View of /trunk/rochester_problib/setVectorCalculus3/ur_vc_13_3.pg

    1 ##DESCRIPTION
    2 #
    3 # File Created: 6/4/2000
    4 # Last Modified: 6/4/2000
    5 # Problem Author: Joseph Neisendorfer
    6 # WeBWorK Entry: Victoria Sweetser
    7 # Location: University of Rochester
    8 #
    9 ##ENDDESCRIPTION
   10 
   11 ##KEYWORDS('Vector','Surface Integral','Field')
   12 
   13 
   14 DOCUMENT();   # This should be the first executable line in the problem.
   15 
   16 loadMacros("PG.pl",
   17            "PGbasicmacros.pl",
   18            "PGchoicemacros.pl",
   19            "PGanswermacros.pl",
   20            "PGauxiliaryFunctions.pl"
   21           );
   22 
   23 TEXT(&beginproblem);
   24 $showPartialCorrectAnswers = 1;
   25 
   26 $a = random(1, 5, 1);
   27 $b = random(1, 5, 1);
   28 $c = random(1, 5, 1);
   29 $d = $a**2;
   30 
   31 BEGIN_TEXT
   32 A fluid has density $c and velocity field
   33 \( \mathbf{v} = -y\mathbf{i} + x\mathbf{j} + $b\!z\mathbf{k} \).$BR
   34 Find the rate of flow outward through the sphere
   35 \( x^{2} + y^{2} + z^{2} = $d \)
   36 $PAR
   37 \{ ans_rule(40) \}
   38 END_TEXT
   39 
   40 ANS( num_cmp( (4*$b*$c*$d*$a*3.14159)/3 ) );
   41 
   42 ENDDOCUMENT();    # This should be the last executable line in the problem.