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Tue Nov 1 02:43:54 2011 UTC (18 months, 2 weeks ago) by nwodarz
File size: 1843 byte(s)
`Importing Section 2.7 files`

```    1 ##DESCRIPTION
2 ##   Mathematical modeling -- Rectangular field
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('7')
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 TEXT(&beginproblem);
37
38 \$max_x = random(50,1000,50);
39 \$P = \$max_x*4;
40
41 \$area = Formula("x (\$P/2 - x)");
42
43 ###################################
44 # Main text
45
46 Context()->texStrings;
47
48 BEGIN_TEXT
49 \${BBOLD}Enclosing a Rectangular Field.\$EBOLD David has available \$P meters of fencing and wishes to enclose a rectangular area.
50 \$PAR
51 Express the area \(A\) of the rectangle as a function of the width \(x\) of the rectangle. \(A = \) \{ans_rule(15)\} (Use appropriate \{helpLink('units')\})\$PAR
52 What is the domain of \(A\)? \{ans_rule(10)\} (Use \{helpLink('interval notation')\})\$PAR
53 Graph \(A = A(x)\) using a graphing utility. For what value of \(x\) is the area largest? \(x = \) \{ans_rule(10)\} (Use appropriate \{helpLink('units')\})
54 END_TEXT
55 Context()->normalStrings;
56
57 ###################################
59
60 ANS(FormulaWithUnits(\$area,"m^2")->cmp);
61 Context("Interval");
62 ANS(Interval("(0,\$P/2)")->cmp);
63 ANS(NumberWithUnits(\$max_x,"m")->cmp);
64
65 END_PROBLEM();
66 ENDDOCUMENT();
```