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nandorsiebennandorsieben
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New problems.
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6 files changed

+187
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‎Contrib/NAU/setCalcIII/DrAcula.pg‎

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -60,13 +60,13 @@ c. The gradient of \( S \) is \( \nabla S(r,h) = \) ( \{ $ans3->ans_rule(15)\}
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$PAR
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d. The gradient of \( V \) is \( \nabla V(r,h) = \) ( \{ $ans5->ans_rule(15)\} , \{ $ans6->ans_rule(15)\} ).
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$PAR
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In the last century it became fashionable to serve plasma in cans that have a volume of \( $v \) cubic huvelyk. Dr. Acula likes to follow current trends.
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In the last century it became fashionable to serve plasma in cans that have a volume of \( $v \) cubic inches. Dr. Acula likes to follow current trends.
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$PAR
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e. The best choice for the radius of the can is \( r_{\text{opt}} = \) \{ $ans7->ans_rule(15)\} huvelyk.
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e. The best choice for the radius of the can is \( r_{\text{opt}} = \) \{ $ans7->ans_rule(15)\} inches.
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$PAR
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f. The best choice for the height of the can is \( h_{\text{opt}} = \) \{ $ans8->ans_rule(15)\} huvelyk.
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f. The best choice for the height of the can is \( h_{\text{opt}} = \) \{ $ans8->ans_rule(15)\} inches.
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$PAR
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g. The surface area of the can cannot be smaller than \( S(r_{\text{opt}},h_{\text{opt}}) = \) \{ $ans9->ans_rule(35)\} square huvelyk.
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g. The surface area of the can cannot be smaller than \( S(r_{\text{opt}},h_{\text{opt}}) = \) \{ $ans9->ans_rule(35)\} square inches.
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END_TEXT

‎Contrib/NAU/setCalcIII/crossWithParam.pg‎

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##DESCRIPTION
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## DBsubject(Geometry)
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## DBchapter(Vector geometry)
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## DBsection(Cross product)
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## Institution(NAU)
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## Author(Nandor Sieben)
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## Level(3)
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## MO(1)
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##ENDDESCRIPTION
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# File Created: 1/16/22
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DOCUMENT();
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loadMacros(
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"PGstandard.pl",
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"MathObjects.pl",
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"AnswerFormatHelp.pl",
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"unorderedAnswer.pl",
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);
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TEXT(beginproblem());
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Context("Numeric");
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$p = random(0,9,1);
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$answer1 = Compute("-sqrt(1+$p)");
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$answer2 = Compute("sqrt(1+$p)");
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Context()->texStrings;
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BEGIN_TEXT
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Let \( x=(a,2,$p) \) and \( y=(1,2,a)\). Find \( a \) if the second component of \( x\times y \) is \( -1 \).
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$BR
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\( a = \)
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\{ ans_rule(5) \}
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or
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\( a = \)
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\{ ans_rule(5) \}
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END_TEXT
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Context()->normalStrings;
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$showPartialCorrectAnswers = 1;
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UNORDERED_ANS(
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$answer1->cmp(),
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$answer2->cmp(),
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);
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ENDDOCUMENT();

‎Contrib/NAU/setCalcIII/divergence2D.pg‎

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -1,10 +1,10 @@
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##DESCRIPTION
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## DBsubject(Calculus - multivariable)
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## DBchapter(Fundamental theorems)
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## DBsection(Divergence theorem)
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## DBsection(Green's theorem)
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## Institution(NAU)
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## Author(Nandor Sieben)
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## Level(2)
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## Level(3)
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## MO(1)
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##ENDDESCRIPTION
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# File Created: 4/2/17
@@ -28,7 +28,7 @@ TEXT(beginproblem());
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Context()->texStrings;
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BEGIN_TEXT
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Let \(F(x,y)=($a x , $b y ) \). Find the area of the region \( R\subseteq \mathbb{R}^2 \) if the flux of \( F \) through the boundary \(\partial R \) of \( R \) is \(\int_{\partial R}F\cdot N = $c \).
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Let \(F(x,y)=($a x , $b y ) \). Find the area of the closed, bounded region \( R\subseteq \mathbb{R}^2 \) if the flux of \( F \) through the boundary \(\partial R \) of \( R \) is \(\int_{\partial R}F\cdot N = $c \).
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$BR
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area\( (R)= \) \{ ans_rule(35) \}
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‎Contrib/NAU/setCalcIII/dotWithParam.pg‎

Lines changed: 48 additions & 0 deletions
Original file line numberDiff line numberDiff line change
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##DESCRIPTION
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## DBsubject(Geometry)
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## DBchapter(Vector geometry)
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## DBsection(Dot product, length, and unit vectors)
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## Institution(NAU)
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## Author(Nandor Sieben)
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## Level(3)
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## MO(1)
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##ENDDESCRIPTION
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# File Created: 1/16/22
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DOCUMENT();
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loadMacros(
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"PGstandard.pl",
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"MathObjects.pl",
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"AnswerFormatHelp.pl",
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"unorderedAnswer.pl",
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);
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TEXT(beginproblem());
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Context("Numeric");
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$answer1 = Compute("-1/2");
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$answer2 = Compute("1");
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Context()->texStrings;
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BEGIN_TEXT
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Find \( x \) if the vectors \( (x-3,x+3,1) \) and \( (x,x-1,2)\) are orthogonal.
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$BR
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\( x = \)
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\{ ans_rule(5) \}
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or
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\( x = \)
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\{ ans_rule(5) \}
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END_TEXT
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Context()->normalStrings;
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$showPartialCorrectAnswers = 1;
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UNORDERED_ANS(
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$answer1->cmp(),
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$answer2->cmp(),
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);
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ENDDOCUMENT();

‎Contrib/NAU/setCalcIII/initialValue.pg‎

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##DESCRIPTION
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## DBsubject(Calculus - multivariable)
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## DBchapter(Calculus of vector valued functions)
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## DBsection(Integrals)
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## Institution(NAU)
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## Author(Nandor Sieben)
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## Level(3)
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## MO(1)
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##ENDDESCRIPTION
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# File Created: 1/16/22
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DOCUMENT();
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loadMacros(
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"PGstandard.pl",
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"MathObjects.pl",
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"AnswerFormatHelp.pl",
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);
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TEXT(beginproblem());
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Context("Numeric");
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$p = non_zero_random(-9,9,1);
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$answer = Compute("sqrt(1+($p)^2)");
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BEGIN_TEXT
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Find \( \|r(0)\| \) if \( r'(t)=(\cos(2t),2t,e^t) \) and \( r(0)=($p,1,0) \).
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$BR
32+
\( \|r(0)\| = \)
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\{ ans_rule(5) \}
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END_TEXT
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$showPartialCorrectAnswers = 1;
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ANS( $answer->cmp() );
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ENDDOCUMENT();

‎Contrib/NAU/setCalcIII/vectorMultWithParam.pg‎

Lines changed: 42 additions & 0 deletions
Original file line numberDiff line numberDiff line change
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##DESCRIPTION
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## DBsubject(Geometry)
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## DBchapter(Vector geometry)
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## DBsection(Vectors and vector arithmetic)
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## Institution(NAU)
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## Author(Nandor Sieben)
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## Level(3)
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## MO(1)
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##ENDDESCRIPTION
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# File Created: 1/16/22
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DOCUMENT();
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loadMacros(
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"PGstandard.pl",
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"MathObjects.pl",
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"AnswerFormatHelp.pl",
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);
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TEXT(beginproblem());
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Context("Numeric");
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$p = random(-9,9,1);
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$answer = Compute("(1+2*$p)/3");
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# Context()->texStrings;
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BEGIN_TEXT
31+
Let \( A=(4,0,$p) \), \( B=(1,a,b)\), and \( X=(a,b,c)\). Find \( c \) if \( \overrightarrow{AB} = 3 \overrightarrow{AX} \).
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$BR
33+
\( c = \)
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\{ ans_rule(5) \}
35+
END_TEXT
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# Context()->normalStrings;
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$showPartialCorrectAnswers = 1;
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ANS( $answer->cmp() );
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ENDDOCUMENT();

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