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Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 1429 byte(s)
`Rogawski problems contributed by publisher WHFreeman. These are a subset of the problems available to instructors who use the Rogawski textbook. The remainder can be obtained from the publisher.`

```    1 ## DBsubject('Calculus')
2 ## DBchapter('Introduction to Differential Equations')
3 ## DBsection('Parametric Equations')
4 ## KEYWORDS('calculus', 'parametric', 'parametric equations')
5 ## TitleText1('Calculus: Early Transcendentals')
6 ## EditionText1('2')
7 ## AuthorText1('Rogawski')
8 ## Section1('11.1')
9 ## Problem1('7')
10 ## Author('Christopher Sira')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
17
18 \$context = Context("Point");
21
22 \$a = Real(random(1, 6, 1));
23 \$b = Real(random(2, 6, 1));
24 \$c = Real(random(1, 10, 1));
25
26 \$xform = Formula("t + \$a");
27 \$txform = Formula("x - \$a");
28
29 \$yform = Formula("\$b * t + \$c");
30
31 \$ans = \$yform->substitute(t=>\$txform)->reduce();
32
33
34 Context()->texStrings;
35 BEGIN_TEXT
36 \{ beginproblem() \}
37 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","7") \}
38 \$PAR
39 Express \( x = \$xform \), \( y = \$yform \) in the form \( y = f(x) \) by eliminating the parameter.
40 \$PAR
41 y = \{ans_rule()\}
42 END_TEXT
43 Context()->normalStrings;
44
45 ANS(\$ans->cmp);
46
47 Context()->texStrings;
48 SOLUTION(EV3(<<'END_SOLUTION'));
49 \$PAR
50 \$SOL
51 We eliminate the parameter.  Since \( x = \$xform \), we have \( t = \$txform \).  Substituting into \( y = \$yform \) we obtain
52 \$PAR
53 \( y = \$ans \)
54 END_SOLUTION
55
56 ENDDOCUMENT();
57
```