Answer:
Step-by-step explanation:
We are given that G be a finite group with have two elements of order two.
We have to prove that <x,y> is either abelian or isomorphic to a dihedral group.
<x,y> means the group generated by two elements of order 2.
We know that is a cyclic group and number of elements of order 2 is always odd in number and generated by one element .So , given group is not isomorphic to
But we are given that two elements of order 2 in given group
Therefore, group G can be or dihedral group
Because the groups generated by two elements of order 2 are and dihedral group.
We know that is abelian group of order 4 and every element of is of order 2 except identity element and generated by 2 elements of order 2 and dihedral group can be also generated by two elements of order 2
Hence, <x,y> is isomorphic to or .
For this case we have that by definition, the area of a circle is given by:
Where:
r: It is the radius of the circle.
So, we have that the area of the shaded region is given by:
We divide between 4 on both sides of the equation:
We apply root to both sides:
We choose the positive value of the root:
Finally, the value of "x" is 9
Answer:
6 kilometers = 6000 meters
1 kilometer = 1000 meters
So, 1000 × 6
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