Problem 3 - Discrete Mathematics with Applications

Question

The Celsius and Fahrenheit scales are related by the formula \(F=\frac{9}{5} C+32\). $$g(-3.4)$$

Step-by-Step Solution

Answer

To find the Fahrenheit value when Celsius is -3.4, substitute the value into the given formula: \(F = \frac{9}{5} (-3.4) + 32\). After calculation, we find that \(g(-3.4) = 25.88\), which means -3.4 degrees Celsius is equivalent to 25.88 degrees Fahrenheit.

Step 1: Identify the given formula and the value to substitute

We are given the formula to convert Celsius to Fahrenheit: \(F = \frac{9}{5} C + 32\), and we need to find the Fahrenheit value when Celsius is -3.4, that is, \(g(-3.4)\).

Step 2: Substitute the given Celsius value into the formula

Replace C with -3.4 in the formula: \(F = \frac{9}{5} (-3.4) + 32\).

Step 3: Calculate the value inside the brackets

Multiply -3.4 by the fraction \(\frac{9}{5}\): \((-3.4) \times \frac{9}{5} = -6.12\)

Step 4: Add 32 to the result from Step 3

Now add 32 to -6.12: \(-6.12 + 32 = 25.88\)

Step 5: Simplify and give the final answer

So, \(g(-3.4) = 25.88\). Converting -3.4 degrees Celsius to Fahrenheit results in 25.88 degrees Fahrenheit.

Key Concepts

Discrete Mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers which have the property of varying