View of /trunk/NationalProblemLibrary/Rochester/setParametric1Curves/ur_pa_1_2.pg

    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 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.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