/Designs/Measuring_instruments/Echo01A/DOC/sonar.nb
0,0 → 1,700
(* Content-type: application/vnd.wolfram.mathematica *)
 
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
 
(* CreatedBy='Mathematica 8.0' *)
 
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 157, 7]
NotebookDataLength[ 21630, 691]
NotebookOptionsPosition[ 20709, 656]
NotebookOutlinePosition[ 21044, 671]
CellTagsIndexPosition[ 21001, 668]
WindowFrame->Normal*)
 
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
RowBox[{"Simplify", "[",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"f", "\[Equal]",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"y", "^", "2"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "Xl"}], ")"}], "^", "2"}]}], "]"}], " ", "+",
" ",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"x", "^", "2"}], "+",
RowBox[{"y", "^", "2"}]}], "]"}]}]}], ",",
RowBox[{"g", "\[Equal]",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"y", "^", "2"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "Xr"}], ")"}], "^", "2"}]}], "]"}], " ", "+",
" ",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"x", "^", "2"}], "+",
RowBox[{"y", "^", "2"}]}], "]"}]}]}]}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{"x", ",", "y"}], "}"}]}], "]"}], "]"}]], "Input",
CellChangeTimes->{{3.515426716401871*^9, 3.51542694508688*^9}, {
3.515494250442916*^9, 3.515494312592763*^9}, {3.515494443619315*^9,
3.515494481698374*^9}, {3.515495886073002*^9, 3.515495892041057*^9}, {
3.515496075998226*^9, 3.515496077798789*^9}}],
 
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"x", "\[Rule]",
FractionBox[
RowBox[{
RowBox[{
SuperscriptBox["f", "2"], " ", "g"}], "-",
RowBox[{"g", " ",
SuperscriptBox["Xl", "2"]}], "+",
RowBox[{"f", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
SuperscriptBox["g", "2"]}], "+",
SuperscriptBox["Xr", "2"]}], ")"}]}]}],
RowBox[{
RowBox[{
RowBox[{"-", "2"}], " ", "g", " ", "Xl"}], "+",
RowBox[{"2", " ", "f", " ", "Xr"}]}]]}], ",",
RowBox[{"y", "\[Rule]",
RowBox[{"-",
FractionBox[
SqrtBox[
RowBox[{"-",
FractionBox[
RowBox[{
SuperscriptBox["g", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
SuperscriptBox["Xl", "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
RowBox[{"2", " ", "f", " ", "g"}], "+",
SuperscriptBox["g", "2"], "-",
SuperscriptBox[
RowBox[{"(",
RowBox[{"Xl", "-", "Xr"}], ")"}], "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["g", "2"], "-",
SuperscriptBox["Xr", "2"]}], ")"}]}],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]}]],
RowBox[{"2", " ", "g"}]]}]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"x", "\[Rule]",
FractionBox[
RowBox[{
RowBox[{
SuperscriptBox["f", "2"], " ", "g"}], "-",
RowBox[{"g", " ",
SuperscriptBox["Xl", "2"]}], "+",
RowBox[{"f", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
SuperscriptBox["g", "2"]}], "+",
SuperscriptBox["Xr", "2"]}], ")"}]}]}],
RowBox[{
RowBox[{
RowBox[{"-", "2"}], " ", "g", " ", "Xl"}], "+",
RowBox[{"2", " ", "f", " ", "Xr"}]}]]}], ",",
RowBox[{"y", "\[Rule]",
FractionBox[
SqrtBox[
RowBox[{"-",
FractionBox[
RowBox[{
SuperscriptBox["g", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
SuperscriptBox["Xl", "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
RowBox[{"2", " ", "f", " ", "g"}], "+",
SuperscriptBox["g", "2"], "-",
SuperscriptBox[
RowBox[{"(",
RowBox[{"Xl", "-", "Xr"}], ")"}], "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["g", "2"], "-",
SuperscriptBox["Xr", "2"]}], ")"}]}],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]}]],
RowBox[{"2", " ", "g"}]]}]}], "}"}]}], "}"}]], "Input",
CellChangeTimes->{{3.515496935952406*^9, 3.515496938796506*^9}}],
 
Cell[BoxData[
RowBox[{
RowBox[{"position", "[",
RowBox[{"f_", ",", "g_"}], "]"}], ":=",
RowBox[{"{",
RowBox[{
FractionBox[
RowBox[{
RowBox[{
SuperscriptBox["f", "2"], " ", "g"}], "-",
RowBox[{"g", " ",
SuperscriptBox["Xl", "2"]}], "+",
RowBox[{"f", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
SuperscriptBox["g", "2"]}], "+",
SuperscriptBox["Xr", "2"]}], ")"}]}]}],
RowBox[{
RowBox[{
RowBox[{"-", "2"}], " ", "g", " ", "Xl"}], "+",
RowBox[{"2", " ", "f", " ", "Xr"}]}]], ",",
FractionBox[
SqrtBox[
RowBox[{"-",
FractionBox[
RowBox[{
SuperscriptBox["g", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
SuperscriptBox["Xl", "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
RowBox[{"2", " ", "f", " ", "g"}], "+",
SuperscriptBox["g", "2"], "-",
SuperscriptBox[
RowBox[{"(",
RowBox[{"Xl", "-", "Xr"}], ")"}], "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["g", "2"], "-",
SuperscriptBox["Xr", "2"]}], ")"}]}],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]}]],
RowBox[{"2", " ", "g"}]]}], "}"}]}]], "Input",
CellChangeTimes->{{3.515496295181325*^9, 3.515496373145641*^9}}],
 
Cell[BoxData[
RowBox[{
RowBox[{"distance", "[",
RowBox[{"x_", ",", "y_"}], "]"}], ":=",
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"y", "^", "2"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "Xl"}], ")"}], "^", "2"}]}], "]"}], " ", "+", " ",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"x", "^", "2"}], "+",
RowBox[{"y", "^", "2"}]}], "]"}]}], ",",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"y", "^", "2"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "Xr"}], ")"}], "^", "2"}]}], "]"}], " ", "+", " ",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"x", "^", "2"}], "+",
RowBox[{"y", "^", "2"}]}], "]"}]}]}], "}"}]}]], "Input",
CellChangeTimes->{{3.515496905741654*^9, 3.515496944394813*^9}}],
 
Cell[CellGroupData[{
 
Cell[BoxData[
RowBox[{"distance", "[",
RowBox[{"0.3", ",", "7.4"}], "]"}]], "Input",
CellChangeTimes->{{3.515496403004589*^9, 3.515496473593597*^9}, {
3.515496631709924*^9, 3.515496675661791*^9}, {3.515496758217258*^9,
3.51549676557555*^9}, {3.515496952775792*^9, 3.515496982312476*^9}}],
 
Cell[BoxData[
RowBox[{"{",
RowBox[{"14.919400087018944`", ",", "14.839112958173462`"}],
"}"}]], "Output",
CellChangeTimes->{3.515496996655669*^9}]
}, Open ]],
 
Cell[CellGroupData[{
 
Cell[BoxData[
RowBox[{"position", "[",
RowBox[{"14.919400087018944`", ",", "14.839112958173462`"}], "]"}]], "Input",
CellChangeTimes->{{3.515496988909477*^9, 3.515497012744518*^9}}],
 
Cell[BoxData[
RowBox[{"{",
RowBox[{"0.3000000000000122`", ",", "7.399999999999991`"}], "}"}]], "Output",\
 
CellChangeTimes->{3.515497013951068*^9}]
}, Open ]],
 
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.515496949744564*^9, 3.515496949783665*^9}}],
 
Cell[CellGroupData[{
 
Cell[BoxData[
RowBox[{"Simplify", "[",
RowBox[{"Solve", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"f", "\[Equal]",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"y", "^", "2"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "Xl"}], ")"}], "^", "2"}]}], "]"}], " ", "+",
" ",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"x", "^", "2"}], "+",
RowBox[{"y", "^", "2"}]}], "]"}]}]}], ",",
RowBox[{"g", "\[Equal]",
RowBox[{
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"y", "^", "2"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "Xr"}], ")"}], "^", "2"}]}], "]"}], " ", "+",
" ",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"x", "^", "2"}], "+",
RowBox[{"y", "^", "2"}]}], "]"}]}]}], ",",
RowBox[{"a", "==",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"y", "^", "2"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "Xl"}], ")"}], "^", "2"}]}], "]"}]}], ",",
RowBox[{"b", "==",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"y", "^", "2"}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "Xr"}], ")"}], "^", "2"}]}], "]"}]}], ",",
RowBox[{"c", "==",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"x", "^", "2"}], "+",
RowBox[{"y", "^", "2"}]}], "]"}]}]}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{"x", ",", "y", ",", "a", ",", "b", ",", "c"}], "}"}]}], "]"}],
"]"}]], "Input",
CellChangeTimes->{{3.515497849255536*^9, 3.515497856520988*^9}, {
3.515497888462276*^9, 3.515497937952609*^9}},
FontWeight->"Plain"],
 
Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"x", "\[Rule]",
FractionBox[
RowBox[{
RowBox[{
SuperscriptBox["f", "2"], " ", "g"}], "-",
RowBox[{"g", " ",
SuperscriptBox["Xl", "2"]}], "+",
RowBox[{"f", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
SuperscriptBox["g", "2"]}], "+",
SuperscriptBox["Xr", "2"]}], ")"}]}]}],
RowBox[{
RowBox[{
RowBox[{"-", "2"}], " ", "g", " ", "Xl"}], "+",
RowBox[{"2", " ", "f", " ", "Xr"}]}]]}], ",",
RowBox[{"y", "\[Rule]",
RowBox[{"-",
FractionBox[
SqrtBox[
RowBox[{"-",
FractionBox[
RowBox[{
SuperscriptBox["g", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
SuperscriptBox["Xl", "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
RowBox[{"2", " ", "f", " ", "g"}], "+",
SuperscriptBox["g", "2"], "-",
SuperscriptBox[
RowBox[{"(",
RowBox[{"Xl", "-", "Xr"}], ")"}], "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["g", "2"], "-",
SuperscriptBox["Xr", "2"]}], ")"}]}],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]}]],
RowBox[{"2", " ", "g"}]]}]}], ",",
RowBox[{"a", "\[Rule]",
RowBox[{"f", "-",
RowBox[{
FractionBox["1", "2"], " ",
SqrtBox[
FractionBox[
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["g", "2"], " ", "Xl"}], "-",
RowBox[{"Xr", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "+",
RowBox[{"Xl", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "Xl"}], "+", "Xr"}], ")"}]}]}], ")"}]}]}],
")"}], "2"],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]]}]}]}], ",",
RowBox[{"b", "\[Rule]",
RowBox[{"g", "-",
RowBox[{
FractionBox["1", "2"], " ",
SqrtBox[
FractionBox[
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["g", "2"], " ", "Xl"}], "-",
RowBox[{"Xr", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "+",
RowBox[{"Xl", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "Xl"}], "+", "Xr"}], ")"}]}]}], ")"}]}]}],
")"}], "2"],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]]}]}]}], ",",
RowBox[{"c", "\[Rule]",
RowBox[{
FractionBox["1", "2"], " ",
SqrtBox[
FractionBox[
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["g", "2"], " ", "Xl"}], "-",
RowBox[{"Xr", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "+",
RowBox[{"Xl", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "Xl"}], "+", "Xr"}], ")"}]}]}], ")"}]}]}],
")"}], "2"],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]]}]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"x", "\[Rule]",
FractionBox[
RowBox[{
RowBox[{
SuperscriptBox["f", "2"], " ", "g"}], "-",
RowBox[{"g", " ",
SuperscriptBox["Xl", "2"]}], "+",
RowBox[{"f", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-",
SuperscriptBox["g", "2"]}], "+",
SuperscriptBox["Xr", "2"]}], ")"}]}]}],
RowBox[{
RowBox[{
RowBox[{"-", "2"}], " ", "g", " ", "Xl"}], "+",
RowBox[{"2", " ", "f", " ", "Xr"}]}]]}], ",",
RowBox[{"y", "\[Rule]",
FractionBox[
SqrtBox[
RowBox[{"-",
FractionBox[
RowBox[{
SuperscriptBox["g", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
SuperscriptBox["Xl", "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
RowBox[{"2", " ", "f", " ", "g"}], "+",
SuperscriptBox["g", "2"], "-",
SuperscriptBox[
RowBox[{"(",
RowBox[{"Xl", "-", "Xr"}], ")"}], "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["g", "2"], "-",
SuperscriptBox["Xr", "2"]}], ")"}]}],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]}]],
RowBox[{"2", " ", "g"}]]}], ",",
RowBox[{"a", "\[Rule]",
RowBox[{"f", "-",
RowBox[{
FractionBox["1", "2"], " ",
SqrtBox[
FractionBox[
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["g", "2"], " ", "Xl"}], "-",
RowBox[{"Xr", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "+",
RowBox[{"Xl", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "Xl"}], "+", "Xr"}], ")"}]}]}], ")"}]}]}],
")"}], "2"],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]]}]}]}], ",",
RowBox[{"b", "\[Rule]",
RowBox[{"g", "-",
RowBox[{
FractionBox["1", "2"], " ",
SqrtBox[
FractionBox[
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["g", "2"], " ", "Xl"}], "-",
RowBox[{"Xr", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "+",
RowBox[{"Xl", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "Xl"}], "+", "Xr"}], ")"}]}]}], ")"}]}]}],
")"}], "2"],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]]}]}]}], ",",
RowBox[{"c", "\[Rule]",
RowBox[{
FractionBox["1", "2"], " ",
SqrtBox[
FractionBox[
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{
SuperscriptBox["g", "2"], " ", "Xl"}], "-",
RowBox[{"Xr", " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "+",
RowBox[{"Xl", " ",
RowBox[{"(",
RowBox[{
RowBox[{"-", "Xl"}], "+", "Xr"}], ")"}]}]}], ")"}]}]}],
")"}], "2"],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]]}]}]}], "}"}]}],
"}"}]], "Output",
CellChangeTimes->{3.515497857789938*^9, 3.515497938817161*^9,
3.515498443550477*^9, 3.515498495049169*^9}]
}, Open ]],
 
Cell[CellGroupData[{
 
Cell[BoxData[
RowBox[{"CForm", "[",
FractionBox[
SqrtBox[
RowBox[{"-",
FractionBox[
RowBox[{
SuperscriptBox["g", "2"], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
SuperscriptBox["Xl", "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["f", "2"], "-",
RowBox[{"2", " ", "f", " ", "g"}], "+",
SuperscriptBox["g", "2"], "-",
SuperscriptBox[
RowBox[{"(",
RowBox[{"Xl", "-", "Xr"}], ")"}], "2"]}], ")"}], " ",
RowBox[{"(",
RowBox[{
SuperscriptBox["g", "2"], "-",
SuperscriptBox["Xr", "2"]}], ")"}]}],
SuperscriptBox[
RowBox[{"(",
RowBox[{
RowBox[{"g", " ", "Xl"}], "-",
RowBox[{"f", " ", "Xr"}]}], ")"}], "2"]]}]],
RowBox[{"2", " ", "g"}]], "]"}]], "Input",
CellChangeTimes->{{3.515498536581236*^9, 3.515498539213621*^9}, {
3.515498650974364*^9, 3.515498653572732*^9}, {3.515499109832382*^9,
3.515499111554484*^9}, 3.515499287277104*^9}],
 
Cell["\<\
Sqrt(-((Power(g,2)*(Power(f,2) - Power(Xl,2))*
(Power(f,2) - 2*f*g + Power(g,2) - Power(Xl - Xr,2))*
(Power(g,2) - Power(Xr,2)))/Power(g*Xl - f*Xr,2)))/(2.*g)\
\>", "Output",
GeneratedCell->False,
CellAutoOverwrite->False,
CellChangeTimes->{{3.515498539771723*^9, 3.515498545680778*^9},
3.515498654644995*^9, 3.515499112485191*^9, 3.515499287974278*^9}],
 
Cell["\<\
(Power(f,2)*g - g*Power(Xl,2) + f*(-Power(g,2) + Power(Xr,2)))/
(-2*g*Xl + 2*f*Xr)\
\>", "Output",
GeneratedCell->False,
CellAutoOverwrite->False,
CellChangeTimes->{{3.515498539771723*^9, 3.515498545680778*^9},
3.515498654644995*^9, 3.515499112485191*^9}],
 
Cell["\<\
g - Sqrt(Power(Power(g,2)*Xl - Xr*(Power(f,2) + Xl*(-Xl + Xr)),
2)/Power(g*Xl - f*Xr,2))/2.\
\>", "Output",
GeneratedCell->False,
CellAutoOverwrite->False,
CellChangeTimes->{{3.515498539771723*^9, 3.515498545680778*^9},
3.515498654644995*^9}]
}, Open ]]
},
WindowSize->{1280, 723},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"8.0 for Linux x86 (32-bit) (October 10, 2011)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
 
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 1292, 37, 30, "Input"],
Cell[1852, 59, 3322, 100, 176, "Input"],
Cell[5177, 161, 1590, 50, 88, "Input"],
Cell[6770, 213, 894, 30, 30, "Input"],
Cell[CellGroupData[{
Cell[7689, 247, 297, 5, 30, "Input"],
Cell[7989, 254, 154, 4, 30, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[8180, 263, 186, 3, 30, "Input"],
Cell[8369, 268, 152, 4, 30, "Output"]
}, Open ]],
Cell[8536, 275, 92, 1, 30, "Input"],
Cell[CellGroupData[{
Cell[8653, 280, 1821, 56, 50, "Input"],
Cell[10477, 338, 8155, 250, 297, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[18669, 593, 1086, 32, 88, "Input"],
Cell[19758, 627, 388, 8, 62, "Output"],
Cell[20149, 637, 275, 7, 46, "Output"],
Cell[20427, 646, 266, 7, 46, "Output"]
}, Open ]]
}
]
*)
 
(* End of internal cache information *)