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Chapter 2: Problem 25

Solve each problem. As of \(2009,\) the highest temperature ever recorded in Tennessee was \(45^{\circ} \mathrm{C} .\) Find the corresponding Fahrenheit temperature.

Short Answer

Expert verified
113^{\text{掳}} \text{F}

Step by step solution

01

- Understand the formula for converting Celsius to Fahrenheit

To convert from Celsius to Fahrenheit, use the formula: \[ F = \frac{9}{5}C + 32 \] where \( F \) represents the temperature in Fahrenheit and \( C \) represents the temperature in Celsius.
02

- Substitute the given Celsius temperature into the formula

Replace \( C \) with \( 45 \) in the formula: \[ F = \frac{9}{5}(45) + 32 \]
03

- Calculate the Fahrenheit temperature

First, multiply \( \frac{9}{5} \) by \( 45 \): \[ \frac{9}{5} \times 45 = 81 \] Then add \( 32 \) to the result: \[ 81 + 32 = 113 \] Thus, the Fahrenheit temperature is \( 113^{\text{掳}} \text{F} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Temperature Conversion
Temperature conversion is transforming temperature measurements from one unit to another. The two most common temperature scales are Celsius (掳C) and Fahrenheit (掳F). Scientists and most countries around the world use degrees Celsius. However, Fahrenheit is still used in the United States and some Caribbean countries. To convert between these two, you need to understand and apply proper formulas. Converting temperatures is crucial for various fields, including science, engineering, and daily weather reporting.
Here's how you do it:
Fahrenheit Formula
The formula to convert Celsius to Fahrenheit is:
\[ F = \frac{9}{5}C + 32 \]
This formula takes a temperature in Celsius and converts it into Fahrenheit. The 'F' represents degrees Fahrenheit, and 'C' represents degrees Celsius.
  • \( \frac{9}{5} \) part scales the Celsius temperature.
  • Adding 32 modifies the scaled temperature to match the Fahrenheit scale.
Using this formula ensures you get an accurate temperature conversion.
Let's look at the formula in action, using an example of 45掳C:
Arithmetic Operations
Solving the temperature conversion requires some basic arithmetic operations. Let鈥檚 go through them using the example of converting 45掳C to Fahrenheit.
  • First, substitute 45 for C in the formula:
\[ F = \frac{9}{5}(45) + 32 \]
  • Next, perform the multiplication:
\( \frac{9}{5} \times 45 = 81 \)
  • Lastly, add 32 to the result:
\( 81 + 32 = 113 \)
Thus, 45掳C converts to 113掳F. Using simple arithmetic operations - multiplication and addition - you can easily convert between temperature scales.
By breaking down the problem into smaller steps, it becomes manageable and clearer. Always follow each step carefully for accurate results.

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Most popular questions from this chapter

When a consumer loan is paid off ahead of schedule, the finance charge is less than if the loan were paid off over its scheduled life. By one method, called the rule of \(78,\) the amount of unearned interest (the finance charge that need not be paid) is given by $$ u=f \cdot \frac{k(k+1)}{n(n+1)} $$ In the formula, u is the amount of unearned interest (money saved) when a loan scheduled to run for n payments is paid off k payments ahead of schedule. The total scheduled finance charge is \(f .\) Use the formula for the rule of 78 to work Exercises \(37-40\) Donnell Boles bought a truck and agreed to pay it off in 36 monthly payments. The total finance charge on the loan was \(\$ 600 .\) With 12 payments remaining, he decided to pay the loan in full. Find the amount of unearned interest.

Answer the questions in Exercises \(5-8 .\) In a motion problem the rate is given as \(x\) mph and the time is given as 10 min. What variable expression represents the distance in miles?

As mentioned in the chapter introduction, 114.9 million U.S. households owned at least one TV set in 2009. (Source: Nielsen Media Research.) Use this information to work Exercises 43-46. Round answers to the nearest percent in Exercises \(43-44,\) and to the nearest tenth million in Exercises \(45-46 .\) About 62.0 million U.S. households owned 3 or more TV sets in \(2009 .\) What percent of those owning at least one TV set was this?

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\}\) and \(D=\\{4\\} .\) Specify each set. See Examples I and 5. $$ B \cap \emptyset $$

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\}\) and \(D=\\{4\\} .\) Specify each set. See Examples I and 5. $$ A \cap \emptyset $$
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