View of /trunk/NationalProblemLibrary/Rochester/setDerivatives8RelatedRates/s2_8_2.pg

    1 #DESCRIPTION
    2 #KEYWORDS('derivatives', 'related rates')
    3 #TYPE('word problem')
    4 # Related rates -- find rate of change of area of a circle given
    5 #  the rate of change of radius and value of radius.
    6 #ENDDESCRIPTION
    7 
    8 ##KEYWORDS('Derivatives')
    9 ##Tagged by ynw2d
   10 
   11 ##DBsubject('Calculus')
   12 ##DBchapter('Differentiation')
   13 ##DBsection('Related Rates')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('1')
   16 ## AuthorText1('Rogawski')
   17 ## Section1('3.11')
   18 ## Problem1('5')
   19 
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $a1 = random(2,5,1);
   35 $r1 = random(1,5,1);
   36 $deriv1 = 2*3.14159265*$r1*$a1;
   37 TEXT(EV2(<<EOT));
   38 Let \(A\)  be the area of a circle with radius \(r\). If
   39 \( \displaystyle \frac { dr }{ dt } = $a1 \), find
   40 \( \displaystyle \frac { dA }{ dt }  \) when \( r = $r1 \).
   41 \{ans_rule(20) \}
   42 EOT
   43 
   44 $ans = $deriv1;
   45 ANS(num_cmp($ans));
   46 
   47 ENDDOCUMENT();        # This should be the last executable line in the problem.