a) Find the temperatures for which the readings in Celsius and Fahrenheit scales differ by 5°
Plz tell. Very urgent.
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a) Find the temperatures for which the readings in Celsius and Fahrenheit scales differ by 5°
Plz tell. Very urgent.
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Answer:The formulas for converting between degree Celsius and degree Fahrenheit are:
°F=(°C∗9/5)+32
°C=(°F−32)∗5/9
To find the temperature when both are equal, we use an old algebra trick and just set ºF = ºC and solve one of the equations.
°C=(°C∗9/5)+32
°C−(°C∗9/5)=32
−4/5∗°C=32
°C=−32∗5/4
°C=−40
°F=(°F∗9/5)+32
°F−(°F∗9/5)=32
−4/5∗°F=32
°F=−32∗5/4
°F=−40
So the temperature when both the Celsius and Fahrenheit scales are the same is −40degrees.
Explanation:
Verified answer
To find:
The temperatures for which the readings in Celsius and Fahrenheit scales differ by 5°
Calculation:
Case 1 : (When C - F = 5°)
[tex] \therefore \: \rm{ \dfrac{C}{5} = \dfrac{F - 32}{9} }[/tex]
[tex] = > \: \rm{ \dfrac{5 + F}{5} = \dfrac{F - 32}{9} }[/tex]
[tex] \rm{ = > 45 + 9F = 5F - 160}[/tex]
[tex] \rm{ = > 9F - 5F = - 160 - 45}[/tex]
[tex] \rm{ = > 4F = - 205}[/tex]
[tex] \boxed{ \rm{ = > F = - {51.25}^{ \circ} }}[/tex]
So, C = (5 + F) = (5 - 51.25) = 46.25°
Case 2:( F - C = 5°)
[tex] \therefore \: \rm{ \dfrac{C}{5} = \dfrac{F - 32}{9} }[/tex]
[tex] = > \: \rm{ \dfrac{C}{5} = \dfrac{(5 + C) - 32}{9} }[/tex]
[tex] = > \: \rm{ \dfrac{C}{5} = \dfrac{C- 27}{9} }[/tex]
[tex] = > \: \rm{ 9C= 5C - 135 }[/tex]
[tex] = > \: \rm{ 4C = - 135 }[/tex]
[tex] \boxed{ = > \: \rm{ C = - {33.75}^{ \circ} }}[/tex]
F = (5 + C) = -28.75°
Hope It Helps.