We appreciate your visit to tex begin array c c c c c c hline text Range 1 text Range 2 text Value 1 text Value 2 text Value 3. 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 start by writing the table in a matrix-like form, where each row represents a list of six numbers. For instance, the first five rows are:
[tex]$$
\begin{array}{cccccc}
97250 & 97300 & 20219 & 15796 & 20679 & 18571 \\
97300 & 97350 & 20233 & 15809 & 20693 & 18584 \\
97350 & 97400 & 20247 & 15821 & 20707 & 18596 \\
97400 & 97450 & 20261 & 15834 & 20721 & 18609 \\
97450 & 97500 & 20275 & 15846 & 20735 & 18621 \\
\end{array}
$$[/tex]
and there are 15 rows in total.
The task is to compute the differences between each pair of consecutive entries in every column. In other words, for each column, if an entry in row [tex]$i$[/tex] is denoted by [tex]$a_{i}$[/tex] and the next entry (in row [tex]$i+1$[/tex]) by [tex]$a_{i+1}$[/tex], then the difference computed is:
[tex]$$
\Delta a = a_{i+1} - a_i.
$$[/tex]
We now examine each column:
1. Column 1:
The entries are:
[tex]$$
97250,\; 97300,\; 97350,\; 97400,\; 97450,\; \ldots,\; 97950.
$$[/tex]
The difference between consecutive entries is:
[tex]$$
97300 - 97250 = 50,\quad 97350 - 97300 = 50,\quad \ldots
$$[/tex]
Hence, the difference for every successive pair is [tex]$50$[/tex]. For 15 rows there are 14 differences and they all equal [tex]$50$[/tex]:
[tex]$$
[50, 50, 50, \ldots, 50].
$$[/tex]
2. Column 2:
The entries are:
[tex]$$
97300,\; 97350,\; 97400,\; 97450,\; 97500,\; \ldots,\; 98000.
$$[/tex]
Calculating the differences:
[tex]$$
97350 - 97300 = 50,\quad 97400 - 97350 = 50,\quad \ldots
$$[/tex]
Thus, every difference is also [tex]$50$[/tex]:
[tex]$$
[50, 50, 50, \ldots, 50].
$$[/tex]
3. Column 3:
The entries here are:
[tex]$$
20219,\; 20233,\; 20247,\; 20261,\; 20275,\; \ldots,\; 20415.
$$[/tex]
Each difference is:
[tex]$$
20233 - 20219 = 14,\quad 20247 - 20233 = 14,\quad \ldots
$$[/tex]
So, all computed differences equal [tex]$14$[/tex]:
[tex]$$
[14, 14, 14, \ldots, 14].
$$[/tex]
4. Column 4:
In this column the entries are:
[tex]$$
15796,\; 15809,\; 15821,\; 15834,\; 15846,\; \ldots,\; 15971.
$$[/tex]
Now, when we compute:
[tex]$$
15809 - 15796 = 13,\\[1mm]
15821 - 15809 = 12,\\[1mm]
15834 - 15821 = 13,\\[1mm]
15846 - 15834 = 12,\\[1mm]
\text{etc.}
$$[/tex]
The differences alternate between [tex]$13$[/tex] and [tex]$12$[/tex]. Thus, the sequence of differences is:
[tex]$$
[13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12].
$$[/tex]
5. Column 5:
The values in this column are:
[tex]$$
20679,\; 20693,\; 20707,\; 20721,\; 20735,\; \ldots,\; 20875.
$$[/tex]
The differences are:
[tex]$$
20693 - 20679 = 14,\quad 20707 - 20693 = 14,\quad \ldots
$$[/tex]
Thus, each difference is [tex]$14$[/tex], giving:
[tex]$$
[14, 14, 14, \ldots, 14].
$$[/tex]
6. Column 6:
The column has entries:
[tex]$$
18571,\; 18584,\; 18596,\; 18609,\; 18621,\; \ldots,\; 18746.
$$[/tex]
The differences are computed as:
[tex]$$
18584 - 18571 = 13,\\[1mm]
18596 - 18584 = 12,\\[1mm]
18609 - 18596 = 13,\\[1mm]
18621 - 18609 = 12,\quad \text{etc.}
$$[/tex]
So, the pattern here alternates as well:
[tex]$$
[13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12].
$$[/tex]
The final results are therefore given as:
- The table (with all 15 rows and 6 columns) is
[tex]$$
\begin{array}{cccccc}
97250 & 97300 & 20219 & 15796 & 20679 & 18571 \\
97300 & 97350 & 20233 & 15809 & 20693 & 18584 \\
97350 & 97400 & 20247 & 15821 & 20707 & 18596 \\
97400 & 97450 & 20261 & 15834 & 20721 & 18609 \\
97450 & 97500 & 20275 & 15846 & 20735 & 18621 \\
97500 & 97550 & 20289 & 15859 & 20749 & 18634 \\
97550 & 97600 & 20303 & 15871 & 20763 & 18646 \\
97600 & 97650 & 20317 & 15884 & 20777 & 18659 \\
97650 & 97700 & 20331 & 15896 & 20791 & 18671 \\
97700 & 97750 & 20345 & 15909 & 20805 & 18684 \\
97750 & 97800 & 20359 & 15921 & 20819 & 18696 \\
97800 & 97850 & 20373 & 15934 & 20833 & 18709 \\
97850 & 97900 & 20387 & 15946 & 20847 & 18721 \\
97900 & 97950 & 20401 & 15959 & 20861 & 18734 \\
97950 & 98000 & 20415 & 15971 & 20875 & 18746 \\
\end{array}
$$[/tex]
- The computed column differences are:
- Column 1:
[tex]$$
[50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50]
$$[/tex]
- Column 2:
[tex]$$
[50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50]
$$[/tex]
- Column 3:
[tex]$$
[14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14]
$$[/tex]
- Column 4:
[tex]$$
[13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12]
$$[/tex]
- Column 5:
[tex]$$
[14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14]
$$[/tex]
- Column 6:
[tex]$$
[13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12]
$$[/tex]
This completes the step-by-step solution.
[tex]$$
\begin{array}{cccccc}
97250 & 97300 & 20219 & 15796 & 20679 & 18571 \\
97300 & 97350 & 20233 & 15809 & 20693 & 18584 \\
97350 & 97400 & 20247 & 15821 & 20707 & 18596 \\
97400 & 97450 & 20261 & 15834 & 20721 & 18609 \\
97450 & 97500 & 20275 & 15846 & 20735 & 18621 \\
\end{array}
$$[/tex]
and there are 15 rows in total.
The task is to compute the differences between each pair of consecutive entries in every column. In other words, for each column, if an entry in row [tex]$i$[/tex] is denoted by [tex]$a_{i}$[/tex] and the next entry (in row [tex]$i+1$[/tex]) by [tex]$a_{i+1}$[/tex], then the difference computed is:
[tex]$$
\Delta a = a_{i+1} - a_i.
$$[/tex]
We now examine each column:
1. Column 1:
The entries are:
[tex]$$
97250,\; 97300,\; 97350,\; 97400,\; 97450,\; \ldots,\; 97950.
$$[/tex]
The difference between consecutive entries is:
[tex]$$
97300 - 97250 = 50,\quad 97350 - 97300 = 50,\quad \ldots
$$[/tex]
Hence, the difference for every successive pair is [tex]$50$[/tex]. For 15 rows there are 14 differences and they all equal [tex]$50$[/tex]:
[tex]$$
[50, 50, 50, \ldots, 50].
$$[/tex]
2. Column 2:
The entries are:
[tex]$$
97300,\; 97350,\; 97400,\; 97450,\; 97500,\; \ldots,\; 98000.
$$[/tex]
Calculating the differences:
[tex]$$
97350 - 97300 = 50,\quad 97400 - 97350 = 50,\quad \ldots
$$[/tex]
Thus, every difference is also [tex]$50$[/tex]:
[tex]$$
[50, 50, 50, \ldots, 50].
$$[/tex]
3. Column 3:
The entries here are:
[tex]$$
20219,\; 20233,\; 20247,\; 20261,\; 20275,\; \ldots,\; 20415.
$$[/tex]
Each difference is:
[tex]$$
20233 - 20219 = 14,\quad 20247 - 20233 = 14,\quad \ldots
$$[/tex]
So, all computed differences equal [tex]$14$[/tex]:
[tex]$$
[14, 14, 14, \ldots, 14].
$$[/tex]
4. Column 4:
In this column the entries are:
[tex]$$
15796,\; 15809,\; 15821,\; 15834,\; 15846,\; \ldots,\; 15971.
$$[/tex]
Now, when we compute:
[tex]$$
15809 - 15796 = 13,\\[1mm]
15821 - 15809 = 12,\\[1mm]
15834 - 15821 = 13,\\[1mm]
15846 - 15834 = 12,\\[1mm]
\text{etc.}
$$[/tex]
The differences alternate between [tex]$13$[/tex] and [tex]$12$[/tex]. Thus, the sequence of differences is:
[tex]$$
[13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12].
$$[/tex]
5. Column 5:
The values in this column are:
[tex]$$
20679,\; 20693,\; 20707,\; 20721,\; 20735,\; \ldots,\; 20875.
$$[/tex]
The differences are:
[tex]$$
20693 - 20679 = 14,\quad 20707 - 20693 = 14,\quad \ldots
$$[/tex]
Thus, each difference is [tex]$14$[/tex], giving:
[tex]$$
[14, 14, 14, \ldots, 14].
$$[/tex]
6. Column 6:
The column has entries:
[tex]$$
18571,\; 18584,\; 18596,\; 18609,\; 18621,\; \ldots,\; 18746.
$$[/tex]
The differences are computed as:
[tex]$$
18584 - 18571 = 13,\\[1mm]
18596 - 18584 = 12,\\[1mm]
18609 - 18596 = 13,\\[1mm]
18621 - 18609 = 12,\quad \text{etc.}
$$[/tex]
So, the pattern here alternates as well:
[tex]$$
[13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12].
$$[/tex]
The final results are therefore given as:
- The table (with all 15 rows and 6 columns) is
[tex]$$
\begin{array}{cccccc}
97250 & 97300 & 20219 & 15796 & 20679 & 18571 \\
97300 & 97350 & 20233 & 15809 & 20693 & 18584 \\
97350 & 97400 & 20247 & 15821 & 20707 & 18596 \\
97400 & 97450 & 20261 & 15834 & 20721 & 18609 \\
97450 & 97500 & 20275 & 15846 & 20735 & 18621 \\
97500 & 97550 & 20289 & 15859 & 20749 & 18634 \\
97550 & 97600 & 20303 & 15871 & 20763 & 18646 \\
97600 & 97650 & 20317 & 15884 & 20777 & 18659 \\
97650 & 97700 & 20331 & 15896 & 20791 & 18671 \\
97700 & 97750 & 20345 & 15909 & 20805 & 18684 \\
97750 & 97800 & 20359 & 15921 & 20819 & 18696 \\
97800 & 97850 & 20373 & 15934 & 20833 & 18709 \\
97850 & 97900 & 20387 & 15946 & 20847 & 18721 \\
97900 & 97950 & 20401 & 15959 & 20861 & 18734 \\
97950 & 98000 & 20415 & 15971 & 20875 & 18746 \\
\end{array}
$$[/tex]
- The computed column differences are:
- Column 1:
[tex]$$
[50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50]
$$[/tex]
- Column 2:
[tex]$$
[50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50,\, 50]
$$[/tex]
- Column 3:
[tex]$$
[14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14]
$$[/tex]
- Column 4:
[tex]$$
[13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12]
$$[/tex]
- Column 5:
[tex]$$
[14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14,\, 14]
$$[/tex]
- Column 6:
[tex]$$
[13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12,\, 13,\, 12]
$$[/tex]
This completes the step-by-step solution.
Thanks for taking the time to read tex begin array c c c c c c hline text Range 1 text Range 2 text Value 1 text Value 2 text Value 3. 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
