Hi all,
In the problem below, the first answer blank is supposed to only accept $R1*$c-$R2*Q/($V-2*t) but it seems to also accept $R1*$c-$R2*Q/($V + 2*t) and $R1*$c-$R2*Q/($V). Any ideas about what is going on?
Thanks,
Jason
## DESCRIPTION
## First order ODEs: Applications
## ENDDESCRIPTION
## DBsubject(Differential equations)
## DBchapter(First order differential equations)
## DBsection(Application)
## Date(01/01/2012)
## Institution(University of Arizona)
## Author(May Yeap)
## KEYWORDS('differential equations','newtonian mechanics','first order', 'linear')
##############################
# Initialization
DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"AnswerFormatHelp.pl",
"PGunion.pl",
"PGcourse.pl",
"PGbasicmacros.pl",
"PGML.pl",
"contextPiecewiseFunction.pl"
);
TEXT(beginproblem());
#############################
# Setup
Context()->variables->add(t=>"Real");
Context()->variables->add(Q=>"Real");
$c = random(1.1,5,0.2);
$R1 = random(3,7,1);
$R2 = Compute("$R1+2");
$V = random(100,1000,20);
$answer1 = Compute("$R1*$c-$R2*Q/($V-2*t)");
$answer2 = Compute("($c*$R1)*(-2*t+((1-2*t/$V)**($R2/2))*(-$V)+$V)/(-2+$R2)");
$answer3 = Compute("$V/2");
#############################
# Main text
BEGIN_PGML
A tank initially contains [$V] gal of pure water. Brine containing [$c] lb/gal of salt is poured into the tank at a rate of [$R1] gal/min. Suppose the solution in the tank is instantly well mixed and drained out at a rate of [$R2] gal/min.
Let [`Q=Q(t)`] be the quantity of salt in the tank at time [`t`] minutes.
What is the initial condition?
[`Q(0)=`][___________]{"0"}[`lb`]
Set up the differential equation for the quantity of salt in the tank:
[`Q^{\, \prime}=`][__________________]{$anwser1->cmp} lb/min.
Find the particular solution:
[`Q(t)=`][__________________]{$answer2->cmp} lb.
When does this differential equation become invalid?
[`t=`][_______________]{$answer3->cmp} min.
END_PGML
##############################
# Answer evaluation
$showPartialCorrectAnswers = 1;
ENDDOCUMENT();