Maths-
General
Easy

Question

With the usual meaning for a, b, c and s if straight capital delta be the area of a triangle then the error in straight capital delta resulting from a small error in the measurement of c, is

  1. fraction numerator capital delta over denominator 4 end fraction open parentheses fraction numerator 1 over denominator s end fraction plus fraction numerator 1 over denominator s minus a end fraction plus fraction numerator 1 over denominator s minus b end fraction minus fraction numerator 1 over denominator s minus c end fraction close parentheses delta c    
  2. fraction numerator 1 over denominator 4 end fraction open parentheses fraction numerator 1 over denominator s end fraction plus fraction numerator 1 over denominator s minus a end fraction plus fraction numerator 1 over denominator s minus b end fraction plus fraction numerator 1 over denominator s minus c end fraction close parentheses delta c    
  3. fraction numerator capital delta over denominator 4 end fraction open parentheses fraction numerator 1 over denominator s end fraction plus fraction numerator 1 over denominator s minus a end fraction plus fraction numerator 1 over denominator s minus b end fraction plus fraction numerator 1 over denominator s minus c end fraction close parentheses    
  4. open parentheses fraction numerator 1 over denominator s end fraction plus fraction numerator 1 over denominator s minus a end fraction plus fraction numerator 1 over denominator s minus b end fraction plus fraction numerator 1 over denominator s minus c end fraction close parentheses delta c    

The correct answer is: fraction numerator capital delta over denominator 4 end fraction open parentheses fraction numerator 1 over denominator s end fraction plus fraction numerator 1 over denominator s minus a end fraction plus fraction numerator 1 over denominator s minus b end fraction minus fraction numerator 1 over denominator s minus c end fraction close parentheses delta c


    table row cell capital delta equals square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root end cell row cell l o g invisible function application capital delta equals fraction numerator 1 over denominator 2 end fraction left square bracket left parenthesis l o g invisible function application s plus l o g invisible function application left parenthesis s minus a right parenthesis end cell row cell plus l o g invisible function application left parenthesis s minus b right parenthesis plus l o g invisible function application left parenthesis s minus c right parenthesis right square bracket end cell row cell S equals fraction numerator a plus b plus c over denominator 2 end fraction end cell end table

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