question_answer 38)

                  Calculate the temperature which has same numeral value on Celsius and Fahrenheit scale.                

Answer:

                  Let \[{{\theta }_{1}}\] be the temperature at which Celsius and Fahrenheit scales coincide, i.e., \[{{t}_{C}}={{t}_{F}}={{\theta }_{1}}\].                 From \[{{t}_{C}}=\frac{5}{9}({{t}_{F}}-32),\,{{\theta }_{1}}=\frac{5}{9}({{\theta }_{1}}-32)\]                 or  \[9{{\theta }_{1}}=5{{\theta }_{1}}-160\] or \[{{\theta }_{1}}=-{{40}^{o}}\]