Question

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?

1 A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.
2 A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
3 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

Answer 1

Answer:

option D)

C = (5/9)(F-32)......1

=> C(9/5) + 32 = F......2

(1) let there is 1degree rise in F

therefore

C' = (5/9) ( F+1-32)

putting value of F from equation 2

we get,

C' = (5/9) { C(9/5) + 32 +1 -32}

=> C' = (5/9) { C(9/5) +1 }

=> C' = C + 5/9

so for 1 degree rise in Fahrenheit ther is 5/9 degree rise in celcius

(2) let there is 1degree rise in celcius scale

=> C+1 = (5/9)(F'-32)

putting value of C from equation 1

we get,

=> (5/9)(F-32) + 1 = (5/9)(F'-32)

=> (5/9)F - (5/9)32 + 1 = (5/9)F' - (5/9)32

=> (5/9)F' - (5/9)F = 1

=> (5/9)( F' -F) = 1

=> F'-F = (1)(9/5)

=> F'-F = 1.8

so for 1degree change in celcius scale, there is 1.8 degree change in Fahrenheit scale

as only option D has both I & II , so it would be answer