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# View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh4S2/problem_1.pg

Wed Mar 22 22:31:23 2006 UTC (7 years, 2 months ago) by jj
File size: 1084 byte(s)
Import of new files.


    1 ## -*- perl -*- ##
2 ## Line above puts emacs in perl mode
3 ##
4 ## Description
5 ##   Asks for the length of a parametric curve
6 ## EndDescription
7
8 DOCUMENT();
10            "PGbasicmacros.pl",
11            "PGchoicemacros.pl",
13            "PGauxiliaryFunctions.pl",
14            "PGgraphmacros.pl",
15            "Dartmouthmacros.pl");
16
17
18 ## Do NOT show partial correct answers
19 $showPartialCorrectAnswers = 1; 20 21 ## Lots of set up goes here 22$a = non_zero_random( -5, 5, 1 );
23 $a_t = clean_scalar_string($a, "t");
24 $b = non_zero_random( -5, 5, 1 ); 25$b_sin_t = clean_scalar_string($b, "\sin t"); 26$b_cos_t = clean_scalar_string($b, "\cos t"); 27$c = random( -5, -1, 1 );
28 $d = random( 1, 5, 1 ); 29 30 31 ## Ok, we are ready to begin the problem... 32 ## 33 TEXT(beginproblem()); 34 35 36 37 BEGIN_TEXT 38$BR
39 Find the length of the given curve:
40 $BR 41 42 $$\mathbf{r} \left( t \right) = \left( a_t, b_sin_t, b_cos_t 43 \right)$$ where $$c \leq t \leq d$$.$PAR
44
45 \{ans_rule(10)\}
46
47 END_TEXT
48
49
50 $ans = ($d - $c) * sqrt($a**2 + $b**2 ); 51 ANS( std_num_cmp($ans ) );
52
53 ENDDOCUMENT();
54
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