View of /trunk/NationalProblemLibrary/Rochester/setLinearAlgebra2SystemsApplications/ur_la_2_5.pg

    1 ## DESCRIPTION
    2 ## Linear Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('linear algebra','linear system','chemistry')
    6 ## Tagged by cmd6a 5/3/06
    7 
    8 ## DBsubject('Linear Algebra')
    9 ## DBchapter('Systems of Linear Equations and Matrices')
   10 ## DBsection('Introduction to Systems of Linear Equations')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGgraphmacros.pl",
   28 "PGnumericalmacros.pl",
   29 "PGauxiliaryFunctions.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 
   35 @reac = ('\[a NO_2 + b H_2 O \rightarrow c HNO_2 + d HNO_3,\]',
   36          '\[a P_4O_{10} + b CaF_2 \rightarrow c PF_5 + d Ca_3(PO_4)_2,\]',
   37          '\[a NH_3 + b O_2 \rightarrow c NO + d H_2 O,\]',
   38          '\[a Al + b H_2O \rightarrow c Al(OH)_3 + d H_2,\]',
   39          '\[a N_2H_4 + b N_2O_4 \rightarrow c N_2+d H_2O,\]',
   40          '\[a CH_4 + b O_2 \rightarrow c CO_2 + d H_2O,\]',
   41    '\[a C_2H_6 + b CO_2 + c H_2O \rightarrow d C_2H_5OH,\]');
   42 
   43 @eq = ('\[2a+b=2c+3d.\]', '\[10a=8d.\]', '\[2b=c+d.\]',
   44        '\[b=3c.\]', '\[4b=d.\]', '\[2b=2c+d.\]', '\[2b+c=d.\]');
   45 
   46 @ansa = (2, 4,  4, 2, 2, 1, 6);
   47 @ansb = (1, 15, 5, 6, 1, 2, 2);
   48 @ansc = (1, 6,  4, 2, 3, 1, 3);
   49 @ansd = (1, 5,  6, 3, 4, 2, 7);
   50 
   51 $tag = random(0,6,1);
   52 
   53 BEGIN_TEXT
   54 
   55 Consider the chemical reaction $reac[$tag] where \(a,\) \(b,\) \(c,\) and \(d\) are unknown positive
   56 integers. The reaction mush be balanced; that is, the number of atoms of each element must be the same
   57 before and after the reaction. For example, because the number of oxygen atoms must remain the
   58 same, $eq[$tag] While there are many possible choices for \(a,\) \(b,\) \(c,\) and \(d\) that balance
   59 the reaction, it is customary to use the smallest possible integers. Balance this reaction.
   60 $BR
   61 \(a=\)\{ans_rule(10)\} $BR
   62 \(b=\)\{ans_rule(10)\} $BR
   63 \(c=\)\{ans_rule(10)\} $BR
   64 \(d=\)\{ans_rule(10)\} $BR
   65 
   66 END_TEXT
   67 
   68 ANS(num_cmp($ansa[$tag]));
   69 ANS(num_cmp($ansb[$tag]));
   70 ANS(num_cmp($ansc[$tag]));
   71 ANS(num_cmp($ansd[$tag]));
   72 
   73 ENDDOCUMENT();       # This should be the last executable line in the problem.
   74