We appreciate your visit to The temperature on Mars roughly ranges from 70 degrees Fahrenheit to 220 degrees Fahrenheit Write an absolute value inequality that represents the given information. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To express the temperature range on Mars as an absolute value inequality, you can follow these steps:
1. Identify the Limits of the Range:
The given temperature range on Mars is from -70 degrees Fahrenheit to 220 degrees Fahrenheit.
2. Find the Midpoint of the Range:
To write an absolute value inequality, first, find the midpoint (or center) of the temperature range. This is done by averaging the two extremes of the range:
[tex]\[
\text{Midpoint} = \frac{-70 + 220}{2} = 75
\][/tex]
So, the midpoint is 75 degrees Fahrenheit.
3. Calculate the Deviation:
Next, determine how far the endpoints of the range are from this midpoint. You can use either endpoint for this calculation. We'll use 220 degrees:
[tex]\[
\text{Deviation} = 220 - 75 = 145
\][/tex]
4. Write the Absolute Value Inequality:
With the midpoint and deviation determined, you can write the absolute value inequality. The inequality represents all temperatures, [tex]\( x \)[/tex], that are within 145 degrees of 75 degrees:
[tex]\[
|x - 75| \leq 145
\][/tex]
This inequality captures the range of temperatures on Mars, meaning the actual temperature [tex]\( x \)[/tex] can be as low as -70 degrees or as high as 220 degrees.
1. Identify the Limits of the Range:
The given temperature range on Mars is from -70 degrees Fahrenheit to 220 degrees Fahrenheit.
2. Find the Midpoint of the Range:
To write an absolute value inequality, first, find the midpoint (or center) of the temperature range. This is done by averaging the two extremes of the range:
[tex]\[
\text{Midpoint} = \frac{-70 + 220}{2} = 75
\][/tex]
So, the midpoint is 75 degrees Fahrenheit.
3. Calculate the Deviation:
Next, determine how far the endpoints of the range are from this midpoint. You can use either endpoint for this calculation. We'll use 220 degrees:
[tex]\[
\text{Deviation} = 220 - 75 = 145
\][/tex]
4. Write the Absolute Value Inequality:
With the midpoint and deviation determined, you can write the absolute value inequality. The inequality represents all temperatures, [tex]\( x \)[/tex], that are within 145 degrees of 75 degrees:
[tex]\[
|x - 75| \leq 145
\][/tex]
This inequality captures the range of temperatures on Mars, meaning the actual temperature [tex]\( x \)[/tex] can be as low as -70 degrees or as high as 220 degrees.
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