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
Step-by-step explanation:
Correct option is
D
I and II only
Given:- C=
9
5
(F−32)
⇒F=
5
9
C+32
(I) If F' = F + 1
C
′
=
9
5
(F
′
−32)
C
′
=
9
5
(F+1−32)
C
′
=
9
5
(F−32)+
9
5
×1
C
′
=C+
9
5
Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
9
5
degree Celsius.
Therefore, statement I is true.
(II) If C' = C + 1
F
′
=
5
9
C
′
+32
F
′
=
5
9
(C+1)+32
F
′
=(
5
9
C+32)+
5
9
F
′
=F+
5
9
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+
9
5
C
′
=
9
5
(F
′
−32)
C
′
=
9
5
(F+
9
5
−32)
C
′
=
9
5
(F−32)+
9
5
×
9
5
C
′
=C+
81
25
Hence, a temperature increase of
9
5
degree Fahrenheit is equivalent to a temperature increase of
81
25
degree Celsius.
Therefore, statement III is false.
>The final answer is D ( I and II only )
ANSWER EXPLANATION:
Think of the equation as an equation for a line
y=mx+b
where in this case
C=5/9(F−32)
or
C=5/9F−5/9(32)
You can see the slope of the graph is 5/9, which means that for an increase of 1 degree Fahrenheit, the increase is 5/9
of 1 degree Celsius.
C=5/9(F)
C=5/9(1)=5/9
Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9/5 degrees Fahrenheit.
C=5/9(F)
1=5/9(F)
(F)=9/5
Since
9/5 = 1.8, statement II is true.
The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of 5/9 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:
C=5/9(F)
C=5/9(5/9)
C=25/81
(whichis≠1)
An increase of 5/9
degree Fahrenheit leads to an increase of
25/81, not 1 degree, Celsius, and so Statement III is not true.
The final answer is D.