Question

${\huge{{\mathcal{\blue{question  :-}}}}}$

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?

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

 
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ise solve krke dikhaao ab ...xD xD
without using the help of G.O.O.G.L.E .. xD ​

Answer 1

GiveN :-

• The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius.
• $\sf \dfrac{C}{5}=\dfrac{F-32}{9}$

To FinD :-

• Which of the following options are correct .

SolutioN :-

The correct options provided to us are,

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

$\sf \to$ A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

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

$\rule{200}2$

Let's check the given options one by one whether they are correct or not .

$\large\underline\red{\sf Statement - 1 }$

Let us take the intial temperature be x , then on increasing 1°F ,the temperature will be x + 1 .

$\sf :\implies \pink{ \dfrac{C}{5}=\dfrac{F-32}{9}}\\\\\sf:\implies \dfrac{C}{5}=\dfrac{x + 1 -32 }{9} \\\\\sf:\implies C =\dfrac{5}{9}( x + 1 -32 ) \\\\\sf:\implies \dfrac{5}{9}[( x -32 )+1] \\\\\sf:\implies C = \dfrac{5}{9}(x-32) +\dfrac{5}{9}$

Now we know that this 5/9 ( x -32 ) was the initial termperature in terms of Celsius . So , we can substitute C Initial .

$\sf:\implies\boxed{\pink{\frak{ C_{(new)}=C_{(Initial)}+ \dfrac{5}{9} }}}$

Hence on increasing 1°F, the temperature increase is equal to increase in of 5/9°C .

$\to \textsf{\textbf{\orange{ Hence option I is correct . }}}$

$\rule{200}2$

$\large\underline\red{\sf Statement - 2 }$

Again let us take the initial temperature be y , the the increase in one °C will be y + 1 .

$\sf :\implies \pink{ \dfrac{C}{5}=\dfrac{F-32}{9}}\\\\\sf:\implies F =\dfrac{9}{5}C + 32 \\\\\sf:\implies F = \dfrac{9}{5}(y+1) +32 \\\\\sf:\implies F = \dfrac{9}{5}y +\dfrac{9}{5} + 32 \\\\\sf:\implies F =\bigg(\dfrac{9}{5}y + 32 \bigg) + \dfrac{9}{5}\\\\\sf:\implies F = \bigg(\dfrac{9}{5}y + 32 \bigg) + 1.8$

Basically after breaking the brackets we rearranged the terms. On rearranging we see that this 9/5y +32 is equal to the intial Farenheit temperature. So we can substitute F Initial in place of that .

$\sf:\implies\boxed{\pink{\frak{ F_{(new)}=F_{(Initial)}+ 1.8 }}}$

Hence on increasing one degree Celsius , the temperature increases by 1.8° F .

$\to \textsf{\textbf{\orange{ Hence option II is correct . }}}$

$\rule{200}2$

$\large\underline\red{\sf Statement - 3}$

Let us take the intial temperature be z , then the final temperature will be , z + 1 .

$\sf:\implies\pink{ \dfrac{C}{5}=\dfrac{F-32}{9}}\\\\\sf:\implies C = \dfrac{5}{9}\bigg( z + \dfrac{5}{9} -32 \bigg) \\\\\sf:\implies C = \dfrac{5}{9}( z - 32) +\dfrac{5}{9}\times \dfrac{5}{9}\\\\\sf:\implies C= \dfrac{5}{9}( z -32) +\dfrac{25}{81}$

And Similarly we can substitute 5/9( z -32) as C Initial . Therefore ,

$\sf:\implies\boxed{\pink{\frak{ C_{(new)}=C_{(Initial)}+ \dfrac{25}{81} }}}$

Therefore on increasing 5/9 °F is equivalent to increase in 25/81 °C . Therefore the given statement is wrong .

$\to \textsf{\textbf{\orange{ Hence option III is wrong . }}}$

$\rule{200}2$

Overall option D is correct . Option I and II only .

Answer 2

$❥คɴᎦᴡєя$

option D is correct . Option I and II only .