![]() 18 ° may be forecast for a cold winter day in Michigan, while a temperature of 43 ° may be predicted for a hot summer day in Arizona.) ![]() If the United States were to adopt the Celsius scale, forecast temperatures would rarely go below -30 ° or above 45 °. On the Celsius scale, water freezes at 0 ° and boils at 100 °. #TEMPERATURE CONVERSION EQUATIONS HOW TO#Learning about the different scales-including how to convert between them-will help you figure out what the weather is going to be like, no matter which country you find yourself in.įahrenheit and Celsius are two different scales for measuring temperature.Ī thermometer measuring a temperature of 22 ° Celsius is shown here. In the United States, temperatures are usually measured using the Fahrenheit scale, while most countries that use the metric system use the Celsius scale to record temperatures. The difference is that the two countries use different temperature scales. #TEMPERATURE CONVERSION EQUATIONS TV#For example, a TV weatherman in San Diego may forecast a high of 89 °, but a similar forecaster in Tijuana, Mexico-which is only 20 miles south-may look at the same weather pattern and say that the day’s high temperature is going to be 32 °. If you have been to other countries, though, you may notice that meteorologists measure heat and cold differently outside of the United States. A hot summer day may reach 100 ° in Philadelphia, while a cool spring day may have a low of 40 ° in Seattle. In addition to telling you what the weather conditions will be like (sunny, cloudy, rainy, muggy), they also tell you the day’s forecast for high and low temperatures. Independent variable so we can rewrite this, using function notation, asĪnd this function converts the temperature in degrees Fahrenheit to theĬorresponding temperature in degrees Celsius.Turn on the television any morning and you will see meteorologists talking about the day’s weather forecast. We are used to $y$ being the dependent variable and $x$ being the Sides of the equation and then multiplying both sides of the new equation by In degrees Celsius we switch the roles of $x$ and $y$ in the equation above,Īnd solve for $x$ in terms of $y$. If we wish to have a function that takes a temperature in degrees Fahrenheit and gives its equivalent Takes a temperature in degrees Celsius and gives its equivalent in degrees Fahrenheit. Our function, $f$, described by the equation ![]() While for temperatures below $-40$ the temperature in degreesįahrenheit is less than the corresponding temperature in degrees Celsius. For temperatures above $-40$, the temperature inĭegrees Fahrenheit will be greater than the corresponding temperature in degrees Celsius The temperature which registers the same on the Fahrenheit and Celsius Solving for $a$ gives $a = \fracx 32 = x$ for $x$, Namely that 100 degrees Celsius converts to 212 degrees Fahrenheit: In order to find the slope, $a$, we can use the second piece of data given, ![]() We are given that zero degrees Celsius converts to Since $f$ is a linear function of $x$, the temperature in degrees Celsius, we can write $f(x) = ax b$. This is a subtle but important argument, one that eventually leads to more advanced topics like continuity and the Intermediate Value Theorem. ![]() Since there is a linear relationship between $F$ and $C$, there must then be some value of $C$ between $C=-100$ and $C=0$ where in fact $F=C$. Namely, we can first easily check that $F\lt C$ when, say, $C=-100$, and that $F\gt C$ when, for example, $C=0$. In part (c), students could also argue try to give an intuitive argument for the existence of such a point, reasoning via the linear relationship between degrees Fahrenheit (F) and degrees Celsius (C). Reasoning about quantities and/or solving a linear equation. The inverse of a linear function while the third part requires The first part of this task provides an opportunity to constructĪ linear function given two input-output pairs. Temperature conversions provide a rich source of linear functions whichĪre encountered not only in science but also in our every day lives when we ![]()
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