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Applications with Inequalities

Story problems, set notation, interval notation

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The Deep Earth

Credit: NASA
Source: http://commons.wikimedia.org/wiki/File:Earth_Western_Hemisphere_transparent_background.png
License: CC BY-NC 3.0

Have you ever wondered what makes up the Earth's interior? Like an onion, the Earth is actually composed of layers, and each layer has very unique characteristics. Using your knowledge of compound inequalities, you can describe various properties of the Earth's crust.

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The Earth is composed of four basic layers: a solid inner core, a liquid outer core, a thick mantle, and the outermost crust. The crust is solid and made up of various types of rock. The depth of the Earth's crust ranges from about 5 to 70 kilometers. Continental crust, which makes up landmasses, tends to be thicker than the oceanic crust found beneath the oceans. The majority of continental crust is between 30 to 50 km thick. (There are portions that are greater than 50 km thick, but they are rare and account for less than 10% of the Earth's continental crust.) Oceanic crust is usually between 5 to 10 km thick.

Credit: Jeremy Kemp
Source: http://commons.wikimedia.org/wiki/File:Earth-crust-cutaway-english.png
License: CC BY-NC 3.0

We can use compound inequalities to describe the above characteristics of the Earth's crust. Why compound inequalities? Well, a compound inequality can show that something is greater than one value but less than another value—both values are needed to get the whole picture. As far as the depth of Earth's crust is concerned, we'd have the following setup: \begin{align*}5 \le d \le 70\end{align*}, where \begin{align*}d\end{align*} represents depth in km. This compound inequality shows us that the crust's depth is greater than (or equal to) 5 km but less than (or equal to) 70 km. Likewise, the compound inequalities \begin{align*}30 \le t_{continental} \le 50\end{align*} and \begin{align*}5 \le t_{oceanic} \le 10\end{align*} can be used to represent the typical thicknesses of continental and oceanic crust, respectively.

See for yourself: http://www.youtube.com/watch?v=3MFr2cC3erk

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Check out the first link below to review your knowledge of compound inequalities. Watch the next video to learn more about the Earth's interior. (Keep an eye out for more properties of the Earth's layers that can be expressed as compound inequalities!)



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