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

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## 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')

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##############################

# Initialization

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DOCUMENT();

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loadMacros(

"PGstandard.pl",

"MathObjects.pl",

"AnswerFormatHelp.pl",

"PGunion.pl",

"PGcourse.pl",

"PGbasicmacros.pl",

"PGML.pl",

"contextPiecewiseFunction.pl"

);

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TEXT(beginproblem());

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#############################

# Setup

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Context()->variables->add(t=>"Real");

Context()->variables->add(Q=>"Real");

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$c = random(1.1,5,0.2);

$R1 = random(3,7,1);

$R2 = Compute("$R1+2");

$V = random(100,1000,20);

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$answer1 = Compute("$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");

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#############################

# Main text

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BEGIN_PGML

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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.

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Let [`Q=Q(t)`] be the quantity of salt in the tank at time [`t`] minutes.

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What is the initial condition?

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[`Q(0)=`][___________]{"0"}[`lb`]

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Set up the differential equation for the quantity of salt in the tank:

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[`Q^{\, \prime}=`][__________________]{$anwser1->cmp} lb/min.

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Find the particular solution:

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[`Q(t)=`][__________________]{$answer2->cmp} lb.

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When does this differential equation become invalid?

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[`t=`][_______________]{$answer3->cmp} min.

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END_PGML

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##############################

# Answer evaluation

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$showPartialCorrectAnswers = 1;

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ENDDOCUMENT();