(*^
::[ Information =
"This is a Mathematica Notebook file. It contains ASCII text, and can be
transferred by email, ftp, or other text-file transfer utility. It should
be read or edited using a copy of Mathematica or MathReader. If you
received this as email, use your mail application or copy/paste to save
everything from the line containing (*^ down to the line containing ^*)
into a plain text file. On some systems you may have to give the file a
name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
The line below identifies what version of Mathematica created this file,
but it can be opened using any other version as well.";
FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2";
MacintoshStandardFontEncoding;
fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times";
fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times";
fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times";
fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times";
fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times";
fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times";
fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier";
fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier";
fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier";
fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier";
fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva";
fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = leftheader, inactive, L2, 12, "Times";
fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times";
fontset = leftfooter, inactive, L2, 12, "Times";
fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
paletteColors = 128; automaticGrouping; currentKernel;
]
:[font = input; preserveAspect]
ClearAll;
$DefaultFont = {"Times-Roman",12};
Needs["Statistics`DataManipulation`"];
Needs["Graphics`Graphics`"];
a = 1;
c = 11/4.8;
b = 11/68;
xmin = 1; xmax = 10;
xh = 0.8 xmin + 0.2 xmax;
xg = 0.5 xmin + 0.5 xmax;
h[x_]:= (229 x^(-1/4))/60;
g[x_]:= 11.2 x^(3/4);
ell1a:= ParametricPlot[{xh,t},{t,0,h[xh]},
PlotStyle -> Dashing[{0.01,0.01}]];
ell1b:= ParametricPlot[{t,h[xh]},{t,0,xh},
PlotStyle -> Dashing[{0.01,0.01}]];
ell2a:= ParametricPlot[{c h[xh],c t},{t,0,xh},
PlotStyle -> Dashing[{0.01,0.01}]];
ell2b:= ParametricPlot[{c t,c xh},{t,0,h[xh]},
PlotStyle -> Dashing[{0.01,0.01}]];
ell3a:= ParametricPlot[{xg,t},{t,0,g[xg]},
PlotStyle -> Dashing[{0.01,0.01}]];
ell3b:= ParametricPlot[{t,g[xg]},{t,0,xg},
PlotStyle -> Dashing[{0.01,0.01}]];
ell4a:= ParametricPlot[{b g[xg],b t},{t,0,xg},
PlotStyle -> Dashing[{0.01,0.01}]];
ell4b:= ParametricPlot[{b t,b xg},{t,0,g[xg]},
PlotStyle -> Dashing[{0.01,0.01}]];
plota:= ParametricPlot[{x,h[x]},{x,1,10},
AspectRatio -> a,
PlotRange -> {{0,11},{0,4.8}},
PlotLabel -> "y = h(x)",
Ticks->{{{1,1},{2.8,"x"},{10,10}},
{{0,"0"},{2.1,2.1},{h[2.8],"y"},{3.8,3.8}}}];
plotb:= ParametricPlot[{c h[x],c x},{x,1,10},
AspectRatio -> 1/a,
PlotRange -> {{0,4.8 c},{0,11 c}},
PlotLabel -> "x = g(y)",
Ticks->{{{0,"0"},{3.8 c,3.8},{c h[2.8],"y"},{2.1 c,2.1}},
{{c,1},{2.8 c,"x"},{10 c,10}}}];
plotc:= ParametricPlot[{x,g[x]},{x,1,10},
AspectRatio -> a,
PlotRange -> {{0,11},{0,68}},
PlotLabel -> "z = q(x)",
Ticks->{{{1,1},{5.5,"x"},{10,10}},
{{0,"0"},{11.2,11},{g[5.5],"z"},{63,63}}}];
plotd:= ParametricPlot[{b g[x],b x},{x,1,10},
AspectRatio -> 1/a,
PlotRange -> {{0,68 b},{0,11 b}},
PlotLabel -> "x = r(z)",
Ticks->{{{0,"0"},{11.2 b,11},{b g[5.5],"z"},{63 b,63}},
{{b,1},{5.5 b,"x"},{10 b,10}}}];
plottl:= Show[plota,ell1a,ell1b];
plottr:= Show[plotb,ell2a,ell2b];
plotbl:= Show[plotc,ell3a,ell3b];
plotbr:= Show[plotd,ell4a,ell4b];
Show[GraphicsArray[{{plottl,plottr},{plotbl,plotbr}}],
PlotLabel -> "Figure 1.2"]
^*)