(the second isomorphism theorem). let u and w be subspaces of a vector space v.
(a) show that the map t: w → (u+w)/u defined by
t(w) =w+u
is surjective. (you do not need to check that it is linear, though it evidently is.)
(b) by applying the first isomorphism theorem to t, conclude that
w/(un w) ≅ (u+w)/u.

He was paid 23 dollars for each lawn

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Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.