WeBWorK Problems

Answer (in the form of a function) is not graded correctly

Answer (in the form of a function) is not graded correctly

by Bentley Garrett -
Number of replies: 2
Hi:

We posted a problem with correct answer:

2/(t^2sqrt(8e^t-8e+1))

A student entered an incorrect answer:

1/(-(t^4)(8(e^t)-1-8e))^(1/2)

but it was graded as correct by WW.

This was the code that assigned the correct answer:

Context("Numeric");
Context()->variables->are(
t=>"Real"
);
parser::Assignment->Allow; 

$answer = Formula(" 2/(t^2sqrt(8e^t-8e+1)) ")->with(limits=>[1,5]);

The code for the comparison was:

ANS( $answer->cmp());

Can anyone tell what I did wrong?

Thanks!

In reply to Bentley Garrett

Re: Answer (in the form of a function) is not graded correctly

by Davide Cervone -
I am not able to reproduce the problem. The answer is marked incorrect for me. Can you provide the complete .pg file and the seed used in the problem?
In reply to Davide Cervone

Re: Answer (in the form of a function) is not graded correctly

by Bentley Garrett -
Hi Davide:

Thanks for your prompt reply!

The seed was: 176.

Below is the complete code for the .pg file. Sorry about the length, but I included everything to be safe.

Also, if it means anything, we are using version 2.4 right now. 

## DESCRIPTION
## First order ODEs: Bernoulli
## ENDDESCRIPTION

## KEYWORDS('differential equations','first order','Bernoulli')

## DBsubject('Differential Equations')
## DBchapter('First Order Differential Equations')
## DBsection('Bernoulli')
## Date('10/10/2012')
## Author('ZH')
## Institution('UTD')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


##############################
#  Initialization

DOCUMENT(); 

loadMacros(
"PGbasicmacros.pl",
"PGstandard.pl",
"MathObjects.pl",
"AnswerFormatHelp.pl",
"parserAssignment.pl",
);

TEXT(beginproblem());


#############################
#  Setup

Context("Numeric");
Context()->variables->are(
t=>"Real"
);
parser::Assignment->Allow; 

$answer = Formula(" 2/(t^2sqrt(8e^t-8e+1)) ")->with(limits=>[1,5]);

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


Context()->texStrings;

BEGIN_TEXT

Solve the following Initial Value Problem
$BR
$BR
 \(    \begin{cases} ty' + 2y + t^5y^3e^t = 0 \\ y(1)=2 \end{cases}     \)
$BR
$BR

\( y=\) \{ ans_rule(60) \}

\{ AnswerFormatHelp("formulas") \}

END_TEXT

Context()->normalStrings;



Context()->texStrings;


SOLUTION(EV3(<<'END_SOLUTION'));

$PAR SOLUTION $PAR


This is a Bernoulli equation
$BR
$BR
\[ y' + \frac2t y = -t^4y^3e^t \]
$BR
$BR
Thus, we use the substitution \( u = y^{1-3} = y^{-2} \), i.e. \( y = u^{-\frac12} \) and \( y' = -\frac12 u^{-\frac32}u' \) and we get
$BR
$BR
\[ -\frac12u^{-\frac32}u' + \frac2t u^{-\frac12} = -t^4u^{-\frac32}e^t \iff u' - \frac4tu = 2t^4e^t \]
$BR
$BR
The last equation is linear, therefore we use the integrating factor \( \mu = e^{-\int \frac{4dt}t} = \frac1{t^4} \) and we get
$BR
$BR
\[
\frac d{dt}\left(\frac u{t^4}\right)=2e^t\;\; \Leftrightarrow\;\; y^{-2}=u=2t ^4e^t+Ct^4
\]

$BR
$BR
And we obtain the following general solution:
$BR
$BR
\[ y = \frac{\pm 1}{\sqrt{2t^4e^t+Ct^4}}, \text{ and } y \equiv 0 \]
$BR
$BR
The initial value gives us:
$BR
$BR
\[ 2 = \frac{1}{\sqrt{2e+C}} \Rightarrow 2e+C = \frac14 \Rightarrow C = \frac{1-8e}{4} \]
$BR
$BR
which leads to the solution
$BR
$BR
\[ y = \frac2{t^2\sqrt{8e^t-8e+1}} \]
END_SOLUTION

Context()->normalStrings;


######################
#  Answer evaluation

$showPartialCorrectAnswers = 1;

ANS( $answer->cmp( ));

COMMENT("MathObject version.");

ENDDOCUMENT();