View of /branches/UWSP/SS4e/Chapter_02/Section_07/SS4e_02_07_007.pg

    1 ##DESCRIPTION
    2 ##   Mathematical modeling -- Rectangular field
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('modeling','optimization')
    6 
    7 ## DBsubject('Algebra')
    8 ## DBchapter('Functions')
    9 ## DBsection('Modeling with Functions')
   10 ## Author('Nathan Wodarz')
   11 ## Institution('UWSP')
   12 ## TitleText1('Precalculus Enhanced with Graphing Utilities')
   13 ## EditionText1('4')
   14 ## AuthorText1('Sullivan, Sullivan')
   15 ## Section1('2.7')
   16 ## Problem1('7')
   17 #
   18 # First comes some stuff that appears at the beginning of every problem
   19 #
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros(
   24 # Always call these
   25 "PGstandard.pl",
   26 "MathObjects.pl",
   27 "PGcourse.pl",
   28 "PGunion.pl",
   29 # Extra calls for this problem
   30 "parserNumberWithUnits.pl",
   31 "parserFormulaWithUnits.pl",
   32 );
   33 
   34 
   35 TEXT(&beginproblem);
   36 $showPartialCorrectAnswers = 1;
   37 
   38 $max_x = random(50,1000,50);
   39 $P = $max_x*4;
   40 
   41 $area = Formula("x ($P/2 - x)");
   42 
   43 ###################################
   44 # Main text
   45 
   46 Context()->texStrings;
   47 
   48 BEGIN_TEXT
   49 ${BBOLD}Enclosing a Rectangular Field.$EBOLD David has available $P meters of fencing and wishes to enclose a rectangular area.
   50 $PAR
   51 Express the area \(A\) of the rectangle as a function of the width \(x\) of the rectangle. \(A = \) \{ans_rule(15)\} (Use appropriate \{helpLink('units')\})$PAR
   52 What is the domain of \(A\)? \{ans_rule(10)\} (Use \{helpLink('interval notation')\})$PAR
   53 Graph \(A = A(x)\) using a graphing utility. For what value of \(x\) is the area largest? \(x = \) \{ans_rule(10)\} (Use appropriate \{helpLink('units')\})
   54 END_TEXT
   55 Context()->normalStrings;
   56 
   57 ###################################
   58 # Answer checking
   59 
   60 ANS(FormulaWithUnits($area,"m^2")->cmp);
   61 Context("Interval");
   62 ANS(Interval("(0,$P/2)")->cmp);
   63 ANS(NumberWithUnits($max_x,"m")->cmp);
   64 
   65 END_PROBLEM();
   66 ENDDOCUMENT();