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, ![[ab]_K](https://tex.z-dn.net/?f=%20%5Bab%5D_K%20)
is equal to ![[ba]_K](https://tex.z-dn.net/?f=%20%5Bba%5D_K%20)
, 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, ![[ab]_H = [ba]_H](https://tex.z-dn.net/?f=%20%5Bab%5D_H%20%3D%20%5Bba%5D_H%20)
. Since a and b were generic elements of H, then H/G is abelian.
1.) 3+2=? ?=5 brothers 2.) 54+9=? ?=63 students 3.) 15-9=? ?=4
4.) 60-20=? ?=40 children 5.) 50-15=? ?=35 trees 6.) 14+4=? ?=18 times
Don't know why you needed help with this but ok.
Angle of taller building Tan 45° = opposite (height of the building)/
adjacent 50 feet (distance between Kathy and the taller building
Tan 45° = 1
Height of taller building from eye level = multiplying adjacent
50 feet * Angle (Tan 45°) 1 = 50 feet opposite
Angle of smaller building Tan 38° = 0.781
Height of smaller building from eye level = Angle * adjacent
50 feet = 39.06 feet
Difference of eye level from ground is 5 feet
Taller building height is 50 + 5
Total height of taller building is 55 feet.
Smaller building height is 39.06 + 5
Total height of smaller building is 44.06 feet
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Use the formula of the area of a trapezoid.
A=(B+b)·h/2
B=10ft
b=8 ft
A=95 ft
(10+8)·h/2=95|·2
18h=95·2
18h=190
h=190:18
h=10,5 ft
<em>Answer: 10,5 ft</em>
