πR.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Circumference of a Circle

The circumference of a circle is the distance around it, calculated using the formula C = 2πr, where r is the radius. In this context, the radius of the reel is 2 inches, so the circumference represents the length of fishing line that is reeled in with each complete revolution of the reel.
추천 영상:
5:10
Evaluate Composite Functions - Values on Unit Circle

Linear Relationship

A linear relationship describes how one variable changes in relation to another. In this case, the amount of line L that is reeled in is directly proportional to the number of revolutions R made by the reel, which can be expressed as L = C * R, where C is the circumference of the reel.
추천 영상:
가이드 코스
07:17
Linearization

Rate of Revolution

The rate of revolution indicates how quickly the reel is turned, measured in revolutions per second (rev/s). Here, the angler turns the reel at a rate of 1.5 rev/s, which helps determine how fast the line is being reeled in over time, linking the concepts of time, revolutions, and the length of line.
추천 영상:
가이드 코스
04:16
Intro To Related Rates
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