Consider S_5. Write answers below in STANDARD NOTATION. (a) How many of the elem

Question

Consider S_5. Write answers below in STANDARD NOTATION. (a) How many of the elements are 5-cycles (that is, cycles of length 5)? List three. (b) How many are 4 cycles? (yes, S_5 can certainly contain 4-cycles.) List three (c) How many of the elements are 3-cycles? List three. (d) How many of the elements are 2-cycles? List three. (e) How many of the elements are 1-cycles? List them all. (f) How many are disjoint products of a 3-cycle and a 2-cycle? List three. (g) How many are disjoint products of two 2-cycles? List three.

Explanation / Answer

(a) density of fresh water is _water = 1000 kg/m³

F = 0

- (_wood)g(V_wood) + (_water)g(v_wood) = 0

(v_wood)/(V_wood) = (_wood)/(_water)

(10 * 10 * h)/(10 * 10 * 10) = (720)/(1000)

h = 7.2 cm

the distance from the top of the block to the water is 10 - 7.2 = 2.8 cm

(b).

density of seawater is _sea = 1030 kg/m³

(v_wood)/(V_wood) = (_wood)/(_sea)

(10 * 10 * h')/(10 * 10 * 10) = (720)/(1030)
h' = 6.99029 cm
the distance from the top of the block to the water is 10 - 6.99029 = 3.00971 cm

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