QuestionBased on the equation $C=\frac{5}{9}(F-32)$ , which statements about temperature changes are true? A) I only B) II only C) III only D) I and II only

Studdy Solution

STEP 1

Assumptions1. The formula for converting Fahrenheit to Celsius is given by $C=\frac{5}{9}(-32)$ . We are asked to verify the truth of three statements about temperature conversion.

STEP 2

Let's start with the first statement "A temperature increase of1 degree Fahrenheit is equivalent to a temperature increase of $\frac{5}{9}$ degree Celsius."To check this, we can use the given formula. If we increase the Fahrenheit temperature by1, the new Fahrenheit temperature will be $+1$ .We can substitute this into the formula to find the corresponding Celsius temperature.
$C'=\frac{5}{9}((+1)-32)$

STEP 3

implify the equation by distributing the $\frac{5}{9}$ .
$C'=\frac{5}{9}+\frac{5}{9}-\frac{160}{9}$

STEP 4

Subtract the original Celsius temperature from the new Celsius temperature to find the increase in Celsius temperature.
$\Delta C = C' - C$ $\Delta C = \left(\frac{}{9}+\frac{}{9}-\frac{160}{9}\right) - \left(\frac{}{9}-\frac{160}{9}\right)$

STEP 5

implify the equation to find the increase in Celsius temperature.
$\Delta C = \frac{5}{9}$ This confirms the first statement is true.

STEP 6

Now, let's check the second statement "A temperature increase of1 degree Celsius is equivalent to a temperature increase of1.8 degrees Fahrenheit."
To check this, we can use the given formula. If we increase the Celsius temperature by1, the new Celsius temperature will be $C+1$ .We can rearrange the formula to find the corresponding Fahrenheit temperature.
$' = \frac{9}{5}(C+1) +32$

STEP 7

implify the equation by distributing the $\frac{9}{5}$ .
$' = \frac{9}{5}C + \frac{9}{5} +32$

STEP 8

Subtract the original Fahrenheit temperature from the new Fahrenheit temperature to find the increase in Fahrenheit temperature.
$\Delta F = F' - F$ $\Delta F = \left(\frac{}{5}C + \frac{}{5} +32\right) - \left(\frac{}{5}C +32\right)$

STEP 9

implify the equation to find the increase in Fahrenheit temperature.
$\Delta F =.8$ This confirms the second statement is true.

STEP 10

Finally, let's check the third statement "A temperature increase of $\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of degree Celsius."
To check this, we can use the given formula. If we increase the Fahrenheit temperature by $\frac{5}{9}$ , the new Fahrenheit temperature will be $+\frac{5}{9}$ .We can substitute this into the formula to find the corresponding Celsius temperature.
$C'=\frac{5}{9}((+\frac{5}{9})-32)$

STEP 11

implify the equation by distributing the $\frac{5}{9}$ .
$C'=\frac{5}{9}+\frac{5}{45}-\frac{160}{9}$

STEP 12

Subtract the original Celsius temperature from the new Celsius temperature to find the increase in Celsius temperature.
$\Delta C = C' - C$ $\Delta C = \left(\frac{5}{9}+\frac{5}{45}-\frac{160}{9}\right) - \left(\frac{5}{9}-\frac{160}{9}\right)$

STEP 13

implify the equation to find the increase in Celsius temperature.
$\Delta C = \frac{5}{45}$ This shows that the third statement is false.
Therefore, the correct answer is D) I and II only.

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