Question

Fahrenheit and Celsius In the Fahrenheit temperature scale, water freezes at $32^{\circ} \mathrm{F}$ and boils at $212^{\circ} \mathrm{F}$. In the Celsius scale, water freezes at $0^{\circ} \mathrm{C}$ and boils at $100^{\circ} \mathrm{C}$. Given that the Fahrenheit temperature $F$ and the Celsius temperature $C$ are related by a linear equation, find $F$ in terms of $C$. Use your equation to find the Fahrenheit temperatures corresponding to $30^{\circ} \mathrm{C}, 22^{\circ} \mathrm{C},-10^{\circ} \mathrm{C},$ and $-14^{\circ} \mathrm{C},$ to the nearest degree.

Name: Problem 101, Chapter 1: Finite Mathematics and Applied Calculus
Uploaded: 2021-11-30T01:59:42-08:00
Duration: 2 min 36 s
Channel: Lauren Shelton

   Fahrenheit and Celsius In the Fahrenheit temperature scale, water freezes at $32^{\circ} \mathrm{F}$ and boils at $212^{\circ} \mathrm{F}$. In the Celsius scale, water freezes at $0^{\circ} \mathrm{C}$ and boils at $100^{\circ} \mathrm{C}$. Given that the Fahrenheit temperature $F$ and the Celsius temperature $C$ are related by a linear equation, find $F$ in terms of $C$. Use your equation to find the Fahrenheit temperatures corresponding to $30^{\circ} \mathrm{C}, 22^{\circ} \mathrm{C},-10^{\circ} \mathrm{C},$ and
$-14^{\circ} \mathrm{C},$ to the nearest degree.

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 7th Edition

Chapter 1, Problem 101

Instant Answer

Solved by Expert Lauren Shelton

11/30/2021

Step 1

Step 1: We know that the relationship between Fahrenheit and Celsius is linear, so we can write it in the form of a linear equation: $F = mC + b$, where $F$ is the Fahrenheit temperature, $C$ is the Celsius temperature, $m$ is the slope of the line, and $b$ is the Show more…

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Fahrenheit and Celsius In the Fahrenheit temperature scale, water freezes at $32^{\circ} \mathrm{F}$ and boils at $212^{\circ} \mathrm{F}$. In the Celsius scale, water freezes at $0^{\circ} \mathrm{C}$ and boils at $100^{\circ} \mathrm{C}$. Given that the Fahrenheit temperature $F$ and the Celsius temperature $C$ are related by a linear equation, find $F$ in terms of $C$. Use your equation to find the Fahrenheit temperatures corresponding to $30^{\circ} \mathrm{C}, 22^{\circ} \mathrm{C},-10^{\circ} \mathrm{C},$ and $-14^{\circ} \mathrm{C},$ to the nearest degree.

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Key Concepts

Slope and Intercept

The slope represents the rate of change between the two variables, while the intercept is the value when the independent variable is zero. In temperature conversions, these concepts are crucial as they define the proportional relationship and the fixed offset in the conversion formula.

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. In the context of temperature conversion, the linear equation relates the Fahrenheit and Celsius scales, capturing the constant rate of change between these two systems.

Conversion Formula

A conversion formula is used to translate measurements from one unit system to another. The Fahrenheit-to-Celsius conversion is an example where the relationship between the freezing and boiling points of water in both scales is used to derive a general linear equation linking Fahrenheit and Celsius temperatures.

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