Question

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Answer 1

Answer:

D) I and II only

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

II) A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit

Step-by-step explanation:

- 5/9 and -32 are both constants in this equation, where F and C are variables directly proportional to each other.

Explanation on statement I (Why true?):

- on a degree Celsius by a degree Fahrenheit graph, if our degree Fahrenheit was 0, our degree Celsius would be 5/9 * -32

( 1] imagine this in your head, 2] draw on paper ,or 3] use Desmos )

- in the equation let's focus on  ' F - 32 '

- assume F - 32 = x ,     so C = 5/9 * x  

                                           C = 5x/9x

- if the degree Fahrenheit increases by 1:

(F + 1) - 32 = x + 1

,so C = 5/9 * (x + 1)

     C = 5x/9x + 5/9

This demonstrates if F increases by 1, C increases by 5/9

Explanation on statement II (Why true?) :

C = 5/9 * (F - 32)                  |      C = 5/9 * (F - 32)

if we substitute C with 1      |      if we substitute C with 2

1 = 5/9 * (F - 32)                   |       2 = 5/9 * (F - 32)

1 * (5/9)^ -1 = F - 32              |       2 * (5/9)^ -1 = F - 32

9/5 + 32 = F                         |       18/5 + 32 = F

F = 33.8                                |       F = 35.6

so, increase of degree Celsius is equivalent to 1.8 (35.6 - 33.8)

Explanation on statement III (Why false?) :

C = 5/9 * (F - 32)

if we substitute F with 5/9

C = 5/9 * ([5/9] - 32)           (using calculator here)

C = - 17.469135802 469135802(recurring)...

- C does not equal 1

so, this statement is false