(a) In 1983 the temperature at the Soviet Vostok station in Antarctica reached a record low of `-89.2^@C` , what temperature is this on the Fahrenheit scale ? (b) The highest officially recorded temperature in the continental United States was `134^@F` in Death Valley, California , what is this temperature on the Celsius scale ?

Answer

To solve the problem, we need to convert temperatures between Celsius and Fahrenheit using the appropriate formulas.

### Part (a): Convert -89.2°C to Fahrenheit

1. **Identify the formula for conversion from Celsius to Fahrenheit:**
\[ F = \frac{9}{5}C + 32 \]
where \( F \) is the temperature in Fahrenheit and \( C \) is the temperature in Celsius.

2. **Substitute the value of \( C \) (-89.2°C) into the formula:**
\[ F = \frac{9}{5}(-89.2) + 32 \]

3. **Calculate \( \frac{9}{5} \times -89.2 \):**
\[ \frac{9}{5} \times -89.2 = -160.56 \]

4. **Add 32 to the result:**
\[ F = -160.56 + 32 = -128.56 \]

5. **Round the result:**
\[ F \approx -128.6°F \]

### Part (b): Convert 134°F to Celsius

1. **Identify the formula for conversion from Fahrenheit to Celsius:**
\[ C = \frac{5}{9}(F - 32) \]
where \( C \) is the temperature in Celsius and \( F \) is the temperature in Fahrenheit.

2. **Substitute the value of \( F \) (134°F) into the formula:**
\[ C = \frac{5}{9}(134 - 32) \]

3. **Calculate \( 134 - 32 \):**
\[ 134 - 32 = 102 \]

4. **Now calculate \( \frac{5}{9} \times 102 \):**
\[ C = \frac{5}{9} \times 102 \approx 56.67 \]

5. **Round the result:**
\[ C \approx 56.7°C \]

### Final Answers:
(a) The temperature of -89.2°C is approximately -128.6°F.
(b) The temperature of 134°F is approximately 56.7°C.