Alejandro can do 165 sit-ups in one gym class. How many sit-ups can he do in month if he attends all gym classes?
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Answer:
Lets a,b be elements of G. since G/K is abelian, then there exists k ∈ K such that ab * k = ba (because the class of ab, is equal to
, thus ab and ba are equal or you can obtain one from the other by multiplying by an element of K.
Since K is a subgroup of H, then k ∈ H. This means that you can obtain ba from ab by multiplying by an element of H, k. Thus, . Since a and b were generic elements of H, then H/G is abelian.
Remember that the volume of a cylinder is
so we have that
so the radius is 9.6 milimeters