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(D) The relationship between the temperature on the centigrade scale $(C)$ and the Fahrenheit scale $(F)$ is given by the formula: $F = \frac{9}{5}C +

Vedclass · Accepted Answer

$54$

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(D) The relationship between the temperature on the centigrade scale $(C)$ and the Fahrenheit scale $(F)$ is given by the formula: $F = \frac{9}{5}C + 32$.Let the initial temperature be $C_1$ and the final temperature be $C_2$. The increase in temperature on the centigrade scale is $\Delta C = C_2 - C_1 = 30^{\circ}C$.The corresponding temperatures on the Fahrenheit scale are $F_1 = \frac{9}{5}C_1 + 32$ and $F_2 = \frac{9}{5}C_2 + 32$.The increase in temperature on the Fahrenheit scale is $\Delta F = F_2 - F_1$.Substituting the expressions for $F_1$ and $F_2$:$\Delta F = (\frac{9}{5}C_2 + 32) - (\frac{9}{5}C_1 + 32) = \frac{9}{5}(C_2 - C_1) = \frac{9}{5}(\Delta C)$.Given $\Delta C = 30$,we have:$\Delta F = \frac{9}{5} 	imes 30 = 9 	imes 6 = 54^{\circ}F$.Therefore,the increase in temperature on the Fahrenheit scale is $54^{\circ}F$.

On the centigrade scale,the temperature of a body increases by $30$ degrees. The increase in temperature on the Fahrenheit scale is ..............

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