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    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('7')
   10 ## Author('Christopher Sira')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 
   18 $context = Context("Point");
   19 $context->variables->add(t=>'Real');
   20 #$context->variables->add(x=>'Real');
   21 
   22 $a = Real(random(1, 6, 1));
   23 $b = Real(random(2, 6, 1));
   24 $c = Real(random(1, 10, 1));
   25 
   26 $xform = Formula("t + $a");
   27 $txform = Formula("x - $a");
   28 
   29 $yform = Formula("$b * t + $c");
   30 
   31 $ans = $yform->substitute(t=>$txform)->reduce();
   32 
   33 
   34 Context()->texStrings;
   35 BEGIN_TEXT
   36 \{ beginproblem() \}
   37 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","7") \}
   38 $PAR
   39 Express \( x = $xform \), \( y = $yform \) in the form \( y = f(x) \) by eliminating the parameter.
   40 $PAR
   41 y = \{ans_rule()\}
   42 END_TEXT
   43 Context()->normalStrings;
   44 
   45 ANS($ans->cmp);
   46 
   47 Context()->texStrings;
   48 SOLUTION(EV3(<<'END_SOLUTION'));
   49 $PAR
   50 $SOL
   51 We eliminate the parameter.  Since \( x = $xform \), we have \( t = $txform \).  Substituting into \( y = $yform \) we obtain
   52 $PAR
   53 \( y = $ans \)
   54 END_SOLUTION
   55 
   56 ENDDOCUMENT();
   57