Spacecurve1

A Parametric Curve in Space

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This PG code shows how to ask a parametric curve question with three answer blanks and use MultiAnswer to check the answer.

• File location in OPL: FortLewis/Authoring/Templates/Parametric/Spacecurve1.pg
• PGML location in OPL: FortLewis/Authoring/Templates/Parametric/Spacecurve1_PGML.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( 'PGstandard.pl', 'MathObjects.pl', 'parserMultiAnswer.pl', 'PGML.pl', 'PGcourse.pl' ); TEXT(beginproblem());	Initialization: Since we will have multiple answer blanks that depend on each other, we need to use parserMultiAnswer.pl.
Context("Numeric"); Context()->variables->are(t=>"Real"); Context()->variables->set(t=>{limits=>[0,10]}); $a = random(-5,-2,1); $x = Formula("$a * t**2"); $y = Formula("0"); $z = Formula("t"); $multians = MultiAnswer($x, $y, $z)->with( singleResult => 1, checker => sub { my ( $correct, $student, $self ) = @_; my ( $xstu, $ystu, $zstu ) = @{$student}; return 0 unless $xstu->isFormula; if (($xstu==$a*$zstu**2) && ($ystu==0)) { return 1; } else { return 0; } } );	Setup: We use singleResult => 1 since it doesn't make sense to say that x(t) is correct but z(t) is incorrect since they depend on one another. First, we check that the student hasn't fed us a bogus constant solution such as x=y=z=0 by requiring the x-coordinate to be a formula (not a constant) via return 0 unless $xstu->isFormula;. Then, we check that the student's answers satisfy the parametric equation.
BEGIN_PGML Find a parametrization of the curve [` x = [$a] z^2 `] in the [`xz`]-plane. Use [` t `] as the parameter for all of your answers. - [` x(t) = `] [______________]{$multians} - [` y(t) = `] [______________]{$multians} - [` z(t) = `] [______________]{$multians} [@ helpLink('formulas') @]* END_PGML	Main Text: Notice that we use $multians in each answer blank because they results in the three answers are dependent on each other.
BEGIN_PGML_SOLUTION Solution explanation goes here. END_PGML_SOLUTION ENDDOCUMENT();	Solution:

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