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 the answer d?
Sorry the equation is C= 5/9(F-32)
looks good
To determine which of the statements is true, let's analyze the given equation relating temperature in Fahrenheit (F) and Celsius (C):
F = (9/5) * C + 32
Statement I claims that a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius. To verify this, we need to calculate the change in Celsius temperature when Fahrenheit temperature increases by 1.
F + 1 = (9/5) * C + 32 + 1
F + 1 = (9/5) * C + 33
To find the corresponding Celsius temperature, we solve for C:
(9/5) * C = F + 1 - 33
(9/5) * C = F - 32
C = (5/9) * (F - 32)
Comparing this with the initial equation, we can see that Statement I is true, as an increase of 1 degree Fahrenheit corresponds to an increase of (5/9) degree Celsius.
Statement II claims that a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. To verify this, we need to calculate the change in Fahrenheit temperature when Celsius temperature increases by 1.
F = (9/5) * (C + 1) + 32
F = (9/5) * C + (9/5) + 32
F = (9/5) * C + (9/5) * 32/5 + 32
F = (9/5) * C + (9/5) * 32/5 + (5/5) * 32/5
F = (9/5) * C + (9/5) * 32/5 + (32/5)
Comparing this with the initial equation, we see that Statement II is true, as an increase of 1 degree Celsius corresponds to an increase of 1.8 degrees Fahrenheit.
Statement III claims that a temperature increase of (5/9) degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. To verify this, we need to calculate the change in Celsius temperature when Fahrenheit temperature increases by (5/9).
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
F + (5/9) = (9/5) * C + 32 + (5/9)
Comparing this with the initial equation, we can see that Statement III is not true. The change in Fahrenheit temperature, (5/9) degree, does not correspond to an increase of 1 degree Celsius.
Therefore, the correct answer is D) I and II only.