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| 1 : | jjholt | 314 | ## DESCRIPTION |
| 2 : | ## Related Rates | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 213 | |
| 5 : | jjholt | 314 | ## KEYWORDS('Derivative', 'Related Rates', 'Focal Length') |
| 6 : | ## Tagged by nhamblet | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Differentiation') | ||
| 10 : | ## DBsection('Related Rates') | ||
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('OSU') | ||
| 14 : | ## TitleText1('') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | jj | 213 | 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 : | |||
| 28 : | gage | 269 | TEXT(beginproblem()); |
| 29 : | jj | 213 | $showPartialCorrectAnswers = 1; |
| 30 : | |||
| 31 : | undef($q); | ||
| 32 : | |||
| 33 : | $f = random(1,8,1); | ||
| 34 : | while (not defined($q) or $q == $f) {$q=random(1,8,1)}; | ||
| 35 : | |||
| 36 : | # Present the text. | ||
| 37 : | TEXT(EV2(<<EOF)); | ||
| 38 : | If ${BM}f${EM} is the focal length of a convex lens and an object is | ||
| 39 : | placed at a distance ${BM}p${EM} from the lens, then its image | ||
| 40 : | will be at a distance ${BM}q${EM} from the lens, where ${BM}f${EM}, ${BM}p${EM}, and ${BM}q${EM} | ||
| 41 : | are related by the lens equation | ||
| 42 : | \[ \frac{1}{f} = \frac{1}{p} + \frac{1}{q} \] | ||
| 43 : | $PAR | ||
| 44 : | What is the rate of change of ${BM}p${EM} with respect to ${BM}q${EM} if | ||
| 45 : | ${BM}q = $q ${EM} and ${BM}f = $f${EM}? (Make sure you have the correct sign for the rate. Note that \(f\) is constant.) | ||
| 46 : | $PAR | ||
| 47 : | \{ans_rule(20) \} | ||
| 48 : | EOF | ||
| 49 : | |||
| 50 : | $ans = - $f**2/($q-$f)**2; | ||
| 51 : | gage | 269 | ANS(num_cmp($ans)); |
| 52 : | jj | 213 | |
| 53 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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