2. Mrs. young has her 18 students seated in a circle. They are evenly
spaced and numbered in order. which student is directly opposite these three students?
.student#1?
.student#5?
.student#18?
Just another thought.
N = number of students equally spaced around the circle and numbered sequentially.
The student number opposite a given student number is defined by Sopp = Sg +/- N/2 depending on whether the given student number is less/more tan N/2.
The student opposite student #1 = 1 + 18/2 = #10.
The student opposite student #5 = 5 + 18/2 = #14.
The student opposite student #18 is 18 -- 18/2 = 9.
Draw a picture and figure it out. Put students at 20 degree increments around the circle. The largest number minus the smallest, across from each other, must equal 9.
#1=9
#5=12
#18=8
Ah, the circle of student life, where math and seating arrangements collide. Now, brace yourself for some comedic wisdom!
If Mrs. Young's students are evenly spaced in a circle, then we can use a little magic (and some simple math) to find the students directly opposite.
Let's do this!
For student #1, since there are 18 students in total, we can find the opposite student by subtracting the student's number from half of the total number of students plus one.
Opposite of student #1 = (18 / 2) + 1 - 1 = 9
So, student #9 is directly opposite student #1.
Now, for student #5, we can follow the same rule.
Opposite of student #5 = (18 / 2) + 5 - 1 = 14
Thus, student #14 is directly opposite student #5.
Lastly, for student #18, we use the same logic.
Opposite of student #18 = (18 / 2) + 18 - 1 = 35
Woops, sorry, my comedic circuits must have short-circuited there. As there are only 18 students, there wouldn't be a student #35. So, let's come back down to 18 and wrap it up properly. Since we're working with a circle, we need to find the remainder of 35 divided by 18.
35 mod 18 = 17
Therefore, student #17 is directly opposite student #18 and not student #35 (as much as I'd love to see this mysterious student).
So, student #1 is opposite student #9, student #5 is opposite student #14, and student #18 is opposite student #17.
Voilà! The mystery of the circular seating arrangement has been solved!
To determine which student is directly opposite the three given students, you need to find the pattern in their positions in the circular arrangement.
First, let's find the pattern for the positions of the students. Since there are 18 students evenly spaced in a circle, we can calculate the distance between two adjacent students by dividing 360 degrees (a full circle) by the total number of students:
360 degrees / 18 students = 20 degrees
Now, we can determine the positions of the students based on this pattern:
1. Student #1: The first student is always positioned at the starting point of the circle, which is the 12 o'clock position.
2. Student #5: To find the position of student #5, you need to multiply the distance between adjacent students (20 degrees) by the number of students away from student #1:
20 degrees * (5 - 1) = 80 degrees
So, student #5 is positioned 80 degrees counterclockwise from student #1.
3. Student #18: Similarly, to find the position of student #18, multiply the distance between adjacent students (20 degrees) by the number of students away from student #1:
20 degrees * (18 - 1) = 340 degrees
Hence, student #18 is positioned 340 degrees counterclockwise from student #1.
Finally, to find the student who is directly opposite each of these three students, we need to consider the total degrees in a circle (360 degrees). Subtract the respective positions we calculated from 360 degrees to find the opposite positions:
1. Opposite of student #1: 360 degrees - 0 degrees (opposite of itself) = 360 degrees (same position)
2. Opposite of student #5: 360 degrees - 80 degrees = 280 degrees
3. Opposite of student #18: 360 degrees - 340 degrees = 20 degrees
Therefore, the student directly opposite to these three students would be:
- Student #1: Still student #1
- Student #5: Student #18
- Student #18: Student #5