From 33deb39e422c42b72dd29dfcc1f42619fc793f04 Mon Sep 17 00:00:00 2001 From: Brittni Lorton Date: Fri, 21 Apr 2023 09:39:42 -0600 Subject: [PATCH 1/2] Domain fixes, updated wording, bug fixes --- .../IA_7.1/OpenStax_IA_7.1_23.pg | 23 ++++--------------- .../IA_7.1/OpenStax_IA_7.1_27.pg | 15 ++---------- ...CCCS_Openstax_Calc1_C1-2016-002_3_8_326.pg | 4 ++-- ...CCCS_Openstax_Calc1_C1-2016-002_3_9_334.pg | 7 +++--- ...CCCS_Openstax_Calc1_C1-2016-002_3_9_350.pg | 12 ++++------ ...CCCS_Openstax_Calc1_C1-2016-002_3_9_353.pg | 7 +++--- ...CCCS_Openstax_Calc1_C1-2016-002_4_8_392.pg | 4 ++-- ...CCCS_Openstax_Calc1_C1-2016-002_5_3_182.pg | 15 +++--------- ...CCCS_Openstax_Calc2_C2-2016-002_2_7_300.pg | 6 ++--- ...CCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg | 2 +- ...CCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg | 2 +- ...CCS_Openstax_AlgTrig_AT-1-001-AS_2_5_32.pg | 6 +++-- ...CCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg | 2 +- ...penstax_AlgTrig_AT-1-001-AS_6_3_23_sup1.pg | 4 ++-- ...CCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg | 2 +- 15 files changed, 38 insertions(+), 73 deletions(-) diff --git a/Contrib/CCCS/AlgebraicLiteracy/IA_7.1/OpenStax_IA_7.1_23.pg b/Contrib/CCCS/AlgebraicLiteracy/IA_7.1/OpenStax_IA_7.1_23.pg index c3f25b8967..8a13ff0e0f 100644 --- a/Contrib/CCCS/AlgebraicLiteracy/IA_7.1/OpenStax_IA_7.1_23.pg +++ b/Contrib/CCCS/AlgebraicLiteracy/IA_7.1/OpenStax_IA_7.1_23.pg @@ -25,12 +25,11 @@ loadMacros( "PGgraphmacros.pl", "PGcourse.pl", "contextRationalFunction.pl", - + ); ############################################## - Context("RationalFunction"); $var = list_random('x', 'y', 'z', 'a', 'b', 'c', 't', 'm', 'n', 'p'); Context()->variables->are($var =>'Real'); @@ -44,20 +43,8 @@ $gcf1 = -$a; #Question $g = Formula("($b*$a - $a*$var)/($var^2 - $b**2)")->reduce; -#Answer -#The negative must go in numerator! -$f = Formula("(-$a)/($var + $b)"); - -#custom checker to make sure it is reduced. It checks to see that answers are equivalent and then checks to see that the numerators are the same. Custom checker doesn't enforce polynomial format though... -$cmp = $f->cmp(checker => sub { - my ($correct,$student,$ans) = @_; - return 0 unless $correct == $student; - return 0 unless $student->{tree}->class eq "BOP" && $student->{tree}{bop} eq "/"; - my $cnum = Formula($correct->{tree}{lop}); - my $snum = Formula($student->{tree}{lop}); -Value->Error("Your answer isn't reduced") unless (($cnum == $snum)||($cnum == -$snum)); - return 1; -}); +#Answer, testing at the removed discontinuity to ensure students simplify that factor +$f = Formula("(-$a)/($var + $b)")->with(test_at => [[$b]]); ############################################## @@ -68,7 +55,7 @@ BEGIN_PGML Simplify the rational expression. -[``[$g] = ``] [________]{$cmp} +[``[$g] = ``] [________]{$f} END_PGML @@ -91,7 +78,7 @@ In factored form, the problem is now: [`\displaystyle \frac{[$gcf1]([$var] - [$b])}{([$var] - [$b])([$var] + [$b])}`] -[`([$var] - [$b])`] is a common factor. If we reduce this we are left with [`\displaystyle [$f]`]. +[`([$var] - [$b])`] is a common factor. If we reduce this we are left with [`\displaystyle [$f1]`]. END_PGML_SOLUTION ENDDOCUMENT(); \ No newline at end of file diff --git a/Contrib/CCCS/AlgebraicLiteracy/IA_7.1/OpenStax_IA_7.1_27.pg b/Contrib/CCCS/AlgebraicLiteracy/IA_7.1/OpenStax_IA_7.1_27.pg index 24bfd4b2c8..95c6b52533 100644 --- a/Contrib/CCCS/AlgebraicLiteracy/IA_7.1/OpenStax_IA_7.1_27.pg +++ b/Contrib/CCCS/AlgebraicLiteracy/IA_7.1/OpenStax_IA_7.1_27.pg @@ -52,19 +52,8 @@ $eqn2 = Formula("$var^2 - $b**2")->reduce; $g = Formula("($c*$var^2 + ($a + $c*$b)*$var + $a*$b)/($b**2 - $var^2)")->reduce; #Answer -#The negative is in the numerator -$f = Formula("(-$c*$var - $a)/($var - $b)")->reduce; +$f = Formula("(-$c*$var - $a)/($var - $b)")->with(test_at => [[-$b]])->reduce; -#custom checker to make sure it is reduced. It checks to see that answers are equivalent and then checks to see that the numerators are the same. Custom checker doesn't enforce polynomial format though... -$cmp = $f->cmp(checker => sub { - my ($correct,$student,$ans) = @_; - return 0 unless $correct == $student; - return 0 unless $student->{tree}->class eq "BOP" && $student->{tree}{bop} eq "/"; - my $cnum = Formula($correct->{tree}{lop}); - my $snum = Formula($student->{tree}{lop}); -Value->Error("Your answer isn't reduced") unless (($cnum == $snum)||($cnum == -$snum)); - return 1; -}); ############################################## @@ -75,7 +64,7 @@ BEGIN_PGML Simplify the rational expression. -[``[$g] = ``] [________]{$cmp} +[``[$g] = ``] [________]{$f} END_PGML diff --git a/Contrib/CCCS/CalculusOne/03.8/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_8_326.pg b/Contrib/CCCS/CalculusOne/03.8/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_8_326.pg index 46a9addacb..a8c39e04b0 100644 --- a/Contrib/CCCS/CalculusOne/03.8/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_8_326.pg +++ b/Contrib/CCCS/CalculusOne/03.8/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_8_326.pg @@ -53,12 +53,12 @@ $ans2=$DSA->eval(x=>$a,y=>$b); ##The volume of a rectangular box is `V(x,y)=[$f]` BEGIN_PGML -Consider a closed rectangular box with a square base with side length `x` and height `y`. Find the surface area, `S(x,y)`. If the surface area is [$SA] square feet when [`x=[$a]`] and [`y=[$b]`], find `dy/dx`. +Consider a closed rectangular box with a square base with side length `x` and height `y`. Find the surface area formula, `S(x,y)`. If the surface area remains constant, then find `dy/dx` when [`x=[$a]`] and [`y=[$b]`]. `S(x,y)=` [_______________]{$ans1} [@ AnswerFormatHelp("formulas") @]* -When the surface area is [$SA] square feet, [`x=[$a]`], and [`y=[$b]`], `dy/dx=`[________________]{$ans2}[@ AnswerFormatHelp("numbers") @]* +If the surface area remains constant, then when [`x=[$a]`] and [`y=[$b]`], `dy/dx=`[________________]{$ans2}[@ AnswerFormatHelp("numbers") @]* END_PGML diff --git a/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_334.pg b/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_334.pg index 0656930b0e..d85116aaba 100644 --- a/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_334.pg +++ b/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_334.pg @@ -36,17 +36,16 @@ Context("Numeric"); Context()->variables->add(u => 'Real'); $a=non_zero_random(-10,10,1); -$b=non_zero_random(-10,10,1); +$b=non_zero_random(1,10,1); $f=Formula("sqrt(e^($a x)+$b x)")->reduce; - -$ans=Formula("($a*e^($a*x)+$b)/(2*sqrt(e^($a*x)+$b x))"); +#$ans = $f->D('x'); +$ans=Formula("($a*e^($a*x)+$b)/(2*sqrt(e^($a*x)+$b x))")->with(limits=>[0,12]); ########################### # Main text -## I hope you get [`[$ans1]`], [`[$ans2]`], and [`[$ans3]`]. BEGIN_PGML Find `f^\prime(x)` for [`f(x)=[$f]`]. diff --git a/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_350.pg b/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_350.pg index 56b4619bea..11f12128c7 100644 --- a/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_350.pg +++ b/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_350.pg @@ -33,23 +33,19 @@ $showPartialCorrectAnswers = 1; # Setup Context("Numeric"); -Context()->variables->set(x=>{limits=>[0.1,0.5]}); +#Context()->variables->set(x=>{limits=>[1.1,10]}); $a=non_zero_random(-10,10,1); -$b=non_zero_random(-10,10,1); -$c=non_zero_random(-10,10,1); -$d=random(2,10,1); - +if($a<0){Context()->variables->set(x=>{limits=>[0.1,0.9]});} +elsif($a>0){Context()->variables->set(x=>{limits=>[1.1,10]});} $f=Formula("(x^$a-1)^(ln (x))"); - - + $ans=Formula("(x^$a-1)^ln(x)(ln(x^$a-1)/x+ln(x)($a*x^($a-1)/(x^$a-1)))")->reduce; ########################### # Main text -## I hope you get [`[$ans1]`], [`[$ans2]`], and [`[$ans3]`]. BEGIN_PGML Use logrithmic differentiation to find `\frac{dy}{dx}` for [``y=[$f]``]. diff --git a/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_353.pg b/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_353.pg index 80f5f2c885..f9e50bebf9 100644 --- a/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_353.pg +++ b/Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_353.pg @@ -53,9 +53,9 @@ $exp2 = Compute("$min/$max"); $exp3 = Compute("$h"); Context()->noreduce('(-x)-y','(-x)+y', 'x^(-a)'); -$fun = Formula("x**{$exp1}(x**$b+$c)**{$exp2}($f*x+$g)**$h")->reduce; -$ans=Formula("(1/($a*x)+($exp2*$b*x**($b-1))/(x**$b+$c)+($h*$f)/($f*x+$g))*$fun")->reduce->with(limits=>[9,10]); - +$fun = Formula("x**{$exp1}*(x**$b+$c)**{$exp2}*($f*x+$g)**$h")->reduce; +$ans=Formula("(1/($a*x)+($exp2*$b*x**($b-1))/(x**$b+$c)+($h*$f)/($f*x+$g))*x**{$exp1}*(x**$b+$c)**{$exp2}*($f*x+$g)**$h")->reduce->with(limits=>[9,10]); + ########################### # Main text @@ -63,6 +63,7 @@ BEGIN_PGML Use logarithmic differentiation to find `\frac{dy}{dx}` for [`\displaystyle y= [$fun]`]. + `\frac{dy}{dx}=`[______________________________________________________]{$ans} [@ AnswerFormatHelp("formulas") @]* diff --git a/Contrib/CCCS/CalculusOne/04.8/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_8_392.pg b/Contrib/CCCS/CalculusOne/04.8/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_8_392.pg index ba5300f186..2bb099f178 100644 --- a/Contrib/CCCS/CalculusOne/04.8/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_8_392.pg +++ b/Contrib/CCCS/CalculusOne/04.8/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_8_392.pg @@ -41,11 +41,11 @@ $ans =0; # Main text BEGIN_PGML -Evaluate the limit, [``\lim_{x\to 0}x^{\left(\dfrac{[$a]}{\cos(x)}\right)}``], either with l'Hopital's rule or previously learned methods. +Evaluate the limit, [``\lim_{x\to 0^+}x^{\left(\dfrac{[$a]}{\cos(x)}\right)}``], either with l'Hopital's rule or previously learned methods. -[``\lim_{x\to 0}x^{\left(\dfrac{[$a]}{\cos(x)}\right)}=``][_______________]{$ans } (Enter a number, `\infty,-\infty,` or "DNE".) [@ AnswerFormatHelp("numbers") @]* +[``\lim_{x\to 0^+}x^{\left(\dfrac{[$a]}{\cos(x)}\right)}=``][_______________]{$ans } (Enter a number, `\infty,-\infty,` or "DNE".) [@ AnswerFormatHelp("numbers") @]* diff --git a/Contrib/CCCS/CalculusOne/05.3/CCD_CCCS_Openstax_Calc1_C1-2016-002_5_3_182.pg b/Contrib/CCCS/CalculusOne/05.3/CCD_CCCS_Openstax_Calc1_C1-2016-002_5_3_182.pg index 6e5a48d514..655ea72bed 100644 --- a/Contrib/CCCS/CalculusOne/05.3/CCD_CCCS_Openstax_Calc1_C1-2016-002_5_3_182.pg +++ b/Contrib/CCCS/CalculusOne/05.3/CCD_CCCS_Openstax_Calc1_C1-2016-002_5_3_182.pg @@ -30,7 +30,8 @@ loadMacros( TEXT(beginproblem()); - +########################### +# Setup Context("Numeric"); @@ -38,31 +39,21 @@ Context()->variables->add(y => 'Real'); $f = Formula("x*y*sin(2*pi/y)"); -########################### -# Setup - $a=non_zero_random(-12,12,2); $k=non_zero_random(2,10); - $ans1=0; -#$ans2=Compute("$a*$k*sin(2*pi/$k)"); - -Context()->functions->disable("Trig"); -$ans2 = $f->eval(x=>$a,y=>$k); - +$ans2=Compute("$a*$k*sin(2*pi/$k)"); ########################### # Main text - BEGIN_PGML Evaluate the following integrals using the Fundamental Theorem of Calculus, Part 2. (a) [``\int_{0}^{[$k]\pi}[$a]\cos(\theta) d\theta=``][_________________]{$ans1 }[@ AnswerFormatHelp("numbers") @]* - (b) [``\int_{0}^{2\pi}[$a]\cos\left(\dfrac{\theta}{[$k]}\right) d\theta=``][_________________]{$ans2 }[@ AnswerFormatHelp("numbers") @]* END_PGML diff --git a/Contrib/CCCS/CalculusTwo/02.7/CCD_CCCS_Openstax_Calc2_C2-2016-002_2_7_300.pg b/Contrib/CCCS/CalculusTwo/02.7/CCD_CCCS_Openstax_Calc2_C2-2016-002_2_7_300.pg index d3d73441da..7cfe6b7cac 100644 --- a/Contrib/CCCS/CalculusTwo/02.7/CCD_CCCS_Openstax_Calc2_C2-2016-002_2_7_300.pg +++ b/Contrib/CCCS/CalculusTwo/02.7/CCD_CCCS_Openstax_Calc2_C2-2016-002_2_7_300.pg @@ -40,18 +40,18 @@ $f = Formula("$a*x"); #denominator #derivative -$ans = Formula("($a - $a*ln(x))/($a**2 * x**2)"); +$ans = Formula("($a - $a*ln(x))/($a**2 * x**2)")->with(limits => [1,5]); ########################### # Main text BEGIN_PGML -Find the derivative, [`\frac{dy}{dx}`], for [`y=\frac{\ln(x)}{[$f]}`] +Find the derivative, [``\frac{dy}{dx}``], for [``y=\frac{\ln(x)}{[$f]}``] -[`\frac{dy}{dx}`]= [_______________]{$ans} [@ AnswerFormatHelp("formulas") @]* +[``\frac{dy}{dx}``]= [_______________]{$ans} [@ AnswerFormatHelp("formulas") @]* END_PGML diff --git a/Contrib/CCCS/CollegeAlgebra/5.3/RRCC_CCCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg b/Contrib/CCCS/CollegeAlgebra/5.3/RRCC_CCCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg index 6b9d3ef742..39d610e5a9 100644 --- a/Contrib/CCCS/CollegeAlgebra/5.3/RRCC_CCCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg +++ b/Contrib/CCCS/CollegeAlgebra/5.3/RRCC_CCCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg @@ -37,7 +37,7 @@ Context("Numeric"); $a=non_zero_random(-10,-1, 1); $b=non_zero_random(1,10, 1); -$c=non_zero_random(-10,1, 1); +$c=non_zero_random(-10,-1, 1); $f=Formula("$a*x(x-$b)*(x-$c)")->reduce; $y=$f->eval(x=>0); diff --git a/Contrib/CCCS/CollegeAlgebra/6.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg b/Contrib/CCCS/CollegeAlgebra/6.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg index a2135910b3..f7b0c84c76 100644 --- a/Contrib/CCCS/CollegeAlgebra/6.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg +++ b/Contrib/CCCS/CollegeAlgebra/6.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg @@ -36,7 +36,7 @@ TEXT(beginproblem()); # Setup Context("Numeric"); -Context()->operators->undefine("/"); +Context()->operators->undefine("/", "^"); $ans = Formula("log(x)"); diff --git a/Contrib/CCCS/PreCalculus/2.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_2_5_32.pg b/Contrib/CCCS/PreCalculus/2.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_2_5_32.pg index e480e4dfb2..3d85e3350c 100644 --- a/Contrib/CCCS/PreCalculus/2.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_2_5_32.pg +++ b/Contrib/CCCS/PreCalculus/2.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_2_5_32.pg @@ -45,6 +45,8 @@ $f=Formula("$a*x^2+$b*x+$c")->reduce; $ans = ($b)**2-4*$a*$c; +$ans=0; + if ( $ans>0) {$popup = PopUp( ["?","Two Real Solutions","One Real Solution","Two Complex Solutions"], @@ -56,9 +58,9 @@ elsif ($ans<0) {$popup = PopUp( "Two Complex Solutions",) } -elsif ($ans=0) {$popup = PopUp( +elsif ($ans==0) {$popup = PopUp( ["?","Two Real Solutions","One Real Solution","Two Complex Solutions"], - "One Real Solutions",) + "One Real Solution",) } diff --git a/Contrib/CCCS/PreCalculus/5.3/RRCC_CCCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg b/Contrib/CCCS/PreCalculus/5.3/RRCC_CCCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg index 6b9d3ef742..39d610e5a9 100644 --- a/Contrib/CCCS/PreCalculus/5.3/RRCC_CCCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg +++ b/Contrib/CCCS/PreCalculus/5.3/RRCC_CCCS_Openstax_AlgTrig_AT-1-001-AS_5_3_46.pg @@ -37,7 +37,7 @@ Context("Numeric"); $a=non_zero_random(-10,-1, 1); $b=non_zero_random(1,10, 1); -$c=non_zero_random(-10,1, 1); +$c=non_zero_random(-10,-1, 1); $f=Formula("$a*x(x-$b)*(x-$c)")->reduce; $y=$f->eval(x=>0); diff --git a/Contrib/CCCS/PreCalculus/6.3/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_3_23_sup1.pg b/Contrib/CCCS/PreCalculus/6.3/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_3_23_sup1.pg index ad2ca9f975..4f726d208b 100644 --- a/Contrib/CCCS/PreCalculus/6.3/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_3_23_sup1.pg +++ b/Contrib/CCCS/PreCalculus/6.3/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_3_23_sup1.pg @@ -42,8 +42,8 @@ install_problem_grader(~~&std_problem_grader); # Two random integer to grab letters -$n1 = random(0,10,1); -do{$n2 = random(0,10,1)} until ($n2 != $n1); +$n1 = random(0,9,1); +do{$n2 = random(0,9,1)} until ($n2 != $n1); $root = $letter[$n1]; diff --git a/Contrib/CCCS/PreCalculus/6.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg b/Contrib/CCCS/PreCalculus/6.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg index b9af64583e..1504b8c364 100644 --- a/Contrib/CCCS/PreCalculus/6.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg +++ b/Contrib/CCCS/PreCalculus/6.5/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_5_13.pg @@ -36,7 +36,7 @@ TEXT(beginproblem()); # Setup Context("Numeric"); -Context()->operators->undefine("/"); +Context()->operators->undefine("/", "^"); $ans = Formula("log(x)"); From 52049c244af242966a7d1a840914ffb15f742703 Mon Sep 17 00:00:00 2001 From: Brittni Lorton Date: Wed, 26 Apr 2023 15:30:15 -0600 Subject: [PATCH 2/2] spelling error --- .../6.7/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_7_sup2.pg | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Contrib/CCCS/CollegeAlgebra/6.7/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_7_sup2.pg b/Contrib/CCCS/CollegeAlgebra/6.7/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_7_sup2.pg index 1f7c62e8b8..1540ef5388 100644 --- a/Contrib/CCCS/CollegeAlgebra/6.7/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_7_sup2.pg +++ b/Contrib/CCCS/CollegeAlgebra/6.7/CCD_CCCS_Openstax_AlgTrig_AT-1-001-AS_6_7_sup2.pg @@ -58,7 +58,7 @@ Scaffold::Begin(); BEGIN_PGML -The population of a certain city was [`[$P0]`], then 5 years later the pouplation was [`[$b]`]. +The population of a certain city was [`[$P0]`], then 5 years later the population was [`[$b]`]. END_PGML