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Tue May 9 13:07:16 2006 UTC (7 years ago) by jjholt
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    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('parametric equation')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Parametric Equations and Polar Coordinates')
10 ## DBsection('Curves Defined by Parametric Equations')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33$x1 = random(-2,9);
34 $y1 = random(-10,10); 35$x2 = random(-2,9);
36 $y2 = random(-10,10); 37 38$tcoefx = $x2 -$x1;
39 $tcoefy =$y2 - $y1; 40 41$NO_SPACE = '@{\,}';
42
43 BEGIN_TEXT
44 Suppose parametric equations for the line segment between
45 $$(x1, y1)$$ and $$(x2, y2)$$ have the form:
46 $\begin{array}{r{NO_SPACE}c{NO_SPACE}l} 47 x & = & a + bt \cr 48 y & = & c + dt 49 \end{array}$
50 If the parametric curve starts at $$(x1, y1)$$ when $$t=0$$ and ends at
51 $$(x2, y2)$$ at $$t=1$$, then find $$a$$, $$b$$, $$c$$, and $$d$$.
52 $BR 53 $$a =$$ \{ans_rule(10) \}, 54 END_TEXT 55 56 ANS(num_cmp($x1));
57
58 BEGIN_TEXT
59 $BR 60 $$b =$$ \{ans_rule(10) \}, 61 END_TEXT 62 63 ANS(num_cmp($tcoefx));
64
65 BEGIN_TEXT
66 $BR 67 $$c =$$ \{ans_rule(10) \}, 68 END_TEXT 69 70 ANS(num_cmp($y1));
71
72 BEGIN_TEXT
73 $BR 74 $$d =$$ \{ans_rule(10) \}. 75 END_TEXT 76 77 ANS(num_cmp($tcoefy));
78
79
80 ENDDOCUMENT();
81
82