High School

We appreciate your visit to An unfolded piece of paper is 0 05 mm thick a Define T for the n th term b What is a reasonable domain for. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

An unfolded piece of paper is 0.05 mm thick.

a. Define \( T \) for the \( n \)th term.

b. What is a reasonable domain for the function \( T \)? Explain how you know.

c. Does \( T(0.5) \) make sense? Explain how you know.

Answer :

Final answer:

T(n) refers to the paper's thickness after n folds, growing in a geometric sequence with the ratio of 2 since it doubles with each fold. The function's domain is any non-negative integer since a piece of paper can only be folded a whole number of times. Consequently, T(0.5), indicating a half-fold, would not make sense in this context, implying a non-negative integer domain.

Explanation:

The subject of the question is a geometrical progression related to thickness of a folded piece of paper.

a. Define T for the nth term: T(n) here denotes the thickness of the folded paper after n times it is successfully folded. If a piece of paper is 0.05 mm thick to start with, after folding it once (n=1), the thickness doubles to T(1)= 0.05 x 2. The paper is growing in thickness by a factor of 2 with each fold, hence it is a geometric sequence with a common ratio of 2. Consequently, as a general rule: T(n) = T(1)*2^(n-1).

b. The reasonable domain for the function T is the set of all non-negative integers. This is because you can fold the paper a whole number of times -- for example, zero times (without folding) or 1 time or 2 times, and so on. A half-fold or a negative number of folds do not make physical sense in this context, so anything other than whole numbers would be outside the domain.

c. T(0.5) does not make sense in this context, because it indicates a half-fold, which is not feasible in the real world. As we mentioned in the section on domains, the number of times a physical object can be folded is represented by non-negative integers.

Learn more about Geometric Sequence here:

https://brainly.com/question/33243139

#SPJ1

Thanks for taking the time to read An unfolded piece of paper is 0 05 mm thick a Define T for the n th term b What is a reasonable domain for. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada