\r\n" );
document.write( "Ikleyn took the denominator as\r\n" );
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document.write( "(sin(b)×(x-π)), as it was typed. \r\n" );
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document.write( "However, I purposely changed it to \r\n" );
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document.write( "(sin(b(x-π)).\r\n" );
document.write( "\r\n" );
document.write( "She tried to solve this problem using f(x) as it was written:\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
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document.write( "and found that it was unsolvable for b by ordinary mathematical means.\r\n" );
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document.write( "However, I assumed the student had mistyped, and that f(x) should have been\r\n" );
document.write( "this instead: \r\n" );
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document.write( "
\r\n" );
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document.write( "By making this change, I was able to solve for b using the quadratic formula.\r\n" );
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document.write( "Why did I assume that the student has mistyped?\r\n" );
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document.write( "I reasoned that no professional math problem-creator would have included \r\n" );
document.write( "only one sine function of a constant, in this case, sin(b). If a professional\r\n" );
document.write( "problem-creator included a sine function, they certainly would have used a sine\r\n" );
document.write( "function of a VARIABLE, not the sine of a CONSTANT, which would be a constant\r\n" );
document.write( "itself! So I changed the denominator so that the sine function would be of a\r\n" );
document.write( "variable, not of a constant.\r\n" );
document.write( "\r\n" );
document.write( "Also, no professional math problem-creator would create a problem that would\r\n" );
document.write( "not be solvable by ordinary means taught in normal calculus courses.\r\n" );
document.write( "\r\n" );
document.write( "So I changed the denominator (sin(b)×(x-π)) to (sin(b(x-π)) and was able to\r\n" );
document.write( "solve for b using the quadratic formula.\r\n" );
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document.write( "It made more sense to me that a typo had been made, rather than an incompetent\r\n" );
document.write( "math-problem-creator -- especially since there was a typo of a missing right\r\n" );
document.write( "parenthesis in this: \r\n" );
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document.write( "4(π^(5/ 2 \r\n" );
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document.write( "which Ikleyn mentioned.\r\n" );
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document.write( "Also, when a problem contains k, this letter is nearly always taken as an\r\n" );
document.write( "arbitrary constant, but Ikleyn found k not to be arbitrary at all. \r\n" );
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document.write( "I think my interpretation was the intended problem. Maybe Ikleyn will agree\r\n" );
document.write( "with me on that. \r\n" );
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document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-12.gif\")
