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The linear equation that converts Fahrenheit (F) to Celsius (C ) is given by the relation, `C=(5F-160)/(9)`. (i) If the temperature is `86^(@)` F , what is the temperature in Celsius ? (ii) If the temperature is `35^(@)`C, what is the temperature in Fahrenheit ? (iii) If the temperature is `0^(@)`C, what is the temperature in Fahrenheit and if the temperature is `0^(@)`F, what is the temperature in Celsius ? (iv) What is the numerical value of the temperature which is same in both the scales ? |
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Answer» Given relation is , `C=(5F-160)/(9)` `implies " " 9C=5F-160 implies 5F=9C+160` `implies " " F=(9C+160)/(5)` (i) Given, `F=86^(@)F`, then from Eq. (i), we get `C=(5xx86-160)/(9)=(430-160)/(9)=(270)/(9)=30^(@)C` (ii) Given, `C=35^(@)C`, then from Eq. (ii), we get `F=(9xx35+160)/(5)=(315+160)/(5)=(475)/(5)=95^(@)F` (iii) Given, `C=0^(@)C`, then from Eq. (ii), we get `F=(9xx0+160)/(5)=(160)/(5)=32^(@)F` `F=0^(@)F`, then from Eq. (i), we get `C=(5xx0-160)/(9)=(-160)/(9)=(-(160)/(9)).^(@)C` (iv) By given condition, C=F Put this value in Eq. (i), we get `C=(5C-160)/(9) implies 9C=5C- 160` `implies 9C- 5C= - 160` `implies 4C= - 160 implies C= (-160)/(4) implies C = - 40 = F` |
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