##DESCRIPTION
## Related rates -- find rate of change of area of a circle given
##  the rate of change of radius and value of radius.
##ENDDESCRIPTION

## Shotwell cleaned
## tcao , PAID on 11-24-2003

## DBsubject(Calculus - single variable)
## DBchapter(Applications of differentiation)
## DBsection(Related rates)
## Date(6/3/2002)
## Institution(Univeristy of Utah)
## Author(Utah ww group)
## Level(3)
## TitleText1('Calculus: Early Transcendentals')
## AuthorText1('Stewart')
## EditionText1('6')
## Section1('3.9')
## Problem1('5')
## TitleText2('Calculus: Early Transcendentals')
## AuthorText2('Rogawski')
## EditionText2('1')
## Section2('3.11')
## Problem2('5')
## TitleText3('Calculus I')
## AuthorText3('Jerrold Marsden and Alan Weinstein')
## EditionText3('2')
## Section3('Rates of Change and the Chain Rule')
## Problem3('')
## TitleText4('Calculus')
## AuthorText4('Dale Varberg, Edwin J. Purcell, and Steven E. Rigdon')
## EditionText4('9')
## Section4('The Derivative')
## Problem4('')
## KEYWORDS('derivatives', 'related rates','Calculus')
##TYPE('word problem')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PGbasicmacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"MathObjects.pl",
"parserFunctionPrime.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 0;
Context("Numeric");
parser::FunctionPrime->Enable();
Context()->variables->add(t=> 'Real');
parserFunction("r(t)" => "15");
$r = Formula("r(t)");
$dr = Formula("r'(t)");

$dA = Compute("2 pi $r * $dr");

BEGIN_TEXT
Let \(A(t)\)  be the area of a circle with radius \(r(t)\) at time \(t\), i.e. \(A(t) = \pi[r(t)]^2.\) Compute \(A'(t) \) in terms of \(r(t)\), and \(r'(t)\). Enter "r(t)" for \(r(t)\) and "r'(t)" for \(r'(t)\).
$PAR
\(A'(t) = \)\{ans_rule(30) \}
END_TEXT

ANS($dA->cmp);

#parser::FunctionPrime->Disable();

ENDDOCUMENT();        # This should be the last executable line in the problem.