Expression 14: "y" minus "y" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis equals StartFraction, "y" Subscript, "t" , Baseline prime left parenthesis, "a" , right parenthesis Over "x" Subscript, "t" , Baseline prime left parenthesis, "a" , right parenthesis , EndFraction left parenthesis, "x" minus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis , right parenthesis left brace, StartFraction, "x" Subscript, "t" , Baseline prime left parenthesis, "a" , right parenthesis Over 2 , EndFraction minus StartFraction, StartAbsoluteValue, "x" Subscript, "t" , Baseline prime left parenthesis, "a" , right parenthesis , EndAbsoluteValue Over 2 , EndFraction plus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis less than "x" less than StartFraction, "x" Subscript, "t" , Baseline prime left parenthesis, "a" , right parenthesis Over 2 , EndFraction plus StartFraction, StartAbsoluteValue, "x" Subscript, "t" , Baseline prime left parenthesis, "a" , right parenthesis , EndAbsoluteValue Over 2 , EndFraction plus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis , right bracey−yta=yt′axt′ax−xtaxt′a2−xt′a2+xta<x<xt′a2+xt′a2+xta
14
Expression 15: "y" minus "y" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis equals StartFraction, "y" Subscript, "t" , Baseline prime prime left parenthesis, "a" , right parenthesis Over "x" Subscript, "t" , Baseline prime prime left parenthesis, "a" , right parenthesis , EndFraction left parenthesis, "x" minus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis , right parenthesis left brace, StartFraction, "x" Subscript, "t" , Baseline prime prime left parenthesis, "a" , right parenthesis Over 2 , EndFraction minus StartFraction, StartAbsoluteValue, "x" Subscript, "t" , Baseline prime prime left parenthesis, "a" , right parenthesis , EndAbsoluteValue Over 2 , EndFraction plus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis less than "x" less than StartFraction, "x" Subscript, "t" , Baseline prime prime left parenthesis, "a" , right parenthesis Over 2 , EndFraction plus StartFraction, StartAbsoluteValue, "x" Subscript, "t" , Baseline prime prime left parenthesis, "a" , right parenthesis , EndAbsoluteValue Over 2 , EndFraction plus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis , right bracey−yta=yt′′axt′′ax−xtaxt′′a2−xt′′a2+xta<x<xt′′a2+xt′′a2+xta
15
Show Curvature and Radius Graphs
Hide this folder from students.
16
Label: left parenthesis, "x" Subscript, "c" , Baseline , "y" Subscript, "c" , Baseline , right parenthesisxc,yc
Expression 31: left parenthesis, "x" minus "x" Subscript, "c" , Baseline , right parenthesis squared plus left parenthesis, "y" minus "y" Subscript, "c" , Baseline , right parenthesis squared equals "R" left parenthesis, "a" , right parenthesis squaredx−xc2+y−yc2=Ra2
31
Expression 32: "y" minus "y" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis equals "p" times left parenthesis, "x" minus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis , right parenthesis left brace, "x" Subscript, "c" , Baseline minus StartFraction, left parenthesis, "x" Subscript, "c" , Baseline minus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis , right parenthesis plus "d" Over 2 , EndFraction less than or equal to "x" less than or equal to "x" Subscript, "c" , Baseline minus StartFraction, left parenthesis, "x" Subscript, "c" , Baseline minus "x" Subscript, "t" , Baseline left parenthesis, "a" , right parenthesis , right parenthesis minus "d" Over 2 , EndFraction , right bracey−yta=p·x−xtaxc−xc−xta+d2≤x≤xc−xc−xta−d2
