Start\vec "v" undefined left parenthesis, "t" , right parenthesis→vt
"X" left parenthesis, "t" Subscript, 0 , Baseline , right parenthesisXt0
"Y" left parenthesis, "t" Subscript, 0 , Baseline , right parenthesisYt0
r1c1:
r1c2: 3.9 2 0 2 6 6 33.9202663
r1c3: 0.5 9 6 0 0 7 9 90.59600799
r1c4:
r2c1:
r2c2:
r2c3:
r2c4:
23
"f" left parenthesis, "x" left parenthesis, "t" , right parenthesis , "y" left parenthesis, "t" , right parenthesis , right parenthesisfxt,yt
"f" left parenthesis, "X" left parenthesis, "t" Subscript, 0 , Baseline , right parenthesis , "Y" left parenthesis, "t" Subscript, 0 , Baseline , right parenthesis , right parenthesisfXt0,Yt0
r1c1:
r1c2: 1.6 2 8 9 4 8 51.6289485
r1c3:
r2c1:
r2c2:
r2c3:
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StartFraction, "d" Over "d" "t" , EndFraction "f" left parenthesis, "x" left parenthesis, "t" , right parenthesis , "y" left parenthesis, "t" , right parenthesis , right parenthesisddtfxt,yt
"f" Subscript, "p" "r" "i" "m" "e" , Baseline left parenthesis, "t" Subscript, 0 , Baseline , right parenthesisfprimet0
r1c1:
r1c2: negative 0.1 0 9 0 3 6 2 8−0.10903628
r1c3:
r2c1:
r2c2:
r2c3:
25
Tertiary Input (Points)
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26
"t" Subscript, 00 , Baselinet00
"f" left parenthesis, "X" left parenthesis, "t" Subscript, 00 , Baseline , right parenthesis , "Y" left parenthesis, "t" Subscript, 00 , Baseline , right parenthesis , right parenthesisfXt00,Yt00
"f" Subscript, "p" "r" "i" "m" "e" , Baseline left parenthesis, "t" Subscript, 00 , Baseline , right parenthesisfprimet00
1.81.8
r1c2: 1.3 7 4 4 5 3 81.3744538
r1c3: 0.1 2 3 9 0 3 8 90.12390389
r1c4:
4.54.5
r2c2: 1.3 7 2 4 4 1 81.3724418
r2c3: negative 0.1 1 5 3 9 1 8 6−0.11539186
r2c4:
r3c2:
r3c3:
r3c4:
27
Formulas
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28
Expression 29: StartFraction, "d" Over "d" "t" , EndFraction "f" left parenthesis, "x" left parenthesis, "t" , right parenthesis , "y" left parenthesis, "t" , right parenthesis , right parenthesis equals StartFraction, ∂ "f" Over ∂ "x" , EndFraction times StartFraction, "d" "x" Over "d" "t" , EndFraction positive StartFraction, ∂ "f" Over ∂ "y" , EndFraction times StartFraction, "d" "y" Over "d" "t" , EndFractionddtfxt,yt=∂f∂x·dxdt+∂f∂y·dydt
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Expression 30: StartFraction, "d" Over "d" "t" , EndFraction "f" left parenthesis, "x" left parenthesis, "t" , right parenthesis , "y" left parenthesis, "t" , right parenthesis , right parenthesis equals "f" Subscript, "x" , Baseline left parenthesis, "x" left parenthesis, "t" , right parenthesis , "y" left parenthesis, "t" , right parenthesis , right parenthesis times "x" prime left parenthesis, "t" , right parenthesis positive "f" Subscript, "y" , Baseline left parenthesis, "x" left parenthesis, "t" , right parenthesis , "y" left parenthesis, "t" , right parenthesis , right parenthesis times "y" prime left parenthesis, "t" , right parenthesisddtfxt,yt=fxxt,yt·x′t+fyxt,yt·y′t
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Expression 31: StartFraction, "d" Over "d" "t" , EndFraction "f" left parenthesis, Start\vec "v" undefined left parenthesis, "t" , right parenthesis , right parenthesis equals StartFraction, ∂ "f" Over ∂ "x" , EndFraction left parenthesis, Start\vec "v" undefined left parenthesis, "t" , right parenthesis , right parenthesis StartFraction, "d" "x" Over "d" "t" , EndFraction positive StartFraction, ∂ "f" Over ∂ "y" , EndFraction left parenthesis, Start\vec "v" undefined left parenthesis, "t" , right parenthesis , right parenthesis StartFraction, "d" "y" Over "d" "t" , EndFractionddtf→vt=∂f∂x→vtdxdt+∂f∂y→vtdydt
31
Perspective View
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32
Expression 33: theta Subscript, "h" "o" "r" "i" "z" "o" "n" "t" "a" "l" , Baseline equals negative 0.5θhorizontal=−0.5