We appreciate your visit to Is the data set approximately periodic If so what are its period and amplitude tex begin tabular l c c c c c c c. 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!
Answer :
We begin by examining the hourly data for the number of cars:
[tex]$$
52,\; 76,\; 90,\; 75,\; 91,\; 104,\; 89,\; 105,\; 119,\; 103,\; 121,\; 135.
$$[/tex]
Step 1. Look for a Pattern
Notice that although there is an overall increasing trend throughout the day, there is also a repeating fluctuation. For example, after some increases the data shows a drop (from [tex]$90$[/tex] to [tex]$75$[/tex], and again from [tex]$104$[/tex] to [tex]$89$[/tex]). This suggests that the data might be following a periodic pattern.
Step 2. Identify the Period
Observe the pattern:
- Between hours 1 to 3, the numbers rise and then drop at hour 4.
- A similar drop occurs again after approximately 3 hours (from hour 6 to hour 7).
This behavior indicates that the fluctuations repeat approximately every 3 hours. Hence, we conclude that the period is
[tex]$$
3 \text{ hours}.
$$[/tex]
Step 3. Determine the Amplitude
The amplitude in a periodic (or sinusoidal) function is given by half the difference between the peak (maximum) and the trough (minimum) of the fluctuation. From the observed changes, we see that the drop is around [tex]$15$[/tex] cars. Therefore, the amplitude is approximately calculated as:
[tex]$$
\text{Amplitude} = \frac{15}{2} = 7.5.
$$[/tex]
Conclusion
The data is approximately periodic with a period of [tex]$3$[/tex] hours and an amplitude of about [tex]$7.5$[/tex].
Thus, the final answer is: Periodic with a period of [tex]$3$[/tex] and amplitude of about [tex]$7.5$[/tex].
[tex]$$
52,\; 76,\; 90,\; 75,\; 91,\; 104,\; 89,\; 105,\; 119,\; 103,\; 121,\; 135.
$$[/tex]
Step 1. Look for a Pattern
Notice that although there is an overall increasing trend throughout the day, there is also a repeating fluctuation. For example, after some increases the data shows a drop (from [tex]$90$[/tex] to [tex]$75$[/tex], and again from [tex]$104$[/tex] to [tex]$89$[/tex]). This suggests that the data might be following a periodic pattern.
Step 2. Identify the Period
Observe the pattern:
- Between hours 1 to 3, the numbers rise and then drop at hour 4.
- A similar drop occurs again after approximately 3 hours (from hour 6 to hour 7).
This behavior indicates that the fluctuations repeat approximately every 3 hours. Hence, we conclude that the period is
[tex]$$
3 \text{ hours}.
$$[/tex]
Step 3. Determine the Amplitude
The amplitude in a periodic (or sinusoidal) function is given by half the difference between the peak (maximum) and the trough (minimum) of the fluctuation. From the observed changes, we see that the drop is around [tex]$15$[/tex] cars. Therefore, the amplitude is approximately calculated as:
[tex]$$
\text{Amplitude} = \frac{15}{2} = 7.5.
$$[/tex]
Conclusion
The data is approximately periodic with a period of [tex]$3$[/tex] hours and an amplitude of about [tex]$7.5$[/tex].
Thus, the final answer is: Periodic with a period of [tex]$3$[/tex] and amplitude of about [tex]$7.5$[/tex].
Thanks for taking the time to read Is the data set approximately periodic If so what are its period and amplitude tex begin tabular l c c c c c c c. 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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
