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# Annotation of /branches/UGA/2.2.1.pg

 1 : ted shifri 1457 ## DESCRIPTION 2 : ## Testing for Open Sets 3 : ## ENDDESCRIPTION 4 : 5 : ## KEYWORDS('Open Set', 'Ball') 6 : ## 7 : 8 : ## DBsubject('Calculus') 9 : ## DBchapter('') 10 : ## DBsection('') 11 : ## Date('9/5/2009') 12 : ## Author('Ted Shifrin') 13 : ## Institution('UGA') 14 : ## TitleText1('') 15 : ## EditionText1('') 16 : ## AuthorText1('') 17 : ## Section1('') 18 : ## Problem1('') 19 : 20 : DOCUMENT(); # This should be the first executable line in the problem. 21 : 22 : loadMacros("PG.pl", 23 : "PGbasicmacros.pl", 24 : "PGchoicemacros.pl", 25 : "PGanswermacros.pl", 26 : "PGauxiliaryFunctions.pl", 27 : "MathObjects.pl", 28 : ); 29 : 30 : TEXT(beginproblem()); 31 : $showPartialCorrectAnswers = 1; 32 : Context("Vector"); 33 : 34 :$a1 = non_zero_random(1, 10, 1); 35 : $b1 = non_zero_random(1, 10, 1); 36 :$r = random(1,4,1); 37 : $rr =$r**2; 38 : $a2 = non_zero_random(-5, 5, 1); 39 :$b2 = non_zero_random(-5, 5, 1); 40 : $a3 = random(-10, 10, 1); 41 :$b3 = random($a3+1,$a3+10, 1); 42 : 43 : 44 : $ans1 = min($a1,$b1); 45 :$ans2 = abs(sqrt($a2**2+$b2**2)-$r); 46 :$ans3 = ($b3-$a3)/sqrt(2); 47 : 48 : @points = ("$a1,$b1", "$a2,$b2", "$a3,$b3"); 49 : 50 : @sets = ( "xy \gt 0", "x^2+y^2 \ne $rr", "y \gt x" ); 51 : 52 : @answers = ("$ans1", "$ans2", "$ans3"); 53 : 54 : @choice=NchooseK(3,2); 55 : @subpoints=@points[@choice]; 56 : @subsets=@sets[@choice]; 57 : @subanswers=@answers[@choice]; 58 : 59 : $P0 = ColumnVector("<@subpoints[0]>"); 60 :$P1 = ColumnVector("<$subpoints[1]>"); 61 : 62 : Context()->texStrings; 63 : BEGIN_TEXT 64 : Given the point $$\mathbf a = P0$$ in the set 65 : $$S = \left\{"\{"\} \left(\begin{array}{c}x\\y\end{array}\right): subsets[0] \right\}$$, give the radius $$\delta$$ of the largest ball $$B(\mathbf a,\delta)$$ that is contained in $$S$$.$BR 66 : \{ans_rule(10)\} $BR 67 : 68 : Given the point $$\mathbf a = P1$$ in the set 69 : $$S = \left\{"\{"\} \left(\begin{array}{c}x\\y\end{array}\right): subsets[1] \right\}$$, give the radius $$\delta$$ of the largest ball $$B(\mathbf a,\delta)$$ that is contained in $$S$$.$BR 70 : \{ans_rule(10)\} \$BR 71 : 72 : END_TEXT 73 : 74 : ANS(num_cmp([@subanswers])); 75 : ENDDOCUMENT(); # This should be the last executable line in the problem.