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Tue Nov 1 02:43:54 2011 UTC (18 months, 3 weeks ago) by nwodarz
File size: 2311 byte(s)
`Importing Section 2.7 files`

```    1 ##DESCRIPTION
2 ##   Mathematical modeling -- wire divided into triangle and circle
3 ##ENDDESCRIPTION
4
5 ##KEYWORDS('modeling','optimization')
6
7 ## DBsubject('Algebra')
8 ## DBchapter('Functions')
9 ## DBsection('Modeling with Functions')
10 ## Author('Nathan Wodarz')
11 ## Institution('UWSP')
12 ## TitleText1('Precalculus Enhanced with Graphing Utilities')
13 ## EditionText1('4')
14 ## AuthorText1('Sullivan, Sullivan')
15 ## Section1('2.7')
16 ## Problem1('20')
17 #
18 # First comes some stuff that appears at the beginning of every problem
19 #
20
21 DOCUMENT();        # This should be the first executable line in the problem.
22
24 # Always call these
25 "PGstandard.pl",
26 "MathObjects.pl",
27 "PGcourse.pl",
28 "PGunion.pl",
29 # Extra calls for this problem
30 "parserNumberWithUnits.pl",
31 "parserFormulaWithUnits.pl",
32 );
33
34
35
36 TEXT(&beginproblem);
38
39 \$length = random(5,100,5);
40
41 Context()->flags->set(limits=>[0,\$length]);
42
43 \$area = Formula("x/2*sqrt(x^2-(x/2)^2) + (\$length - 3 x)^2/(4*pi)");
44
45 \$min_x = (3*\$length)/(9 + sqrt(3)*pi) - sqrt(-sqrt(3)*\$length**2*pi + (
46   36*sqrt(3)*\$length**2*pi+12*\$length**2*pi**2)/(36 + 4*sqrt(3)*pi))/(9 + sqrt(3)*pi);
47
48 ###################################
49 # Main text
50
51 Context()->texStrings;
52
53 BEGIN_TEXT
54 A wire \$length meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.\$PAR
55 Express the total area \(A\) enclosed by the pieces of wire as a function of the length \(x\) of a side of the equilateral triangle. \(A(x) = \) \{ans_rule(40)\} (Use appropriate \{helpLink('units')\})\$PAR
56 What is the domain of \(x\)? \{ans_rule(10)\} (Use \{helpLink('interval notation')\})\$PAR
57 Graph \(A = A(x)\). For what value of \(x\) is \(A\) smallest? \(x = \) \{ans_rule(10)\} (Use appropriate \{helpLink('units')\})\$PAR
58 What is the minimum value of \(A\)? \(A = \) \{ans_rule(10)\} (Use appropriate \{helpLink('units')\})\$PAR
59 END_TEXT
60 Context()->normalStrings;
61
62 ###################################