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Understanding the concept of dew point is crucial for anyone studying weather phenomena and physics related to atmospheric conditions. The dew point is the temperature at which air becomes completely saturated with moisture and water vapor begins to condense into dew. This measurement is key in meteorology as it provides valuable information about the moisture content in the air.

The dew point is determined by the amount of water vapor present; the higher the vapor content, the higher the dew point. It's an important concept because it directly relates to human comfort. When the dew point is high, say around \(70^{\rm F}\), the air feels muggy and heavy because the air contains a large amount of moisture. Conversely, a low dew point indicates dry air.

In our exercise, the dew point is given as \(70^{\rm F}\), which can be considered a threshold for the relative humidity calculation using a linear function. This plays into the concept of humidity and comfort as well, offering an understanding of what temperature ranges start to become uncomfortable due to high moisture in the air.

Linear functions are one of the fundamental concepts in algebra and form the basis for understanding various phenomena in both mathematics and real-world applications. A linear function represents a straight line on a graph and is typically written in the form \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

In the context of our exercise, the relative humidity (RH) is described by the linear function \(RH(x)=-2.58x+280\). The slope \(-2.58\) indicates how the humidity decreases as the temperature increases, and \(280\) is where the line would intersect the y-axis, which in this case would be the hypothetical relative humidity if the temperature was 0.

This linear function is used to approximate the relative humidity based on the actual temperature, allowing us to make predictions and understand the relationship between temperature and humidity. By analyzing the coefficients of the linear function, one can determine how changing one variable will affect the other.

An inequality is similar to an equation but instead of expressing equality, it shows a relationship where one side is not necessarily equal to the other but is either less than, greater than, or equal to the other side. Solving inequalities is about finding the values of a variable that make the inequality true.

In our exercise, to find the range of temperatures where the relative humidity is at least 50%, we're given the inequality \(-2.58x + 280 \geq 50\). The steps to solve this involve rearranging the inequality to isolate the variable \(x\), which would then provide us with a range of values that satisfy the condition.

It's important to remember that when you multiply or divide both sides of an inequality by a negative number, as in step 2 of our solution, you must flip the direction of the inequality. The solved inequality indicates the range of temperatures that meet the criteria, providing a practical way to understand intervals in context, such as comfort zones in weather forecasts or constraints in engineering problems.