To determine which set of numbers is arranged in increasing order, let's examine the values of each of the numbers involved:
1. [tex]\(\pi \approx 3.141592653589793\)[/tex]
2. [tex]\(\sqrt{10} \approx 3.162277660168379\)[/tex]
3. [tex]\(3.14\)[/tex] is already given as [tex]\(3.14\)[/tex]
4. [tex]\(\frac{22}{7} \approx 3.142857142857143\)[/tex]
Given these approximations, we need to verify the order of numbers in each set:
### Set A: [tex]\(\pi, \sqrt{10}, 3.14, \frac{22}{7}\)[/tex]
- [tex]\(\pi \approx 3.1416\)[/tex]
- [tex]\(\sqrt{10} \approx 3.1623\)[/tex]
- [tex]\(3.14\)[/tex]
- [tex]\(\frac{22}{7} \approx 3.1429\)[/tex]
The sequence is: [tex]\(3.1416, 3.1623, 3.14, 3.1429\)[/tex]
Clearly, [tex]\(3.14\)[/tex] is out of order here, so Set A is not correct.
### Set B: [tex]\(3.14, \pi, \frac{22}{7}, \sqrt{10}\)[/tex]
- [tex]\(3.14\)[/tex]
- [tex]\(\pi \approx 3.1416\)[/tex]
- [tex]\(\frac{22}{7} \approx 3.1429\)[/tex]
- [tex]\(\sqrt{10} \approx 3.1623\)[/tex]
The sequence is: [tex]\(3.14, 3.1416, 3.1429, 3.1623\)[/tex]
This sequence is in increasing order, so Set B is the correct answer.
### Set C: [tex]\(\frac{22}{7}, \sqrt{10}, 3.14, \pi\)[/tex]
- [tex]\(\frac{22}{7} \approx 3.1429\)[/tex]
- [tex]\(\sqrt{10} \approx 3.1623\)[/tex]
- [tex]\(3.14\)[/tex]
- [tex]\(\pi \approx 3.1416\)[/tex]
The sequence is: [tex]\(3.1429, 3.1623, 3.14, 3.1416\)[/tex]
Clearly, [tex]\(3.14\)[/tex] and [tex]\(\pi\)[/tex] are out of order here, so Set C is not correct.
### Set D: [tex]\(\sqrt{10}, \frac{22}{7}, 3.14, \pi\)[/tex]
- [tex]\(\sqrt{10} \approx 3.1623\)[/tex]
- [tex]\(\frac{22}{7} \approx 3.1429\)[/tex]
- [tex]\(3.14\)[/tex]
- [tex]\(\pi \approx 3.1416\)[/tex]
The sequence is: [tex]\(3.1623, 3.1429, 3.14, 3.1416\)[/tex]
Clearly, this sequence is also not in the increasing order, so Set D is not correct.
Therefore, the set where the numbers are arranged in increasing order is:
[tex]\[
\boxed{B}
\][/tex]
