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Proof that AED = CEF
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Expression 35: StartFraction, "B" Subscript, 2 , Baseline plus "t" Subscript, 2 , Baseline "d" Over negative StartRoot, "R" squared minus left parenthesis, "B" Subscript, 1 , Baseline plus "t" Subscript, 2 , Baseline "c" , right parenthesis squared , EndRoot , EndFraction tilde 1
B
2
+
t
2
d
−
R
2
−
B
1
+
t
2
c
2
~
1
35
Expression 36: "C" Subscript, 1 , Baseline equals "B" Subscript, 1 , Baseline plus "t" Subscript, 2 , Baseline "c"
C
1
=
B
1
+
t
2
c
equals
=
2.2 3 4 2 8 9 5 4 9 1 7
2
.
2
3
4
2
8
9
5
4
9
1
7
36
Expression 37: "C" Subscript, 2 , Baseline equals "B" Subscript, 2 , Baseline plus "t" Subscript, 2 , Baseline "d"
C
2
=
B
2
+
t
2
d
equals
=
negative 5.5 6 8 4 7 8 2 6 7 0 4
−
5
.
5
6
8
4
7
8
2
6
7
0
4
37
Expression 38: theta Subscript, 0 , Baseline equals tangent to the negative 1st power left parenthesis, StartFraction, "B" Subscript, 2 , Baseline minus "M" Subscript, 2 , Baseline Over "B" Subscript, 1 , Baseline minus "M" Subscript, 1 , Baseline , EndFraction , right parenthesis
θ
0
=
t
a
n
−
1
B
2
−
M
2
B
1
−
M
1
equals
=
80.4 1 8 9 3 5 5 5 8 2
8
0
.
4
1
8
9
3
5
5
5
8
2
38
Expression 39: "D" Subscript, 1 , Baseline equals "M" Subscript, 1 , Baseline plus "R" Subscript, 1 , Baseline cosine left parenthesis, theta Subscript, 0 , Baseline plus "B" Subscript, "M" "F" , Baseline , right parenthesis
D
1
=
M
1
+
R
1
c
o
s
θ
0
+
B
M
F
equals
=
negative 2.9 3 8 8 1 3 9 8 9 2 8
−
2
.
9
3
8
8
1
3
9
8
9
2
8
39
Expression 40: "D" Subscript, 2 , Baseline equals "M" Subscript, 2 , Baseline plus "R" Subscript, 1 , Baseline sine left parenthesis, theta Subscript, 0 , Baseline plus "B" Subscript, "M" "F" , Baseline , right parenthesis
D
2
=
M
2
+
R
1
s
i
n
θ
0
+
B
M
F
equals
=
negative 2.2 5 2 1 3 9 3 1 8 6 5
−
2
.
2
5
2
1
3
9
3
1
8
6
5
40
Expression 41: "F" Subscript, 1 , Baseline equals "M" Subscript, 1 , Baseline plus "R" Subscript, 1 , Baseline cosine left parenthesis, theta Subscript, 0 , Baseline minus "B" Subscript, "M" "F" , Baseline , right parenthesis
F
1
=
M
1
+
R
1
c
o
s
θ
0
−
B
M
F
equals
=
1.9 5 8 0 4 1 0 5 4 7 6
1
.
9
5
8
0
4
1
0
5
4
7
6
41
Expression 42: "F" Subscript, 2 , Baseline equals "M" Subscript, 2 , Baseline plus "R" Subscript, 1 , Baseline sine left parenthesis, theta Subscript, 0 , Baseline minus "B" Subscript, "M" "F" , Baseline , right parenthesis
F
2
=
M
2
+
R
1
s
i
n
θ
0
−
B
M
F
equals
=
negative 3.0 7 8 7 1 5 7 9 9 0 3
−
3
.
0
7
8
7
1
5
7
9
9
0
3
42
Expression 43: "G" Subscript, 1 , Baseline equals left parenthesis, "M" Subscript, "O" , Baseline plus "R" Subscript, 1 , Baseline , right parenthesis cosine alpha
G
1
=
M
O
+
R
1
c
o
s
α
equals
=
negative 1.0 6 7 6 6 1 2 7 2 8 4
−
1
.
0
6
7
6
6
1
2
7
2
8
4
43
Expression 44: "G" Subscript, 2 , Baseline equals left parenthesis, "M" Subscript, "O" , Baseline plus "R" Subscript, 1 , Baseline , right parenthesis sine alpha
G
2
=
M
O
+
R
1
s
i
n
α
equals
=
negative 5.9 0 4 2 4 4 1 8 5 8 8
−
5
.
9
0
4
2
4
4
1
8
5
8
8
44
Expression 45: "a" equals "F" Subscript, 1 , Baseline minus "D" Subscript, 1 , Baseline
a
=
F
1
−
D
1
equals
=
4.8 9 6 8 5 5 0 4 4 0 4
4
.
8
9
6
8
5
5
0
4
4
0
4
45
Expression 46: "b" equals "F" Subscript, 2 , Baseline minus "D" Subscript, 2 , Baseline
b
=
F
2
−
D
2
equals
=
negative 0.8 2 6 5 7 6 4 8 0 3 7 7
−
0
.
8
2
6
5
7
6
4
8
0
3
7
7
46
Expression 47: left parenthesis, "D" Subscript, 1 , Baseline plus "t" "a" , "D" Subscript, 2 , Baseline plus "t" "b" , right parenthesis
D
1
+
t
a
,
D
2
+
t
b
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
1
1
domain t Maximum:
47
Expression 48: left parenthesis, "B" Subscript, 1 , Baseline plus "t" left parenthesis, "G" Subscript, 1 , Baseline minus "B" Subscript, 1 , Baseline , right parenthesis , "B" Subscript, 2 , Baseline plus "t" left parenthesis, "G" Subscript, 2 , Baseline minus "B" Subscript, 2 , Baseline , right parenthesis , right parenthesis
B
1
+
t
G
1
−
B
1
,
B
2
+
t
G
2
−
B
2
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
1
1
domain t Maximum:
48
Expression 49: StartFraction, left parenthesis, "G" Subscript, 2 , Baseline minus "B" Subscript, 2 , Baseline , right parenthesis left parenthesis, "D" Subscript, 1 , Baseline plus "t" Subscript, 1 , Baseline "a" minus "B" Subscript, 1 , Baseline , right parenthesis Over left parenthesis, "G" Subscript, 1 , Baseline minus "B" Subscript, 1 , Baseline , right parenthesis left parenthesis, "D" Subscript, 2 , Baseline plus "t" Subscript, 1 , Baseline "b" minus "B" Subscript, 2 , Baseline , right parenthesis , EndFraction tilde 1
G
2
−
B
2
D
1
+
t
1
a
−
B
1
G
1
−
B
1
D
2
+
t
1
b
−
B
2
~
1
49
Expression 50: "E" Subscript, 1 , Baseline equals "D" Subscript, 1 , Baseline plus "t" Subscript, 1 , Baseline "a"
E
1
=
D
1
+
t
1
a
equals
=
- 0.5 1 1 9 6 1 4 6 7 5 5 5
-
0
.
5
1
1
9
6
1
4
6
7
5
5
5
50
Expression 51: "E" Subscript, 2 , Baseline equals "D" Subscript, 2 , Baseline plus "t" Subscript, 1 , Baseline "b"
E
2
=
D
2
+
t
1
b
equals
=
negative 2.6 6 1 7 8 5 7 5 4 5 3
−
2
.
6
6
1
7
8
5
7
5
4
5
3
51
Expression 52: "M" Subscript, 1 , Baseline equals "M" Subscript, "O" , Baseline cosine alpha
M
1
=
M
O
c
o
s
α
equals
=
negative 0.6 0 8 2 1 1 0 3 8 4 3
−
0
.
6
0
8
2
1
1
0
3
8
4
3
52
Expression 53: "M" Subscript, 2 , Baseline equals "M" Subscript, "O" , Baseline sine alpha
M
2
=
M
O
s
i
n
α
equals
=
negative 3.3 6 3 4 5 1 1 0 4 5 6
−
3
.
3
6
3
4
5
1
1
0
4
5
6
53
Graphs
Graphs
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54
Expression 55: "y" less than 30
y
<
3
0
55
Hidden Label: "B" , "G"
B
,
G
Label
equals
=
left parenthesis, 0.9 5 9 3 , 5.9 2 3 , right parenthesis
0
.
9
5
9
3
,
5
.
9
2
3
left parenthesis, negative 1.0 6 8 , negative 5.9 0 4 , right parenthesis
−
1
.
0
6
8
,
−
5
.
9
0
4
56
Expression 57: left parenthesis, "R" cos "t" , "R" sin "t" , right parenthesis
R
c
o
s
t
,
R
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
57
Expression 58: polygon left parenthesis, "B" , "D" , "F" , "D" , "A" , "E" , "C" , right parenthesis
p
o
l
y
g
o
n
B
,
D
,
F
,
D
,
A
,
E
,
C
58
Expression 59: left parenthesis, "M" Subscript, 1 , Baseline plus "R" Subscript, 1 , Baseline cos "t" , "M" Subscript, 2 , Baseline plus "R" Subscript, 1 , Baseline sin "t" , right parenthesis
M
1
+
R
1
c
o
s
t
,
M
2
+
R
1
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
59
Points
Points
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60
NEW.JPG
NEW.JPG
Change Image
Center:
center: left parenthesis, negative 7.4 3 , 3.0 9 , right parenthesis
−
7
.
4
3
,
3
.
0
9
Width:
width: 4.6 8 5
4
.
6
8
5
Angle:
angle: 0
0
Height:
height: 7.5 5 7
7
.
5
5
7
Opacity:
opacity: 1
1
61
O: "O" equals left parenthesis, "O" Subscript, 1 , Baseline , "O" Subscript, 2 , Baseline , right parenthesis
O
=
O
1
,
O
2
Label:
equals
=
left parenthesis, 0 , 0 , right parenthesis
0
,
0
62
A: "A" equals left parenthesis, "A" Subscript, 1 , Baseline , "A" Subscript, 2 , Baseline , right parenthesis
A
=
A
1
,
A
2
Label:
equals
=
left parenthesis, negative 3.9 9 8 1 6 6 5 2 , negative 4.4 7 3 7 7 5 1 9 , right parenthesis
−
3
.
9
9
8
1
6
6
5
2
,
−
4
.
4
7
3
7
7
5
1
9
63
B: "B" equals left parenthesis, "B" Subscript, 1 , Baseline , "B" Subscript, 2 , Baseline , right parenthesis
B
=
B
1
,
B
2
Label:
equals
=
left parenthesis, 0.9 5 9 2 8 7 1 3 , 5.9 2 2 8 1 7 5 9 , right parenthesis
0
.
9
5
9
2
8
7
1
3
,
5
.
9
2
2
8
1
7
5
9
64
C: "C" equals left parenthesis, "C" Subscript, 1 , Baseline , "C" Subscript, 2 , Baseline , right parenthesis
C
=
C
1
,
C
2
Label:
equals
=
left parenthesis, 2.2 3 4 2 8 9 5 5 , negative 5.5 6 8 4 7 8 2 7 , right parenthesis
2
.
2
3
4
2
8
9
5
5
,
−
5
.
5
6
8
4
7
8
2
7
65
D: "D" equals left parenthesis, "D" Subscript, 1 , Baseline , "D" Subscript, 2 , Baseline , right parenthesis
D
=
D
1
,
D
2
Label:
equals
=
left parenthesis, negative 2.9 3 8 8 1 3 9 9 , negative 2.2 5 2 1 3 9 3 2 , right parenthesis
−
2
.
9
3
8
8
1
3
9
9
,
−
2
.
2
5
2
1
3
9
3
2
66
E: "E" equals left parenthesis, "E" Subscript, 1 , Baseline , "E" Subscript, 2 , Baseline , right parenthesis
E
=
E
1
,
E
2
Label:
equals
=
left parenthesis, negative 0.5 1 1 9 6 1 4 7 , negative 2.6 6 1 7 8 5 7 5 , right parenthesis
−
0
.
5
1
1
9
6
1
4
7
,
−
2
.
6
6
1
7
8
5
7
5
67
F: "F" equals left parenthesis, "F" Subscript, 1 , Baseline , "F" Subscript, 2 , Baseline , right parenthesis
F
=
F
1
,
F
2
Label:
equals
=
left parenthesis, 1.9 5 8 0 4 1 0 5 , negative 3.0 7 8 7 1 5 8 , right parenthesis
1
.
9
5
8
0
4
1
0
5
,
−
3
.
0
7
8
7
1
5
8
68
G: "G" equals left parenthesis, "G" Subscript, 1 , Baseline , "G" Subscript, 2 , Baseline , right parenthesis
G
=
G
1
,
G
2
Label:
equals
=
left parenthesis, negative 1.0 6 7 6 6 1 2 7 , negative 5.9 0 4 2 4 4 1 9 , right parenthesis
−
1
.
0
6
7
6
6
1
2
7
,
−
5
.
9
0
4
2
4
4
1
9
69
M: "M" equals left parenthesis, "M" Subscript, 1 , Baseline , "M" Subscript, 2 , Baseline , right parenthesis
M
=
M
1
,
M
2
Label:
equals
=
left parenthesis, negative 0.6 0 8 2 1 1 0 4 , negative 3.3 6 3 4 5 1 1 , right parenthesis
−
0
.
6
0
8
2
1
1
0
4
,
−
3
.
3
6
3
4
5
1
1
70
71
powered by
powered by
O
A
B
C
D
E
F
G
M
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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