C=
5
9
(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
Answers
Answer:
Correct option is
D
I and II only
Given:- C= 95
(F−32)
⇒F= 59
C+32
(I) If F' = F + 1C ' = 95
(F ′−32)C ′ = 95
(F+1−32)C ′ = 95
(F−32)+ 95 ×1C ′ =C+ 95
Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 95 degree Celsius.
Therefore, statement I is true.
(II) If C' = C + 1F ′= 59
C ′ +32F ′= 59
(C+1)+32F ' =( 59C+32)+ 59
F ′ =F+ 59
F ′ =F+1.8
Hence, a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
Therefore, statement II is true.
(III) If F ' =F+ 95
C '= 95
(F ′ −32)C ′= 95
(F+ 95 −32)C ′ = 95
(F−32)+ 95 × 95C ′ =C+ 8125
Hence, a temperature increase of 95
degree Fahrenheit is equivalent to a temperature increase of
8125degree Celsius.
Therefore, statement III is false.