Question

celsius and fahrenheit
the formula to convert from celsius to fahrenheit is $f = \frac{9}{5}c + 32$. use this formula to complete the statements below. round your answers to the nearest tenth as needed.
if the temperature is $65^{\circ}$f, that is equivalent to \boxed{\space}^{\circ}c.
if the temperature is $41^{\circ}$c, that is equivalent to \boxed{\space}^{\circ}f.
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Explanation:

First part: Convert 65°F to °C

Step1: Start with the formula \( F = \frac{9}{5}C + 32 \), solve for \( C \)

Subtract 32 from both sides: \( F - 32 = \frac{9}{5}C \)
Multiply both sides by \( \frac{5}{9} \): \( C = \frac{5}{9}(F - 32) \)

Step2: Substitute \( F = 65 \) into the formula for \( C \)

\( C = \frac{5}{9}(65 - 32) = \frac{5}{9}(33) \approx 18.3 \)

Second part: Convert 41°C to °F

Step1: Use the formula \( F = \frac{9}{5}C + 32 \)

Step2: Substitute \( C = 41 \) into the formula

\( F = \frac{9}{5}(41) + 32 = \frac{369}{5} + 32 = 73.8 + 32 = 105.8 \)

Answer:

If the temperature is \( 65^\circ \text{F} \), that is equivalent to \( \boldsymbol{18.3}^\circ \text{C} \).
If the temperature is \( 41^\circ \text{C} \), that is equivalent to \( \boldsymbol{105.8}^\circ \text{F} \).