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Pending/Berkeley/StewCalcET7e/3.9/3.9.rescue1.pg

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+#DESCRIPTION
+##  Calculus: Related rates
+##ENDDESCRIPTION
+
+
+## DBsubject(Calculus - single variable)
+## DBchapter(Applications of differentiation)
+## DBsection(Related rates)
+## Date(11/29/2010)
+## Institution(University of Minnesota)
+## Author(Justin Sukiennik)
+## MO(1)
+## TitleText1('Calculus: Concepts and Contexts')
+## AuthorText1('Stewart')
+## EditionText1('4 Custom UMTYMP Ed.')
+## Section1('4.1')
+## Problem1('30')
+## KEYWORDS('calculus', 'derivative', 'related rates')
+#
+# (This was UMN/calculusStewartCCC/s_4_1_30.pg)
+
+#####################################################################
+DOCUMENT();        # This should be the first executable line in the problem.
+
+loadMacros(
+  "PGstandard.pl",
+  "MathObjects.pl",
+  "answerHints.pl",
+  "PGcourse.pl", 
+);
+#####################################################################
+
+TEXT(beginproblem());
+
+$showPartialCorrectAnswers = 1;
+
+#####################################################################
+
+Context("Numeric");
+
+$a = random(50,100,25);
+$b = random(2,8,2);
+$c = random(150,300,50);
+
+$ans = Compute("($a/$c^2)*$b");
+
+#####################################################################
+
+Context()->texStrings;
+BEGIN_TEXT
+A kite \($a\text{ft}\) above the ground moves horizontally at a speed of \($b\text{ft/s}.\)  At what rate is the angle between the string and the horizontal decreasing when \($c\text{ft}\) of string has been let out?
+$PAR
+Answer (in radians per second): \{ans_rule(30)\}
+END_TEXT
+Context()->normalStrings;
+
+#####################################################################
+
+ANS($ans->cmp(showTypeWarnings=>0)->withPostFilter(AnswerHints(Compute("-$ans") => ["The problem is asking how fast the angle between the string and the horizontal is decreasing. So the answer should be positive."])));
+
+COMMENT('Uses MathObjects.');
+
+ENDDOCUMENT();        # This should be the last executable line in the problem.