Answer:
a) The order of αβ is 9 and αβ is an even permutation
b) See proof
Step-by-step explanation:
a) Given that: α is a cycle of length 3 and β a cycle of length 9.
We want to find the order of αβ .
The order of αβ is the LCM of the length of the disjoint cycles.
Therefore the order is the LCM of 3 and 9 which is 9.
Since α is a cycle of length 3 and β a cycle of length 9, and (3-1)+(9-1)=10, the permutation αβ is even.
b) We want to show that, for every positive integer n,
Proof:
Expanding from left, we have
Since α and β commutes, we rearrange to get:
We simplify on the right to get:
Answer:
1) 20: 25
2) 15: 3
Step-by-step explanation:
Answer:alright let start replacing
3 x 2 + (6- 3) - 2 x 4
6 + 3 - 8
9- 8
1
:)) sorry i was wrong the first time
Answer:
as shown in the attached file.
Step-by-step explanation:
The detailed, step by step explanation and application of integral with appropriate substitution to get the expression for the time of extinction is as shown in the attachment.
5/6
divide 25 by 5 and divide 30 by five. its their gcf