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? 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. iii. 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

option d) is correct

Explanation:

Given:

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

For statement I

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

let the initial temperature in Fahrenheit  be 0

thus,

C = (5/9)(0) - (5/9)32 = - (5/9)32

for 1° increase in Fahrenheit

we get

C = (5/9)(1) - (5/9)32 = 1 - (5/9)32

thus,

on comparing the results, statement I is true

now for statement II

let the initial temperature in Celsius  be 0

thus,

0 = (5/9)(F) - (5/9)32

or

F =  (9/5)(5/9)32 = 32

for 1° increase in Celsius

we get

1 = (5/9)(F) - (5/9)32

or

(5/9)F = 1 + (5/9)32

or

F = (9/5) + 32

or

F = 1.8 + 32

thus,

on comparing the results, statement II is true

Now, for statement III

let the initial let the initial temperature in Fahrenheit  be 0

thus,

C = (5/9)(0) - (5/9)32 = - (5/9)32 = - 17.77

for (5/9)° increase in Fahrenheit

we get

C = (5/9)(5/9) - (5/9)32 = (0.3086) - 17.77 = -17.469

thus,

on comparing the results, statement III is false

Hence, option d) is correct

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