View of /trunk/NationalProblemLibrary/ASU-topics/setDerivativeBasicFunctions/3-4-88.pg

    1 ## DESCRIPTION
    2 ## Instantaneous Rate of Change
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('instantaneous', 'rate of change', 'application', 'derivative')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('Rates of Change in the Natural and Social Sciences')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('3.3')
   18 ## Problem1('')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('3.7')
   24 ## Problem2('')
   25 
   26 DOCUMENT();
   27 
   28 loadMacros(
   29 "PG.pl",
   30 "PGbasicmacros.pl",
   31 "PGchoicemacros.pl",
   32 "PGanswermacros.pl",
   33 "PGauxiliaryFunctions.pl"
   34 );
   35 
   36 TEXT(beginproblem());
   37 $showpartialcorrectanswers = 1;
   38 
   39 $a = random(15,25, 1);
   40 $b = random(1,4,1);
   41 $c = random(6,8,1);
   42 
   43 TEXT(EV2(<<EOT));
   44 If a person learns \(y\) items in \(x\) hours, as given by
   45 \[ y = $a \sqrt[3]{x^2}, \]
   46 find the rate of learning for a person at the end of:
   47 $BR
   48 (A) $b hours: \{ans_rule(30) \}
   49 $BR
   50 EOT
   51 
   52 $ans = ((2*$a)/3)*($b**(-1/3));
   53 ANS(num_cmp($ans));
   54 
   55 TEXT(EV2(<<EOT));
   56 (B) $c hours: \{ans_rule(30) \}
   57 $BR
   58 EOT
   59 
   60 $ans = ((2*$a)/3)*($c**(-1/3));
   61 ANS(num_cmp($ans));
   62 
   63 
   64 ENDDOCUMENT();