Question

.
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?

1. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature $\huge \: \frac{5}{9}$ degree Celsius.

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

3. A temperature increase of $\huge \: \frac{5}{9}$ 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

Answer 1

$\huge\sf\red{Answer}:$

$\huge\sf\underline{Given}:$

$= \sf \frac{5}{9} (f - 32)$

$\sf \: f = \frac{5}{9}(c) + 32$

$\huge\sf\green{If\: F'\: = F + 1}$

$\sf \: c' = \frac{5}{9} (f' - 32)$

$\sf c' \: = \frac{5}{9} (f + 1 - 32)$

$\sf c' = \frac{5}{9} (f - 32) + \frac{5}{9} \times 1$

$\sf \: hence \: c' \: = c + \frac{5}{9}$

$\huge\sf\fbox\blue{ Hence a temperature increases of 1 Degree of Fahrenheit is equal to a temperature increase of 5 by 9 degree Celsius}$

$\sf\blue{ Hence \: a \: temperature \: increases \: of \: 1 \: Degree \: of \: Fahrenheit \: is \: equal \: to \: a \: temperature \: increase \: of \: \frac{5}{9} degree \: Celsius \: }</p><p>$

$\sf\red{Therefore\: first\: statement\: is\: true\:}$

$\sf(II) \: if \: c' = c + 1$

$\sf \: f' = \frac{9}{5}c' + 32$

$\sf \: f' = \frac{9}{5}(c + 1) + 32$

$\sf \: f' = ( \frac{9}{5}c \: + 32 \: ) + \frac{9}{5}$

$\sf \: f' = f + \frac{9}{5}$

$\sf \: f' = f + 1.8$

$\sf\blue{ Hence \: a \: temperature \: increases \: of \: 1 \: Degree \: of \: Fahrenheit \: is \: equal \: to \: a \: temperature \: increase \: of \: 1.8 \: degree \: fahenheit \: }</p><p>$

$\sf\purple{Therefore\: second\: statement\: is\: true\:}$

Answer 2

hence temprature decresing 1 celcius