View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/11_Parametric_Equations_Polar_Coordinates_and_Conic_Sections/11.1_Parametric_Equations/11.1.23.pg

    1 ## DBsubject('Calculus')
    2 ## DBchapter('Introduction to Differential Equations')
    3 ## DBsection('Parametric Equations')
    4 ## KEYWORDS('calculus', 'parametric', 'parametric equations')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('11.1')
    9 ## Problem1('23')
   10 ## Author('Christopher Sira')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl", "PGchoicemacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 
   18 $context = Context("Point");
   19 $context->variables->add(t=>'Real');
   20 
   21 do {
   22 $a = Real(non_zero_random(-10, 10, 1));
   23 $b = Real(random(1, 10, 1));
   24 } until ($a != $b);
   25 
   26 $question = Formula("$a - $b * x")->reduce();
   27 $questiontex = $question->TeX;
   28 
   29 $answer = Point(Formula("t"), $question->substitute(x=>"t"))->reduce->TeX;
   30 $false1 = Point(Formula("$a * t"), Formula("$b * t"))->reduce->TeX;
   31 $false2 = Point(Formula("t"), Formula("$a + t"))->reduce->TeX;
   32 $false3 = Point(Formula("t"), Formula("$b + t"))->reduce->TeX;
   33 
   34 $fp = Formula("1")->eval();
   35 
   36 $mc = new_multiple_choice();
   37 
   38 $mc->qa("Which is a parametric equation for the curve \( y = $questiontex \)?",
   39         "\( c(t) = $answer \)");
   40 
   41 $mc->extra("\( c(t) = $false1 \)",
   42            "\( c(t) = $false2 \)",
   43            "\( c(t) = $false3 \)" );
   44 
   45 Context()->texStrings;
   46 BEGIN_TEXT
   47 \{ beginproblem() \}
   48 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","23") \}
   49 $PAR
   50 \{$mc->print_q \}
   51 $PAR
   52 \{$mc->print_a \}
   53 END_TEXT
   54 Context()->normalStrings;
   55 
   56 ANS(str_cmp($mc->correct_ans));
   57 
   58 Context()->texStrings;
   59 SOLUTION(EV3(<<'END_SOLUTION'));
   60 $PAR
   61 $SOL
   62 This is a line through \( P = (0, $a) \) with slope \( m = - $b \).  Using the parametric representation of a line, we obtain \( c(t) = $answer \).
   63 END_SOLUTION
   64 
   65 ENDDOCUMENT();