Expresión 21: "I" Subscript, "n" "t" "e" "r" , Baseline left parenthesis, "x" Subscript, 1 , Baseline , "y" Subscript, 1 , Baseline , "r" Subscript, 1 , Baseline , "x" Subscript, 2 , Baseline , "y" Subscript, 2 , Baseline , "r" Subscript, 2 , Baseline , right parenthesis equals left brace, "y" Subscript, 1 , Baseline equals "y" Subscript, 2 , Baseline : left parenthesis, StartFraction, left parenthesis, "x" squared minus "x" squared , right parenthesis minus left parenthesis, "r" squared minus "r" squared , right parenthesis Over 2 left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis , EndFraction , "y" Subscript, 1 , Baseline plus left bracket, 1 , negative 1 , right bracket StartRoot, "r" squared minus left parenthesis, StartFraction, left parenthesis, "x" squared minus "x" squared , right parenthesis minus left parenthesis, "r" squared minus "r" squared , right parenthesis Over 2 left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis , EndFraction minus "x" Subscript, 1 , Baseline , right parenthesis squared , EndRoot , right parenthesis , left parenthesis, StartFraction, negative left parenthesis, left parenthesis, StartNestedFraction, negative left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis NestedOver left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis squared , EndNestedFraction minus 2 "x" Subscript, 1 , Baseline plus StartNestedFraction, 2 "y" Subscript, 1 , Baseline left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis NestedOver "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , EndNestedFraction , right parenthesis , right parenthesis plus left bracket, 1 , negative 1 , right bracket StartRoot, left parenthesis, left parenthesis, StartNestedFraction, negative left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis NestedOver left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis squared , EndNestedFraction minus 2 "x" Subscript, 1 , Baseline plus StartNestedFraction, 2 "y" Subscript, 1 , Baseline left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis NestedOver "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , EndNestedFraction , right parenthesis , right parenthesis squared minus 4 left parenthesis, 1 plus StartNestedFraction, left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis squared NestedOver left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis squared , EndNestedFraction , right parenthesis left parenthesis, StartNestedFraction, left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis squared NestedOver 4 left parenthesis, "y" Subscript, 1 , Baseline minus "y" Subscript, 2 , Baseline , right parenthesis squared , EndNestedFraction minus StartNestedFraction, "y" Subscript, 1 , Baseline left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis NestedOver "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , EndNestedFraction plus "x" squared plus "y" squared minus "r" squared , right parenthesis , EndRoot Over 2 left parenthesis, 1 plus StartNestedFraction, left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis squared NestedOver left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis squared , EndNestedFraction , right parenthesis , EndFraction , StartFraction, negative 2 left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis left parenthesis, StartNestedFraction, negative left parenthesis, left parenthesis, StartNestedFraction, negative left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis NestedOver left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis squared , EndNestedFraction minus 2 "x" Subscript, 1 , Baseline plus StartNestedFraction, 2 "y" Subscript, 1 , Baseline left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis NestedOver "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , EndNestedFraction , right parenthesis , right parenthesis plus left bracket, 1 , negative 1 , right bracket StartRoot, left parenthesis, left parenthesis, StartNestedFraction, negative left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis NestedOver left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis squared , EndNestedFraction minus 2 "x" Subscript, 1 , Baseline plus StartNestedFraction, 2 "y" Subscript, 1 , Baseline left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis NestedOver "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , EndNestedFraction , right parenthesis , right parenthesis squared minus 4 left parenthesis, 1 plus StartNestedFraction, left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis squared NestedOver left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis squared , EndNestedFraction , right parenthesis left parenthesis, StartNestedFraction, left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis squared NestedOver 4 left parenthesis, "y" Subscript, 1 , Baseline minus "y" Subscript, 2 , Baseline , right parenthesis squared , EndNestedFraction minus StartNestedFraction, "y" Subscript, 1 , Baseline left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis NestedOver "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , EndNestedFraction plus "x" squared plus "y" squared minus "r" squared , right parenthesis , EndRoot NestedOver 2 left parenthesis, 1 plus StartNestedFraction, left parenthesis, "x" Subscript, 2 , Baseline minus "x" Subscript, 1 , Baseline , right parenthesis squared NestedOver left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis squared , EndNestedFraction , right parenthesis , EndNestedFraction , right parenthesis plus left parenthesis, left parenthesis, "x" squared minus "x" squared , right parenthesis plus left parenthesis, "y" squared minus "y" squared , right parenthesis plus left parenthesis, "r" squared minus "r" squared , right parenthesis , right parenthesis Over 2 left parenthesis, "y" Subscript, 2 , Baseline minus "y" Subscript, 1 , Baseline , right parenthesis , EndFraction , right parenthesis , right braceInterx1,y1,r1,x2,y2,r2=y1=y2:x22−x21−r22−r212x2−x1,y1+1,−1r21−x22−x21−r22−r212x2−x1−x12,−−x22−x21+y22−y21+r21−r22x2−x1y2−y12−2x1+2y1x2−x1y2−y1+1,−1−x22−x21+y22−y21+r21−r22x2−x1y2−y12−2x1+2y1x2−x1y2−y12−41+x2−x12y2−y12x22−x21+y22−y21+r21−r2224y1−y22−y1x22−x21+y22−y21+r21−r22y2−y1+x21+y21−r2121+x2−x12y2−y12,−2x2−x1−−x22−x21+y22−y21+r21−r22x2−x1y2−y12−2x1+2y1x2−x1y2−y1+1,−1−x22−x21+y22−y21+r21−r22x2−x1y2−y12−2x1+2y1x2−x1y2−y12−41+x2−x12y2−y12x22−x21+y22−y21+r21−r2224y1−y22−y1x22−x21+y22−y21+r21−r22y2−y1+x21+y21−r2121+x2−x12y2−y12+x22−x21+y22−y21+r21−r222y2−y1
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Expresión 34: "i" Subscript, "n" , Baseline left parenthesis, "x" , right parenthesis equals left brace, 0 less than or equal to "x" less than or equal to 1 third : 9 eighths "x" , 1 third less than or equal to "x" less than or equal to 2 thirds : 3 quarters left parenthesis, "x" minus 1 half , right parenthesis plus 1 half , 2 thirds less than or equal to "x" less than or equal to 1 : 9 eighths "x" minus 1 eighth , right braceinx=0≤x≤13:98x,13≤x≤23:34x−12+12,23≤x≤1:98x−18
