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

Sat Sep 8 05:17:01 2007 UTC (5 years, 9 months ago) by sh002i
File size: 1124 byte(s)
Added tags for Rogawski's "Calculus: Early Transcendentals".


    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
24 "PG.pl",
25 "PGbasicmacros.pl",
26 "PGchoicemacros.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.