(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.1' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     72650,       1871]
NotebookOptionsPosition[     65543,       1745]
NotebookOutlinePosition[     65991,       1763]
CellTagsIndexPosition[     65948,       1760]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{"Profits", ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"-", "\[Alpha]"}], " ", "p"}], "+", 
   RowBox[{"e", 
    RowBox[{"(", 
     RowBox[{"f", "-", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"1", "-", "\[Alpha]"}], ")"}], "p"}]}], ")"}]}], "-", "cs", 
   " ", "-", 
   RowBox[{"r", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"\[Alpha]", " ", "p"}], "+", "cs", "+", "f"}], ")"}]}], "+", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"1", "-", "e"}], ")"}], 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"\[Alpha]", " ", "p"}], "+", "cs", "+", "f"}], 
     ")"}]}]}]}]], "Input",
 CellLabel->"In[2]:=",ExpressionUUID->"4bc1b551-f5c4-4026-98ec-c0ea28b5587c"],

Cell[BoxData[{
 RowBox[{"p", ":=", 
  FractionBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}], "\[IndentingNewLine]", 
 RowBox[{"r", ":=", 
  FractionBox[
   RowBox[{
    RowBox[{"2", " ", "k"}], "-", "p", "+", 
    RowBox[{"p", " ", "\[Alpha]"}], "-", "\[Theta]"}], 
   RowBox[{"2", " ", "k"}]]}]}], "Input",
 CellChangeTimes->{{3.84760409464928*^9, 3.847604109967392*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"112e234b-d795-415a-ad63-71162225d88b"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"D", "[", 
  RowBox[{"Profits", ",", "e"}], "]"}]], "Input",
 CellChangeTimes->{{3.847603927875311*^9, 3.847603935283222*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"e5001feb-e8fa-40dc-9845-7839276c7d77"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "cs"}], "+", 
  FractionBox[
   RowBox[{"2", " ", "e", " ", "k", " ", 
    RowBox[{"(", 
     RowBox[{"1", "-", "\[Alpha]"}], ")"}]}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "+", 
  FractionBox[
   RowBox[{"2", " ", "k", " ", "\[Alpha]"}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "-", 
  FractionBox[
   RowBox[{"2", " ", 
    RowBox[{"(", 
     RowBox[{"1", "-", "e"}], ")"}], " ", "k", " ", "\[Alpha]"}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "-", 
  FractionBox[
   RowBox[{
    RowBox[{"(", 
     RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], ")"}]}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "-", 
  FractionBox[
   RowBox[{"\[Alpha]", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], ")"}]}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "-", 
  FractionBox[
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      FractionBox[
       RowBox[{"2", " ", "k"}], 
       RowBox[{
        RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "-", 
      FractionBox[
       RowBox[{"2", " ", "k", " ", "\[Alpha]"}], 
       RowBox[{
        RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{"cs", "+", "f", "+", 
      FractionBox[
       RowBox[{"\[Alpha]", " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], 
         ")"}]}], 
       RowBox[{
        RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}], ")"}]}], 
   RowBox[{"2", " ", "k"}]], "+", 
  FractionBox[
   RowBox[{"\[Alpha]", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"2", " ", "k"}], "-", "\[Theta]", "-", 
      FractionBox[
       RowBox[{
        RowBox[{
         RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], 
       RowBox[{
        RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "+", 
      FractionBox[
       RowBox[{"\[Alpha]", " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{
           RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], 
         ")"}]}], 
       RowBox[{
        RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}], ")"}]}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}]], "Output",
 CellChangeTimes->{3.847603935691065*^9, 3.847604113393174*^9},
 CellLabel->"Out[8]=",ExpressionUUID->"d53ef495-d42b-4cfb-9352-7816854756a9"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Simplify", "[", "%8", "]"}]], "Input",
 NumberMarks->False,
 CellLabel->"In[9]:=",ExpressionUUID->"b93144d3-c913-472e-b3a0-e8c50bb0366f"],

Cell[BoxData[
 FractionBox[
  RowBox[{
   RowBox[{"f", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "-", 
   RowBox[{"4", " ", "e", " ", "k", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}], "+", 
   RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
   RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
  RowBox[{
   RowBox[{"-", "1"}], "+", "\[Alpha]"}]]], "Output",
 CellChangeTimes->{3.847604118191535*^9},
 CellLabel->"Out[9]=",ExpressionUUID->"3e225b47-2ba8-40c2-8384-80380e2c0ba6"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"%", "\[Equal]", "0"}], ",", "e"}], "]"}]], "Input",
 CellChangeTimes->{{3.847604257940753*^9, 3.847604265847411*^9}},
 CellLabel->"In[10]:=",ExpressionUUID->"aa70c68c-3dd7-49dd-a104-1ef2638958ee"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"e", "\[Rule]", 
    FractionBox[
     RowBox[{
      RowBox[{"-", "f"}], "+", 
      RowBox[{"f", " ", "\[Alpha]"}], "+", 
      RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
      RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
     RowBox[{"4", " ", "k", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}]]}], "}"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.847604266315012*^9},
 CellLabel->"Out[10]=",ExpressionUUID->"88aa45be-d922-4baf-ba19-16989cad3c2a"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", 
  "\[IndentingNewLine]"}]], "Input",
 CellChangeTimes->{{3.8476044197381687`*^9, 
  3.847604420084127*^9}},ExpressionUUID->"1f09d665-f21b-4bef-941e-\
f291a1847703"],

Cell[BoxData[
 RowBox[{"Profits", ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"-", "\[Alpha]"}], " ", "p"}], "+", 
   RowBox[{"e", 
    RowBox[{"(", 
     RowBox[{"f", "-", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"1", "-", "\[Alpha]"}], ")"}], "p"}]}], ")"}]}], "-", "cs", 
   " ", "-", 
   RowBox[{"r", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"\[Alpha]", " ", "p"}], "+", "cs", "+", "f"}], ")"}]}], "+", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"1", "-", "e"}], ")"}], 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"\[Alpha]", " ", "p"}], "+", "cs", "+", "f"}], 
     ")"}]}]}]}]], "Input",
 CellLabel->"In[1]:=",ExpressionUUID->"1bb31936-0e42-4d2f-90f4-2da2dbccfeac"],

Cell[BoxData[
 RowBox[{"e", ":=", 
  FractionBox[
   RowBox[{"p", "-", 
    RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], 
   RowBox[{"2", " ", "k"}]]}]], "Input",
 CellChangeTimes->{{3.847604456548092*^9, 3.847604457226687*^9}},
 CellLabel->"In[2]:=",ExpressionUUID->"1ee666dd-6587-4bd8-bd76-8498aab9db11"],

Cell[BoxData[
 RowBox[{"r", ":=", 
  RowBox[{"1", "-", 
   FractionBox[
    RowBox[{"p", "-", 
     RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], 
    RowBox[{"2", " ", "k"}]]}]}]], "Input",
 CellChangeTimes->{{3.847604460527334*^9, 3.8476044662488613`*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"01adb8cc-2282-47df-9fd8-1e53ad00b87a"],

Cell[CellGroupData[{

Cell[BoxData["Profits"], "Input",
 CellChangeTimes->{{3.847604474409842*^9, 3.847604479190753*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"fde5fabc-a7d1-48d8-afc2-299ba4b89028"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "cs"}], "-", 
  RowBox[{"p", " ", "\[Alpha]"}], "+", 
  FractionBox[
   RowBox[{
    RowBox[{"(", 
     RowBox[{"f", "-", 
      RowBox[{"p", " ", 
       RowBox[{"(", 
        RowBox[{"1", "-", "\[Alpha]"}], ")"}]}]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{"p", "-", 
      RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}], 
   RowBox[{"2", " ", "k"}]]}]], "Output",
 CellChangeTimes->{3.847604480067214*^9},
 CellLabel->"Out[4]=",ExpressionUUID->"80975313-3810-453e-b0a8-809870d79677"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"D", "[", 
  RowBox[{"%", ",", "p"}], "]"}]], "Input",
 CellChangeTimes->{{3.847604484032296*^9, 3.8476044901379557`*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"83dc9ced-6793-4d8c-ab09-97f1c6407ec2"],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{
    RowBox[{"(", 
     RowBox[{"f", "-", 
      RowBox[{"p", " ", 
       RowBox[{"(", 
        RowBox[{"1", "-", "\[Alpha]"}], ")"}]}]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{"1", "-", "\[Alpha]"}], ")"}]}], 
   RowBox[{"2", " ", "k"}]], "-", "\[Alpha]", "+", 
  FractionBox[
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{"p", "-", 
      RowBox[{"p", " ", "\[Alpha]"}], "+", "\[Theta]"}], ")"}]}], 
   RowBox[{"2", " ", "k"}]]}]], "Output",
 CellChangeTimes->{3.84760449153371*^9},
 CellLabel->"Out[5]=",ExpressionUUID->"e3919eef-d5b9-4f25-baec-fe6210199691"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"%", "\[Equal]", "0"}], ",", "p"}], "]"}]], "Input",
 CellChangeTimes->{{3.847604494412036*^9, 3.847604504939644*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"07885560-5ebc-4563-81a6-578e8b75a2f9"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"p", "\[Rule]", 
    FractionBox[
     RowBox[{"f", "-", 
      RowBox[{"f", " ", "\[Alpha]"}], "-", 
      RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
      RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
     RowBox[{"2", " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], "}"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.847604506435852*^9},
 CellLabel->"Out[6]=",ExpressionUUID->"93682421-b443-44cf-97a2-77de6357b847"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"P", ":=", 
  FractionBox[
   RowBox[{"f", "-", 
    RowBox[{"f", " ", "\[Alpha]"}], "-", 
    RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
    RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
   RowBox[{"2", " ", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}]], "Input",
 CellChangeTimes->{{3.847604526924065*^9, 3.847604535472856*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"79fa97b5-b003-4bb9-83a8-541f1e2dd78c"],

Cell[BoxData[
 RowBox[{"P", ":=", 
  FractionBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}]], "Input",
 CellChangeTimes->{{3.847604635403722*^9, 3.8476046464186983`*^9}},
 CellLabel->"In[2]:=",ExpressionUUID->"3938cf76-493c-4425-9388-2b0794db9dd6"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{
       RowBox[{
        RowBox[{"-", "2"}], " ", "e", " ", "k"}], "+", "\[Theta]"}], 
      RowBox[{
       RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "-", 
     FractionBox[
      RowBox[{"f", "-", 
       RowBox[{"f", " ", "\[Alpha]"}], "-", 
       RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
       RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
      RowBox[{"2", " ", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]}], "\[Equal]",
     "0"}], ",", "e"}], "]"}]], "Input",
 CellChangeTimes->{{3.8476045584794397`*^9, 3.847604573026394*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"1a058b2b-3b4c-4729-b7a5-5cd2f79c0b30"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"e", "\[Rule]", 
    FractionBox[
     RowBox[{
      RowBox[{"-", "f"}], "+", 
      RowBox[{"f", " ", "\[Alpha]"}], "+", 
      RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
      RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
     RowBox[{"4", " ", "k", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}]]}], "}"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.847604684562624*^9},
 CellLabel->"Out[3]=",ExpressionUUID->"6c7a4366-3935-45ff-9c95-ece08ef3f178"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"e0", ":=", 
  RowBox[{
   FractionBox[
    RowBox[{
     RowBox[{"-", "f"}], "+", 
     RowBox[{"f", " ", "\[Alpha]"}], "+", 
     RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
     RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
    RowBox[{"4", " ", "k", " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}]], "-", 
   RowBox[{"(", 
    RowBox[{
     FractionBox["\[Alpha]", 
      RowBox[{
       RowBox[{"-", "1"}], "+", "\[Alpha]"}]], "+", 
     FractionBox[
      SqrtBox[
       RowBox[{"k", " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"cv", " ", 
           SuperscriptBox[
            RowBox[{"(", 
             RowBox[{
              RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", 
          RowBox[{"k", " ", 
           SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", 
          RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]], 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"1", "-", "\[Alpha]"}], ")"}], "k"}]]}], ")"}]}]}]], "Input",
 CellChangeTimes->{{3.847604812810193*^9, 3.84760490251401*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"c754a26c-d75f-4b90-a77e-35b9284746bc"],

Cell[CellGroupData[{

Cell[BoxData["e0"], "Input",
 CellChangeTimes->{{3.847604867246388*^9, 3.847604867487176*^9}},
 CellLabel->"In[9]:=",ExpressionUUID->"8a56e3b9-76a2-4e61-8890-07237ad33df4"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", 
   FractionBox["\[Alpha]", 
    RowBox[{
     RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}], "-", 
  FractionBox[
   SqrtBox[
    RowBox[{"k", " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"cv", " ", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", 
       RowBox[{"k", " ", 
        SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", 
       RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]], 
   RowBox[{"k", " ", 
    RowBox[{"(", 
     RowBox[{"1", "-", "\[Alpha]"}], ")"}]}]], "+", 
  FractionBox[
   RowBox[{
    RowBox[{"-", "f"}], "+", 
    RowBox[{"f", " ", "\[Alpha]"}], "+", 
    RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
    RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
   RowBox[{"4", " ", "k", " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}]]}]], "Output",
 CellChangeTimes->{3.847604868474559*^9, 3.847604909236305*^9},
 CellLabel->"Out[9]=",ExpressionUUID->"288e88c2-4671-478f-afe3-a974351cc573"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Simplify", "[", 
  RowBox[{
   RowBox[{"-", 
    FractionBox["\[Alpha]", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}], "-", 
   FractionBox[
    SqrtBox[
     RowBox[{"k", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"cv", " ", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", 
        RowBox[{"k", " ", 
         SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", 
        RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]], 
    RowBox[{"k", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "\[Alpha]"}], ")"}]}]], "+", 
   FractionBox[
    RowBox[{
     RowBox[{"-", "f"}], "+", 
     RowBox[{"f", " ", "\[Alpha]"}], "+", 
     RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
     RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], 
    RowBox[{"4", " ", "k", " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}]}]]}], "]"}]], "Input",
 NumberMarks->False,
 CellLabel->"In[10]:=",ExpressionUUID->"f1a1700f-0f1c-450d-919f-31ff178803f3"],

Cell[BoxData[
 FractionBox[
  RowBox[{"f", "-", 
   RowBox[{"f", " ", "\[Alpha]"}], "+", 
   RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-", 
   RowBox[{"\[Alpha]", " ", "\[Theta]"}], "-", 
   RowBox[{"4", " ", 
    SqrtBox[
     RowBox[{"k", " ", 
      RowBox[{"(", 
       RowBox[{"cv", "-", 
        RowBox[{"2", " ", "cv", " ", "\[Alpha]"}], "+", 
        RowBox[{"cv", " ", 
         SuperscriptBox["\[Alpha]", "2"]}], "+", 
        RowBox[{"k", " ", 
         SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", 
        RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}]}], 
  RowBox[{
   RowBox[{"4", " ", "k"}], "-", 
   RowBox[{"4", " ", "k", " ", "\[Alpha]"}]}]]], "Output",
 CellChangeTimes->{3.847604916113783*^9},
 CellLabel->"Out[10]=",ExpressionUUID->"2c51541e-3d24-4c57-882d-f95530d6f84c"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", 
  
  RowBox[{
   RowBox[{"\[Alpha]", ":=", "0.2"}], "\[IndentingNewLine]", 
   RowBox[{"k", ":=", "100"}], "\[IndentingNewLine]", 
   RowBox[{"\[Theta]", ":=", "50"}], "\[IndentingNewLine]", 
   RowBox[{"cs", ":=", "50"}]}]}]], "Input",
 CellChangeTimes->{{3.847606019148917*^9, 3.84760604484729*^9}, {
  3.847606277872908*^9, 3.847606278866959*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"662f2e8f-60ec-4662-a87f-597ac9747634"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"f", "-", 
     RowBox[{"f", " ", "\[Alpha]"}], "+", 
     RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-", 
     RowBox[{"\[Alpha]", " ", "\[Theta]"}], "-", 
     RowBox[{"4", " ", 
      SqrtBox[
       RowBox[{"k", " ", 
        RowBox[{"(", 
         RowBox[{"cv", "-", 
          RowBox[{"2", " ", "cv", " ", "\[Alpha]"}], "+", 
          RowBox[{"cv", " ", 
           SuperscriptBox["\[Alpha]", "2"]}], "+", 
          RowBox[{"k", " ", 
           SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", 
          RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}]}], "\[Equal]", 
    "0"}], ",", "f"}], "]"}]], "Input",
 CellChangeTimes->{{3.847606051723064*^9, 3.847606072291988*^9}, {
  3.847606106422761*^9, 3.847606107561355*^9}, {3.8476062132159767`*^9, 
  3.8476062137852507`*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"045a09c8-371d-4bd3-9c1a-2d5cf4f65f2e"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"f", "\[Rule]", 
    FractionBox[
     RowBox[{
      RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-", 
      RowBox[{"\[Alpha]", " ", "\[Theta]"}], "-", 
      RowBox[{"4", " ", 
       SqrtBox[
        RowBox[{"k", " ", 
         RowBox[{"(", 
          RowBox[{"cv", "-", 
           RowBox[{"2", " ", "cv", " ", "\[Alpha]"}], "+", 
           RowBox[{"cv", " ", 
            SuperscriptBox["\[Alpha]", "2"]}], "+", 
           RowBox[{"k", " ", 
            SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", 
           RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}]}], 
     RowBox[{
      RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}], "}"}], "}"}]], "Output",
 CellChangeTimes->{3.84760616440495*^9, 3.847606215419405*^9},
 CellLabel->"Out[4]=",ExpressionUUID->"f5ca4652-1558-446d-a1c5-2319ac77a812"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"f", ":=", 
  FractionBox[
   RowBox[{
    RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-", 
    RowBox[{"\[Alpha]", " ", "\[Theta]"}], "-", 
    RowBox[{"4", " ", 
     SqrtBox[
      RowBox[{"k", " ", 
       RowBox[{"(", 
        RowBox[{"cv", "-", 
         RowBox[{"2", " ", "cv", " ", "\[Alpha]"}], "+", 
         RowBox[{"cv", " ", 
          SuperscriptBox["\[Alpha]", "2"]}], "+", 
         RowBox[{"k", " ", 
          SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", 
         RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}]}], 
   RowBox[{
    RowBox[{"-", "1"}], "+", "\[Alpha]"}]]}]], "Input",
 CellChangeTimes->{{3.847606253948923*^9, 3.847606263613615*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"9c2f93b4-741c-43e1-9a6d-3d080e8c3107"],

Cell[CellGroupData[{

Cell[BoxData["f"], "Input",
 CellChangeTimes->{3.847606302054188*^9},
 CellLabel->"In[6]:=",ExpressionUUID->"81634571-9073-4129-8783-224b57489b79"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "1.25`"}], " ", 
  RowBox[{"(", 
   RowBox[{"80.`", "\[VeryThinSpace]", "-", 
    RowBox[{"40", " ", 
     SqrtBox[
      RowBox[{"44.`", "\[VeryThinSpace]", "+", 
       RowBox[{"0.64`", " ", "cv"}]}]]}]}], ")"}]}]], "Output",
 CellChangeTimes->{3.847606302524468*^9},
 CellLabel->"Out[6]=",ExpressionUUID->"db55d115-8d92-4419-b065-4483b53bb980"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"f1", ":=", 
  RowBox[{
   RowBox[{"2", "k"}], "-", "\[Theta]"}]}]], "Input",
 CellChangeTimes->{{3.847606384367157*^9, 3.847606392948236*^9}, {
  3.8476068108740597`*^9, 3.847606811805193*^9}},
 CellLabel->"In[28]:=",ExpressionUUID->"e6155ea7-1b35-4079-b81c-d6067a9d42ef"],

Cell[CellGroupData[{

Cell[BoxData["f1"], "Input",
 CellChangeTimes->{{3.8476063955394573`*^9, 3.847606396159827*^9}},
 CellLabel->"In[9]:=",ExpressionUUID->"629c6967-cb15-470d-bd0b-00653f49ced1"],

Cell[BoxData["250"], "Output",
 CellChangeTimes->{3.847606396659258*^9},
 CellLabel->"Out[9]=",ExpressionUUID->"18090fec-0319-4d9a-a54c-96cdcfe9eba6"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"f2", ":=", 
  RowBox[{
   SqrtBox[
    RowBox[{
     RowBox[{"(", 
      RowBox[{"cs", "+", "cv", "+", "\[Theta]"}], ")"}], " ", "4", " ", "k", 
     " "}]], "-", "\[Theta]"}]}]], "Input",
 CellChangeTimes->{{3.8476065839893007`*^9, 3.847606637577847*^9}},
 CellLabel->"In[19]:=",ExpressionUUID->"00049345-f656-49d2-ad9c-d8dbb6d8f688"],

Cell[CellGroupData[{

Cell[BoxData["f2"], "Input",
 CellChangeTimes->{{3.847606644940626*^9, 3.847606645353243*^9}},
 CellLabel->"In[20]:=",ExpressionUUID->"b003375b-a6d6-42c8-a0f1-07a7934834a1"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", "50"}], "+", 
  RowBox[{"20", " ", 
   SqrtBox[
    RowBox[{"100", "+", "cv"}]]}]}]], "Output",
 CellChangeTimes->{3.847606645883613*^9},
 CellLabel->"Out[20]=",ExpressionUUID->"0c8b994c-24a9-4a5c-bd8c-313bc17746ac"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"pf2", "=", 
  RowBox[{"Plot", "[", 
   RowBox[{"f2", ",", 
    RowBox[{"{", 
     RowBox[{"cv", ",", "0", ",", "20"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.847606649107987*^9, 3.8476066681264353`*^9}, {
  3.8476068623526154`*^9, 3.847606863488332*^9}, {3.84760697410527*^9, 
  3.847606974699642*^9}},
 CellLabel->"In[47]:=",ExpressionUUID->"390cf48e-349d-4315-b071-c0535e85b742"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVz3s0lAkABfCZ9FrGxhY9jRlkGI+Mr7bHxtxCKaNSTZ3Y2nwP0yYVm04x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       "]]},
     Annotation[#, "Charting`Private`Tag$20802#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 150.00000040816326`},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 20}, {150.00000040816326`, 169.0890226294661}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.847606669156096*^9, 3.847606731769198*^9, 
  3.847606864320108*^9, 3.8476069759179153`*^9},
 CellLabel->"Out[47]=",ExpressionUUID->"2cf00f64-0b61-4d63-b9a8-d0fc136237c4"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"pf1", "=", 
  RowBox[{"Plot", "[", 
   RowBox[{"f1", ",", 
    RowBox[{"{", 
     RowBox[{"cv", ",", "0", ",", "20"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.8476064049739*^9, 3.847606421725366*^9}, {
  3.8476064523390207`*^9, 3.847606483087853*^9}, {3.8476068500694523`*^9, 
  3.847606850934148*^9}, {3.84760691606288*^9, 3.8476069174274883`*^9}, {
  3.84760696339968*^9, 3.847606964465641*^9}},
 CellLabel->"In[45]:=",ExpressionUUID->"e1b88fe5-1f02-44e3-9fe7-46c7cb33faab"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQPbcuic0wZbYdAwgcSHJgv/1I/a38SXsYf+Gp+YWv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       "]]},
     Annotation[#, "Charting`Private`Tag$20115#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 20}, {0., 300.}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.847606412556312*^9, 3.847606422357991*^9}, {
   3.847606456055697*^9, 3.847606483578271*^9}, {3.8476068285018587`*^9, 
   3.847606851520982*^9}, 3.847606918563877*^9, 3.84760696580855*^9},
 CellLabel->"Out[45]=",ExpressionUUID->"d7f9da29-9bc1-46b4-b277-bb4149d474e6"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"pf", ":=", 
  RowBox[{"Plot", "[", 
   RowBox[{"f", ",", 
    RowBox[{"{", 
     RowBox[{"cv", ",", "0", ",", "10"}], "}"}]}], 
   "]"}]}], "\[IndentingNewLine]", "pf"}], "Input",
 CellChangeTimes->{{3.847606304835474*^9, 3.847606318316121*^9}, 
   3.847606374653926*^9, {3.847606466308454*^9, 3.847606480767476*^9}, {
   3.847606746751668*^9, 3.84760676267729*^9}, {3.8476068406003523`*^9, 
   3.847606843893456*^9}, {3.847606887312654*^9, 3.847606913696916*^9}, {
   3.8476069452901793`*^9, 3.8476069581235657`*^9}, {3.847607005163208*^9, 
   3.847607006008772*^9}},
 CellLabel->"In[51]:=",ExpressionUUID->"37dc5fc0-56ae-4d63-8d29-0c7cf2d5383f"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVzns0VAkcB3BCa/M4KeuZMeN6NabnnhzZcr8Z2laqjaTGkUyFrbn3xuZo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       "]]},
     Annotation[#, "Charting`Private`Tag$21851#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 231.66247952780338`},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 10}, {231.66247952780338`, 254.96478652602912`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.847606763105978*^9, 3.847606845400547*^9, {3.847606888388516*^9, 
   3.847606907896838*^9}, {3.847606949028451*^9, 3.847606959389319*^9}, {
   3.847606997795546*^9, 3.847607007293334*^9}},
 CellLabel->"Out[52]=",ExpressionUUID->"fa9cadb6-24f7-43f3-80b9-6042470850f1"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{"pf", ",", "pf1", ",", "pf2"}], "]"}]], "Input",
 CellChangeTimes->{{3.8476064303861227`*^9, 3.8476064758521547`*^9}, {
  3.847606675857497*^9, 3.8476066784105473`*^9}},
 CellLabel->"In[53]:=",ExpressionUUID->"bcbbb46a-f252-4780-9c47-064ffa9966af"],

Cell[BoxData[
 GraphicsBox[{{{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJwVzns0VAkcB3BCa/M4KeuZMeN6NabnnhzZcr8Z2laqjaTGkUyFrbn3xuZo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        "]]},
      Annotation[#, "Charting`Private`Tag$22213#1"]& ]}, {}}, {{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQPbcuic0wZbYdAwgcSHJgv/1I/a38SXsYf+Gp+YWv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        "]]},
      Annotation[#, "Charting`Private`Tag$20115#1"]& ]}, {}}, {{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJwVz3s0lAkABfCZ9FrGxhY9jRlkGI+Mr7bHxtxCKaNSTZ3Y2nwP0yYVm04x
u1kltNEkK4/mOAirDtKOdqlFFNUwPUgP0y5JSXLKrJgo++0f99zzO/evKyT3
bWQmcDicQDb/t/oncrKEzvFOEnZwOHUkbrQKZFsFh6XD1kp4sh5vrDkqECRL
27788wjNWl2XYjtJkCVlpnE/3WK9xys6Yti2RLo749Hg6eskWkd3pb+zrZL6
3cvU2jeQmNLxXPTW9ra0UKWUrG4kkXcnN/KN7RPpvc7AuyebSZSVJ3fsce+T
Oi1Iuyl4SkIhvZ/VH2WQhniJbja9JLG3x7lbU2aUDv9da+FsIGEqPCb6ZwkH
1ScS+SoOhVQLrThvpwkGyMdaM3MKZMfmWpPmybh/ycnq5BwKkTePkftEpuCf
cgppFFGo2M/bNGuNOXjSpMfWCynkxYb3eWy1gH9tWeruFRTic8eC/u23RFW/
T+DDQAqc1k5ci5kOulV7YXQbBccDYYc2i62g6JrUb6+g8GLo7Bazv6wxw9B5
hf6Bwtqe3T+mRc7CGfkLWVEchXUvVC58/hwMXx1dWJBCoa+BjLtVOheapmrn
6iwK7pbtNj7f2UA583jGvSIKptKhUL2BD17jxnbu7xRWvw0etpML8GbxEqWk
jsLjepob7CrE2eFrbjYtFCqTbuwQDAnxdeBll/lPKIRNiu7U6exQnBrnK35J
gYqKreRl20MdToTLBiksULjoZKEOCJKlClw/U7j7latZ9NL50FYevDzFjMbV
svgcVxNHSCoC/uDOpBHLFW9ofuaIw+tfp32wp2Gqj/HfqxHBgpin+c2DRk+R
MD1X6YRm5arymOU00p1mT6ySO2ORKe27ag0NVXZYU6hADGHJwXBPOY3g9O06
3isxavWL/Z/tpDHiW2jMrXHBwLYdqXERNLp7Vh6qT3RF8LffV/sdppHvJZnb
EuqGksIw+YTjNEoToi0Vbu5YrbY60XWaRqKcCjAZcgczY9X0ODWNRfq8ksSW
BaDdg7pmXKCR6ZxT2hLgAbOj5K8tlTSO1KVkBlR5wDrJNSu2nkbgXHnhHQcJ
5Krei706Giv2NoVYJktQbm5niHlKI3ce6dA8xO7np4ZyX9FwaCjOWBfiiRob
XVnpIPvPrV78oMYTo30kOeczjTDDxPu3xQTaHQb4MaYMyIpBQfIpAlqriBGO
NYM98ZvG1p4mUOGVwCxkHb1J84h3hsCn4uUPFKyThqJTVRkENsiSL+hYly01
jp5VE0iblr3l3EwGxuvj7UUXCbRuzzm3eDYD1QNeyo0mAuvHXToj5jHILojY
dfw2gWXpHivyWBcc0Pn4awnkl7fltbG+Yq36qNURUMSPhn5jw0AfPH1X60MC
ktaGZ1P5DETds32edxPQj6GhwJaBhyaGf76HgPOIN/8R62UJHUbmFYGuHP0h
UwEDmUh96XUfgS96PrhGso4KF/DfvydwrKpY5S1koFz+s/GygcB+oqA3knWC
+fO2A0MEKsO8Ucg6s7zgl5ERAg3czQNmdgzy4yYqqj8SaIzQ+UpZXwxiVirH
CGTn9GZHsdbYNdp4fyYQnJL/rpB1jcHROD5OYL7fmN8T1v8BYlElMQ==
        "]]},
      Annotation[#, "Charting`Private`Tag$20802#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 231.66247952780338`},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 10}, {231.66247952780338`, 254.96478652602912`}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.847606476701015*^9, 3.847606487901453*^9}, 
   3.8476066788953238`*^9, 3.847606832565096*^9, 3.847606878126081*^9, 
   3.8476069709854097`*^9, {3.8476070020993443`*^9, 3.8476070125928907`*^9}},
 CellLabel->"Out[53]=",ExpressionUUID->"20073024-2146-44ae-8450-c3fca429aea2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"y", ":=", 
  RowBox[{
   FractionBox[
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", 
      RowBox[{"(", 
       RowBox[{"f", "-", "\[Theta]"}], ")"}]}], "-", 
     RowBox[{"2", "\[Alpha]", " ", "k"}]}], 
    RowBox[{"2", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"]}]], "-", 
   FractionBox[
    RowBox[{
     RowBox[{
      RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
     RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", 
     RowBox[{"2", " ", 
      SqrtBox[
       RowBox[{
        RowBox[{"cv", " ", "k"}], "-", 
        RowBox[{"2", " ", "cv", " ", "k", " ", "\[Alpha]"}], "+", 
        RowBox[{"cv", " ", "k", " ", 
         SuperscriptBox["\[Alpha]", "2"]}], "+", 
        RowBox[{
         SuperscriptBox["k", "2"], " ", 
         SuperscriptBox["\[Alpha]", "2"]}], "+", 
        RowBox[{"k", " ", "\[Theta]"}], "-", 
        RowBox[{"k", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], 
    RowBox[{"1", "-", 
     RowBox[{"2", " ", "\[Alpha]"}], "+", 
     SuperscriptBox["\[Alpha]", "2"]}]]}]}]], "Input",
 CellChangeTimes->{{3.8476075863587513`*^9, 3.847607601228586*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"e969b9d4-3c33-4dcf-a7ab-667cbf551e12"],

Cell[BoxData[
 FractionBox[
  RowBox[{"f", "-", 
   RowBox[{"f", " ", "\[Alpha]"}], "+", 
   RowBox[{"2", " ", "k", " ", "\[Alpha]"}], "+", "\[Theta]", "-", 
   RowBox[{"\[Alpha]", " ", "\[Theta]"}], "-", 
   RowBox[{"4", " ", 
    SqrtBox[
     RowBox[{"k", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"cv", " ", 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{
            RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}], "+", 
        RowBox[{"k", " ", 
         SuperscriptBox["\[Alpha]", "2"]}], "+", "\[Theta]", "-", 
        RowBox[{"\[Alpha]", " ", "\[Theta]"}]}], ")"}]}]]}]}], 
  RowBox[{"2", " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]]], "Output",
 CellChangeTimes->{3.847608558547645*^9},
 CellLabel->"Out[13]=",ExpressionUUID->"31d609dd-650d-419c-95a3-1696c22504e1"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     FractionBox[
      RowBox[{
       RowBox[{
        RowBox[{"(", 
         RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", 
        RowBox[{"(", 
         RowBox[{"f", "-", "\[Theta]"}], ")"}]}], "-", 
       RowBox[{"2", "\[Alpha]", " ", "k"}]}], 
      RowBox[{"2", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"]}]], "-", 
     FractionBox[
      RowBox[{
       RowBox[{
        RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
       RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", 
       RowBox[{"2", " ", 
        SqrtBox[
         RowBox[{
          RowBox[{"cv", " ", "k"}], "-", 
          RowBox[{"2", " ", "cv", " ", "k", " ", "\[Alpha]"}], "+", 
          RowBox[{"cv", " ", "k", " ", 
           SuperscriptBox["\[Alpha]", "2"]}], "+", 
          RowBox[{
           SuperscriptBox["k", "2"], " ", 
           SuperscriptBox["\[Alpha]", "2"]}], "+", 
          RowBox[{"k", " ", "\[Theta]"}], "-", 
          RowBox[{"k", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], 
      RowBox[{"1", "-", 
       RowBox[{"2", " ", "\[Alpha]"}], "+", 
       SuperscriptBox["\[Alpha]", "2"]}]]}], "\[Equal]", "0"}], ",", "f"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.847607570933091*^9, 3.847607572051099*^9}, {
  3.8476084933997583`*^9, 3.847608530633265*^9}, {3.847608598925848*^9, 
  3.847608599497033*^9}},
 CellLabel->"In[15]:=",ExpressionUUID->"e4e7ffb2-009e-4f1e-9ffc-7147bb71509b"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"f", "\[Rule]", 
    RowBox[{"2", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", 
     RowBox[{"(", 
      RowBox[{
       FractionBox[
        RowBox[{"k", " ", "\[Alpha]"}], 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"]], "+", 
       FractionBox["\[Theta]", 
        RowBox[{"2", " ", 
         RowBox[{"(", 
          RowBox[{"1", "-", "\[Alpha]"}], ")"}]}]], "+", 
       FractionBox[
        RowBox[{
         RowBox[{
          RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", 
         "+", 
         RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", 
         RowBox[{"2", " ", 
          SqrtBox[
           RowBox[{
            RowBox[{"cv", " ", "k"}], "-", 
            RowBox[{"2", " ", "cv", " ", "k", " ", "\[Alpha]"}], "+", 
            RowBox[{"cv", " ", "k", " ", 
             SuperscriptBox["\[Alpha]", "2"]}], "+", 
            RowBox[{
             SuperscriptBox["k", "2"], " ", 
             SuperscriptBox["\[Alpha]", "2"]}], "+", 
            RowBox[{"k", " ", "\[Theta]"}], "-", 
            RowBox[{"k", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], 
        RowBox[{"1", "-", 
         RowBox[{"2", " ", "\[Alpha]"}], "+", 
         SuperscriptBox["\[Alpha]", "2"]}]]}], ")"}]}]}], "}"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.847608624312448*^9},
 CellLabel->"Out[15]=",ExpressionUUID->"ab959443-c997-47be-911b-76157078be3a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"y", "\[Equal]", "0"}], ",", "cv"}], "]"}]], "Input",
 CellChangeTimes->{{3.847608629839703*^9, 3.8476086445974293`*^9}},
 CellLabel->"In[16]:=",ExpressionUUID->"4d3e751a-a2f6-46bf-83a0-f8f0959488a9"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"cv", "\[Rule]", 
    RowBox[{
     FractionBox["1", 
      RowBox[{"16", " ", "k", " ", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", "\[Alpha]"}], ")"}], "2"]}]], 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox["f", "2"], "-", 
       RowBox[{"2", " ", 
        SuperscriptBox["f", "2"], " ", "\[Alpha]"}], "+", 
       RowBox[{"4", " ", "f", " ", "k", " ", "\[Alpha]"}], "+", 
       RowBox[{
        SuperscriptBox["f", "2"], " ", 
        SuperscriptBox["\[Alpha]", "2"]}], "-", 
       RowBox[{"4", " ", "f", " ", "k", " ", 
        SuperscriptBox["\[Alpha]", "2"]}], "-", 
       RowBox[{"12", " ", 
        SuperscriptBox["k", "2"], " ", 
        SuperscriptBox["\[Alpha]", "2"]}], "+", 
       RowBox[{"2", " ", "f", " ", "\[Theta]"}], "-", 
       RowBox[{"16", " ", "k", " ", "\[Theta]"}], "-", 
       RowBox[{"4", " ", "f", " ", "\[Alpha]", " ", "\[Theta]"}], "+", 
       RowBox[{"20", " ", "k", " ", "\[Alpha]", " ", "\[Theta]"}], "+", 
       RowBox[{"2", " ", "f", " ", 
        SuperscriptBox["\[Alpha]", "2"], " ", "\[Theta]"}], "-", 
       RowBox[{"4", " ", "k", " ", 
        SuperscriptBox["\[Alpha]", "2"], " ", "\[Theta]"}], "+", 
       SuperscriptBox["\[Theta]", "2"], "-", 
       RowBox[{"2", " ", "\[Alpha]", " ", 
        SuperscriptBox["\[Theta]", "2"]}], "+", 
       RowBox[{
        SuperscriptBox["\[Alpha]", "2"], " ", 
        SuperscriptBox["\[Theta]", "2"]}]}], ")"}]}]}], "}"}], 
  "}"}]], "Output",
 CellChangeTimes->{3.847608645098927*^9},
 CellLabel->"Out[16]=",ExpressionUUID->"b6521819-38ba-4db4-b6e1-16f134609741"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{"y", "\[Equal]", "0"}], ","}], "]"}]], "Input",
 CellChangeTimes->{{3.8476086539228153`*^9, 
  3.8476086610664062`*^9}},ExpressionUUID->"579adbd0-2663-4e15-8f6d-\
fc09ce3e3479"],

Cell[BoxData[{
 RowBox[{"\[Alpha]", ":=", "0.2"}], "\[IndentingNewLine]", 
 RowBox[{"k", ":=", "100"}], "\[IndentingNewLine]", 
 RowBox[{"\[Theta]", ":=", "50"}], "\[IndentingNewLine]", 
 RowBox[{"cv", ":=", "50"}], "\[IndentingNewLine]", 
 RowBox[{"f", ":=", 
  RowBox[{"2", " ", 
   RowBox[{"(", 
    RowBox[{"1", "-", "\[Alpha]"}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{
     FractionBox[
      RowBox[{"k", " ", "\[Alpha]"}], 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"1", "-", "\[Alpha]"}], ")"}], "2"]], "+", 
     FractionBox["\[Theta]", 
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{"1", "-", "\[Alpha]"}], ")"}]}]], "+", 
     FractionBox[
      RowBox[{
       RowBox[{
        RowBox[{"-", "2"}], " ", "k", " ", "\[Alpha]"}], "-", "\[Theta]", "+", 
       RowBox[{"\[Alpha]", " ", "\[Theta]"}], "+", 
       RowBox[{"2", " ", 
        SqrtBox[
         RowBox[{
          RowBox[{"cv", " ", "k"}], "-", 
          RowBox[{"2", " ", "cv", " ", "k", " ", "\[Alpha]"}], "+", 
          RowBox[{"cv", " ", "k", " ", 
           SuperscriptBox["\[Alpha]", "2"]}], "+", 
          RowBox[{
           SuperscriptBox["k", "2"], " ", 
           SuperscriptBox["\[Alpha]", "2"]}], "+", 
          RowBox[{"k", " ", "\[Theta]"}], "-", 
          RowBox[{"k", " ", "\[Alpha]", " ", "\[Theta]"}]}]]}]}], 
      RowBox[{"1", "-", 
       RowBox[{"2", " ", "\[Alpha]"}], "+", 
       SuperscriptBox["\[Alpha]", "2"]}]]}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{"f1", ":=", 
  RowBox[{
   RowBox[{"2", "k"}], "-", "\[Theta]"}]}], "\[IndentingNewLine]", 
 RowBox[{"f2", ":=", 
  RowBox[{
   SqrtBox[
    RowBox[{
     RowBox[{"(", 
      RowBox[{"cs", "+", "cv", "+", "\[Theta]"}], ")"}], " ", "4", " ", "k", 
     " "}]], "-", "\[Theta]"}]}]}], "Input",
 CellChangeTimes->{{3.847607806022832*^9, 3.847607833499133*^9}, {
  3.847607894917801*^9, 3.847607895892552*^9}, {3.847607967470442*^9, 
  3.847607987414369*^9}},
 CellLabel->"In[9]:=",ExpressionUUID->"3040f7c1-3349-4b04-808f-c3d8d443e40a"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"pf2", "=", 
  RowBox[{"Plot", "[", 
   RowBox[{"f2", ",", 
    RowBox[{"{", 
     RowBox[{"cs", ",", "0", ",", "10"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.84760806035435*^9, 3.847608079506772*^9}, {
  3.8476081251927347`*^9, 3.8476081271748943`*^9}, {3.847608264697488*^9, 
  3.8476082649617453`*^9}},
 CellLabel->"In[27]:=",ExpressionUUID->"07322907-a209-446b-878e-736999fb0b62"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwV0HtUjHkYB/DaqFTS5FaqufTGMCpmt86RLe+3cKLbCnG2aM37oygTtc0e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       "]]},
     Annotation[#, "Charting`Private`Tag$7773#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 150.00000020408163`},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 10}, {150.00000020408163`, 159.7617694394461}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.847608076477433*^9, 3.8476080802213182`*^9}, 
   3.847608137947172*^9, 3.8476081791479692`*^9, 3.8476082657063913`*^9},
 CellLabel->"Out[27]=",ExpressionUUID->"c7b6bf13-786f-465f-8517-6a18da48cce3"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"pf", "=", 
  RowBox[{"Plot", "[", 
   RowBox[{"f", ",", 
    RowBox[{"{", 
     RowBox[{"cs", ",", "0", ",", "10"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.8476077732805758`*^9, 3.8476078035289087`*^9}, 
   3.8476078484115868`*^9, {3.847607901178157*^9, 3.847607901964849*^9}, {
   3.8476079957839527`*^9, 3.847608015717847*^9}, {3.8476080881520367`*^9, 
   3.847608130131754*^9}, {3.847608248440366*^9, 3.847608261742921*^9}},
 CellLabel->"In[26]:=",ExpressionUUID->"3ea524a5-f0f7-4ba6-9bfb-466bf4b7b0e3"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQPbcuic0wpdvu6s47jLb/ShzYbz9Sfyu/0x7GX3hq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       "]]},
     Annotation[#, "Charting`Private`Tag$7428#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 10}, {0., 671.7797887081348}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.847608103492725*^9, 3.847608140632065*^9, {3.84760825002524*^9, 
   3.847608262553891*^9}},
 CellLabel->"Out[26]=",ExpressionUUID->"6b82efa9-7a11-4c65-8307-37904e495181"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"pf1", "=", 
  RowBox[{"Plot", "[", 
   RowBox[{"f1", ",", 
    RowBox[{"{", 
     RowBox[{"cs", ",", "0", ",", "10"}], "}"}]}], "]"}]}]], "Input",
 CellChangeTimes->{{3.847608109213254*^9, 3.847608134602676*^9}},
 CellLabel->"In[22]:=",ExpressionUUID->"ac341192-0059-4adb-beb8-fa58d11d590e"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQPbcuic0wpduOAQQOJDmw336k/lZ+pz2Mv/DU/MLX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       "]]},
     Annotation[#, "Charting`Private`Tag$6087#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 10}, {0., 300.}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.847608114888988*^9, 3.847608142411322*^9}},
 CellLabel->"Out[22]=",ExpressionUUID->"51e7cf77-2879-4c89-b5a0-3c21aad124fa"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{"pf", ",", "pf1", ",", "pf2"}], "]"}]], "Input",
 CellChangeTimes->{{3.847608145053472*^9, 3.847608152126088*^9}},
 CellLabel->"In[28]:=",ExpressionUUID->"cb9cd8aa-9906-49da-9e25-1eaa71ed40c4"],

Cell[BoxData[
 GraphicsBox[{{{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQPbcuic0wpdvu6s47jLb/ShzYbz9Sfyu/0x7GX3hq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        "]]},
      Annotation[#, "Charting`Private`Tag$7428#1"]& ]}, {}}, {{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJxTTMoPSmViYGAwAWIQPbcuic0wpduOAQQOJDmw336k/lZ+pz2Mv/DU/MLX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        "]]},
      Annotation[#, "Charting`Private`Tag$6087#1"]& ]}, {}}, {{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJwV0HtUjHkYB/DaqFTS5FaqufTGMCpmt86RLe+3cKLbCnG2aM37oygTtc0e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        "]]},
      Annotation[#, "Charting`Private`Tag$7773#1"]& ]}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 10}, {0., 671.7797887081348}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.847608152631983*^9, 3.847608276124222*^9},
 CellLabel->"Out[28]=",ExpressionUUID->"fe937dca-5aa7-4ca0-a589-820ac4b7d90d"]
}, Open  ]]
},
WindowSize->{808, 730},
WindowMargins->{{Automatic, 286}, {Automatic, 39}},
TaggingRules->{"TryRealOnly" -> False},
FrontEndVersion->"12.1 for Mac OS X x86 (64-bit) \
(2020\:5e743\:670813\:65e5)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"7d12b579-08bb-480d-aa58-1aa86e0c628c"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 691, 23, 30, "Input",ExpressionUUID->"4bc1b551-f5c4-4026-98ec-c0ea28b5587c"],
Cell[1252, 45, 558, 15, 89, "Input",ExpressionUUID->"112e234b-d795-415a-ad63-71162225d88b"],
Cell[CellGroupData[{
Cell[1835, 64, 227, 4, 44, "Input",ExpressionUUID->"e5001feb-e8fa-40dc-9845-7839276c7d77"],
Cell[2065, 70, 2565, 84, 100, "Output",ExpressionUUID->"d53ef495-d42b-4cfb-9352-7816854756a9"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4667, 159, 161, 3, 44, "Input",ExpressionUUID->"b93144d3-c913-472e-b3a0-e8c50bb0366f"],
Cell[4831, 164, 584, 16, 52, "Output",ExpressionUUID->"3e225b47-2ba8-40c2-8384-80380e2c0ba6"]
}, Open  ]],
Cell[CellGroupData[{
Cell[5452, 185, 257, 5, 44, "Input",ExpressionUUID->"aa70c68c-3dd7-49dd-a104-1ef2638958ee"],
Cell[5712, 192, 576, 16, 53, "Output",ExpressionUUID->"88aa45be-d922-4baf-ba19-16989cad3c2a"]
}, Open  ]],
Cell[6303, 211, 234, 5, 94, "Input",ExpressionUUID->"1f09d665-f21b-4bef-941e-f291a1847703"],
Cell[6540, 218, 691, 23, 30, "Input",ExpressionUUID->"1bb31936-0e42-4d2f-90f4-2da2dbccfeac"],
Cell[7234, 243, 312, 7, 46, "Input",ExpressionUUID->"1ee666dd-6587-4bd8-bd76-8498aab9db11"],
Cell[7549, 252, 341, 8, 46, "Input",ExpressionUUID->"01adb8cc-2282-47df-9fd8-1e53ad00b87a"],
Cell[CellGroupData[{
Cell[7915, 264, 177, 2, 30, "Input",ExpressionUUID->"fde5fabc-a7d1-48d8-afc2-299ba4b89028"],
Cell[8095, 268, 542, 16, 51, "Output",ExpressionUUID->"80975313-3810-453e-b0a8-809870d79677"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8674, 289, 223, 4, 44, "Input",ExpressionUUID->"83dc9ced-6793-4d8c-ab09-97f1c6407ec2"],
Cell[8900, 295, 706, 22, 51, "Output",ExpressionUUID->"e3919eef-d5b9-4f25-baec-fe6210199691"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9643, 322, 256, 5, 44, "Input",ExpressionUUID->"07885560-5ebc-4563-81a6-578e8b75a2f9"],
Cell[9902, 329, 574, 16, 55, "Output",ExpressionUUID->"93682421-b443-44cf-97a2-77de6357b847"]
}, Open  ]],
Cell[10491, 348, 522, 13, 52, "Input",ExpressionUUID->"79fa97b5-b003-4bb9-83a8-541f1e2dd78c"],
Cell[11016, 363, 355, 9, 49, "Input",ExpressionUUID->"3938cf76-493c-4425-9388-2b0794db9dd6"],
Cell[CellGroupData[{
Cell[11396, 376, 823, 23, 65, "Input",ExpressionUUID->"1a058b2b-3b4c-4729-b7a5-5cd2f79c0b30"],
Cell[12222, 401, 575, 16, 53, "Output",ExpressionUUID->"6c7a4366-3935-45ff-9c95-ece08ef3f178"]
}, Open  ]],
Cell[12812, 420, 1218, 35, 69, "Input",ExpressionUUID->"c754a26c-d75f-4b90-a77e-35b9284746bc"],
Cell[CellGroupData[{
Cell[14055, 459, 172, 2, 30, "Input",ExpressionUUID->"8a56e3b9-76a2-4e61-8890-07237ad33df4"],
Cell[14230, 463, 1113, 33, 59, "Output",ExpressionUUID->"288e88c2-4671-478f-afe3-a974351cc573"]
}, Open  ]],
Cell[CellGroupData[{
Cell[15380, 501, 1135, 34, 73, "Input",ExpressionUUID->"f1a1700f-0f1c-450d-919f-31ff178803f3"],
Cell[16518, 537, 829, 21, 59, "Output",ExpressionUUID->"2c51541e-3d24-4c57-882d-f95530d6f84c"]
}, Open  ]],
Cell[17362, 561, 521, 10, 157, "Input",ExpressionUUID->"662f2e8f-60ec-4662-a87f-597ac9747634"],
Cell[CellGroupData[{
Cell[17908, 575, 965, 23, 53, "Input",ExpressionUUID->"045a09c8-371d-4bd3-9c1a-2d5cf4f65f2e"],
Cell[18876, 600, 885, 22, 59, "Output",ExpressionUUID->"f5ca4652-1558-446d-a1c5-2319ac77a812"]
}, Open  ]],
Cell[19776, 625, 801, 20, 59, "Input",ExpressionUUID->"9c2f93b4-741c-43e1-9a6d-3d080e8c3107"],
Cell[CellGroupData[{
Cell[20602, 649, 147, 2, 30, "Input",ExpressionUUID->"81634571-9073-4129-8783-224b57489b79"],
Cell[20752, 653, 386, 10, 38, "Output",ExpressionUUID->"db55d115-8d92-4419-b065-4483b53bb980"]
}, Open  ]],
Cell[21153, 666, 296, 6, 30, "Input",ExpressionUUID->"e6155ea7-1b35-4079-b81c-d6067a9d42ef"],
Cell[CellGroupData[{
Cell[21474, 676, 174, 2, 30, "Input",ExpressionUUID->"629c6967-cb15-470d-bd0b-00653f49ced1"],
Cell[21651, 680, 150, 2, 34, "Output",ExpressionUUID->"18090fec-0319-4d9a-a54c-96cdcfe9eba6"]
}, Open  ]],
Cell[21816, 685, 359, 9, 34, "Input",ExpressionUUID->"00049345-f656-49d2-ad9c-d8dbb6d8f688"],
Cell[CellGroupData[{
Cell[22200, 698, 173, 2, 30, "Input",ExpressionUUID->"b003375b-a6d6-42c8-a0f1-07a7934834a1"],
Cell[22376, 702, 255, 7, 35, "Output",ExpressionUUID->"0c8b994c-24a9-4a5c-bd8c-313bc17746ac"]
}, Open  ]],
Cell[CellGroupData[{
Cell[22668, 714, 416, 9, 44, "Input",ExpressionUUID->"390cf48e-349d-4315-b071-c0535e85b742"],
Cell[23087, 725, 3489, 75, 242, "Output",ExpressionUUID->"2cf00f64-0b61-4d63-b9a8-d0fc136237c4"]
}, Open  ]],
Cell[CellGroupData[{
Cell[26613, 805, 510, 10, 44, "Input",ExpressionUUID->"e1b88fe5-1f02-44e3-9fe7-46c7cb33faab"],
Cell[27126, 817, 2559, 60, 237, "Output",ExpressionUUID->"d7f9da29-9bc1-46b4-b277-bb4149d474e6"]
}, Open  ]],
Cell[CellGroupData[{
Cell[29722, 882, 672, 13, 67, "Input",ExpressionUUID->"37dc5fc0-56ae-4d63-8d29-0c7cf2d5383f"],
Cell[30397, 897, 3608, 78, 237, "Output",ExpressionUUID->"fa9cadb6-24f7-43f3-80b9-6042470850f1"]
}, Open  ]],
Cell[CellGroupData[{
Cell[34042, 980, 295, 5, 44, "Input",ExpressionUUID->"bcbbb46a-f252-4780-9c47-064ffa9966af"],
Cell[34340, 987, 6362, 125, 237, "Output",ExpressionUUID->"20073024-2146-44ae-8450-c3fca429aea2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[40739, 1117, 1306, 36, 58, "Input",ExpressionUUID->"e969b9d4-3c33-4dcf-a7ab-667cbf551e12"],
Cell[42048, 1155, 892, 25, 62, "Output",ExpressionUUID->"31d609dd-650d-419c-95a3-1696c22504e1"]
}, Open  ]],
Cell[CellGroupData[{
Cell[42977, 1185, 1536, 41, 104, "Input",ExpressionUUID->"e4e7ffb2-009e-4f1e-9ffc-7147bb71509b"],
Cell[44516, 1228, 1508, 41, 60, "Output",ExpressionUUID->"ab959443-c997-47be-911b-76157078be3a"]
}, Open  ]],
Cell[CellGroupData[{
Cell[46061, 1274, 260, 5, 44, "Input",ExpressionUUID->"4d3e751a-a2f6-46bf-83a0-f8f0959488a9"],
Cell[46324, 1281, 1679, 41, 83, "Output",ExpressionUUID->"b6521819-38ba-4db4-b6e1-16f134609741"]
}, Open  ]],
Cell[48018, 1325, 237, 6, 44, "Input",ExpressionUUID->"579adbd0-2663-4e15-8f6d-fc09ce3e3479"],
Cell[48258, 1333, 2036, 53, 193, "Input",ExpressionUUID->"3040f7c1-3349-4b04-808f-c3d8d443e40a"],
Cell[CellGroupData[{
Cell[50319, 1390, 418, 9, 44, "Input",ExpressionUUID->"07322907-a209-446b-878e-736999fb0b62"],
Cell[50740, 1401, 3509, 75, 237, "Output",ExpressionUUID->"c7b6bf13-786f-465f-8517-6a18da48cce3"]
}, Open  ]],
Cell[CellGroupData[{
Cell[54286, 1481, 541, 10, 44, "Input",ExpressionUUID->"3ea524a5-f0f7-4ba6-9bfb-466bf4b7b0e3"],
Cell[54830, 1493, 2480, 60, 241, "Output",ExpressionUUID->"6b82efa9-7a11-4c65-8307-37904e495181"]
}, Open  ]],
Cell[CellGroupData[{
Cell[57347, 1558, 315, 7, 44, "Input",ExpressionUUID->"ac341192-0059-4adb-beb8-fa58d11d590e"],
Cell[57665, 1567, 2413, 58, 237, "Output",ExpressionUUID->"51e7cf77-2879-4c89-b5a0-3c21aad124fa"]
}, Open  ]],
Cell[CellGroupData[{
Cell[60115, 1630, 240, 4, 44, "Input",ExpressionUUID->"cb9cd8aa-9906-49da-9e25-1eaa71ed40c4"],
Cell[60358, 1636, 5169, 106, 241, "Output",ExpressionUUID->"fe937dca-5aa7-4ca0-a589-820ac4b7d90d"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)

