HELP
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
(Is it D I need to know if this is right to see if I am on the right track)
Weird!! Sally and i am dumb are the same person.
Did you enjoy talking to yourself?
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
9
F−
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.
Now if you really want to know what is going on here whatever names the one of you are then start with freezing and boiling of water.
water freezes at 0 C and 32 F
water boils at 100 C and 212 F
find a line that fits those points in the forn
C = m F + b
0 = m(32) + b
100 = m(212 )+ b
so
100 = m(212-32)
100 = 180 m
m = 10/18 = 5/9 remarkable
then
0 = (5/9) (32) + b
b = - (5/9)(32)
so in the end
C = (5/9)(F-32)
now the slope m 5/9 is the change in C / change in F
and
9/5 is therefore the change in F/change in C
To determine which of the options is correct, let's analyze the equation given:
C = (5/9)(F - 32)
From this equation, we can derive the following relationships:
1) For every 1 degree Fahrenheit increase (F), there will be a (5/9) degree Celsius increase (C). This corresponds to option I.
2) To determine the equivalent temperature increase in degrees Fahrenheit for a 1-degree Celsius increase (C), we need to rearrange the equation:
C = (5/9)(F - 32)
1 = (5/9)(F - 32)
Solving for F:
F - 32 = (9/5)
F = (9/5) + 32
F = 1.8 + 32
F = 33.8
Hence, for a 1-degree Celsius increase (C), there will be a 33.8 degrees Fahrenheit increase (F). This corresponds to option II.
Based on these relationships, both option I and II are correct. Therefore, the correct answer is D) I and II only.