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Chapter 3: Problem 118

Rocketry Which is closer to blastoff, - 12 min and counting or \(-17\) min and counting?

Short Answer

Expert verified
\(-12\) min is closer to the blastoff time than \(-17\) min

Step by step solution

01

Understand the meaning of negative numbers in this context

In the context of a rocketry blastoff, a negative number implies that the planned blastoff has been delayed and the magnitude of the number represents the duration of the delay in minutes. Therefore, \(-17\) min means that the blastoff is delayed by 17 minutes, and \(-12\) min means that it is delayed by 12 minutes.
02

Compare the two times

To determine which time is closer to the blastoff, it is necessary to compare \(-17\) and \(-12\). In the number line, numbers get larger as we move to the right. If we think of a number line, -12 is to the right of -17, therefore \(-12\) is greater than \(-17\). Hence, \(-12\) min is closer to the original blastoff time than \(-17\) min.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number Line
Understanding the number line is crucial when dealing with negative numbers. A number line is a straight line where numbers are placed at equal intervals or segments along its length.
It helps to visually represent the position of numbers, allowing us to see not only their value but also the distance and direction from zero.
  • Numbers to the right are positive and they increase as they move further right.
  • Numbers to the left are negative and become more negative as they move further left.
  • Zero is the center or origin of the number line, neither positive nor negative.
When dealing with the context of rocketry, using a number line can help decide which countdown time is closer to zero or blastoff. It provides a clear indication of which negative number is greater (closer to zero) just by looking at their positions on the line.
Comparing Numbers
Comparing numbers, particularly negative numbers, can sometimes be counterintuitive. On a number line, the position of the numbers provides a visual aid in comparison.
When you're comparing negative numbers, the rule is: the number closer to zero is actually greater than a number further from zero.
Consider comparing \(-12\) and \(-17\). On the number line, \(-12\) appears to the right of \(-17\). This means \(-12\) is greater than \(-17\) because it is closer to zero.
In real-life contexts such as rocketry, this indicates that \(-12\) minutes is closer to blastoff compared to \(-17\) minutes.
  • To compare negative numbers, find their positions on the number line.
  • The closer a negative number is to zero, the larger it is.
Integers
Integers are a type of number that includes all whole numbers and their negative counterparts, as well as zero. They do not include fractions or decimals, making them easy to place on a number line.
In everyday situations, such as a countdown to a rocket launch, negative numbers represent a delay, while positive numbers might represent time remaining.
When working with integers:
  • It is important to understand that they include negative values, positive values, and zero.
  • Negative integers can represent various real-world scenarios such as temperature below zero or a delay in schedule.
  • Each integer has a unique position on the number line, providing clear insights for problem-solving.
In our rocketry example, integers help to quantify how far from zero (blastoff) we currently are, and which countdown is closer.

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Most popular questions from this chapter

Evaluate the expression for the given values of the variables. \(x-(-y),\) for \(x=-3\) and \(y=9\)

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