Question

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.

II. 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​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

$\red{\rm :\longmapsto\:C = \dfrac{5}{9}(F - 32)}$

➢ Now, Let we take Condition I.

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

degree Celsius.

➢ Let assume initially when F = y, the corresponding value of C is

$\red{\rm :\longmapsto\:C = \dfrac{5}{9}(y - 32)}$

➢ Let assume that F take the value y + 1 and L let corresponding value of C be x.

So,

${\rm :\longmapsto\:x = \dfrac{5}{9}(y + 1 - 32)}$

${\rm :\longmapsto\:x = \dfrac{5}{9}(y - 32)} + \dfrac{5}{9}$

$\rm :\longmapsto\:x = C + \dfrac{5}{9}$

$\bf\implies \:x \: increased \: by \: \dfrac{5}{9} \: \degree C$

So,

$\bf\implies \:\boxed{ \bf{ \: I \: is \: true}}$

➢ Now, Let we take Condition II.

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

➢ Let assume that C take the value x + 1 and Let assume that corresponding value of F be y.

So,

$\red{\rm :\longmapsto\:C = \dfrac{5}{9}(F - 32)}$

$\red{\rm :\longmapsto\:\dfrac{9}{5} C = F - 32}$

$\red{\rm :\longmapsto\:F = \dfrac{9}{5} C + 32}$

➢ Now, Let assume initially when C = x, then F is

$\red{\rm :\longmapsto\:F = \dfrac{9}{5} x + 32}$

Now, on substituting the values of C and F we get

${\rm :\longmapsto\:y = \dfrac{9}{5}(x + 1) + 32}$

${\rm :\longmapsto\:y = \dfrac{9}{5}x+ 32 + \dfrac{9}{5} }$

${\rm :\longmapsto\:y =F+ \dfrac{9}{5} }$

${\rm :\longmapsto\:y =F+ 1.8 }$

$\bf\implies \:y \: increased \: by \: 1.8 \: \degree F$

$\bf\implies \:\boxed{ \bf{ \: II \: is \: true}}$

➢ Now, Let take Condition III.

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

➢ Let assume that F take the value y + 5/9 and corresponding value of C be x.

So,

${\rm :\longmapsto\:x = \dfrac{5}{9}\bigg(y + \dfrac{5}{9} - 32\bigg)}$

${\rm :\longmapsto\:x = \dfrac{5}{9}\bigg(y - 32\bigg) + \dfrac{25}{81} }$

${\rm :\longmapsto\:x = C + \dfrac{25}{81} }$

$\bf\implies \:x \: increased \: by \: \dfrac{25}{81} \: \degree C$

$\bf\implies \:\boxed{ \bf{ \: III \: is \: false}}$

• Hence, Option (D) is correct