Question

C=59(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 59degree Celsius. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.A temperature increase of 59 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

D

Step-by-step explanation:

C = 5/9(Fahrenheit - 32)

C = 5/9Farenheit - 160/9

F = 9C/5 + 32

As Fahrenheit increases by 1, C increases by 5/9.

As C increases by 1, Fahrenheit increases by 9/5 (1.8)

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9degree Celsius. (True)

A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. (True)

A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. (False)

Answer 2

D

Step-by-step explanation:

Our answer choices are:

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

- A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

- A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

Let's try the first one. We can just choose any temperature and then use the number 1 larger than it; let's do F = 10:

C = (5/9) * (10 - 32) = (5/9) * (-22) ≈ -12.2

When F = 10 + 1 = 11:

C = (5/9) * (11 - 32) = (5/9) * (-21) ≈ -11.7

We see that indeed, -11.7 - (-12.2) ≈ 0.56 ≈ 5/9, so the first is correct.

For the second, let's see what happens when C = 10 and when C = 11:

10 = (5/9) * (F - 32)

F = 50

11 = (5/9) * (F - 32)

F = 51.8

Again we see that indeed 51.8 - 50 = 1.8

So, the second choice is also correct.

Thus, the answer is D.