The linear density in a rod 10 meters long is \frac{8}{\sqrt{x+4}} , where x is measured in...

Question:

The linear density in a rod 10 meters long is {eq}\frac{8}{\sqrt{x+4}} {/eq}, where {eq}x {/eq} is measured in meters from one end of the rod. Find the average density of the rod.

Average density of a Function:

find total mass of the rod by integration . Then divide this total mass by total length of the rod to get the average density of the rod

Answer and Explanation: 1

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Linear mass density is {eq}\rho(x)=\frac{8}{\sqrt{x+4}} {/eq}

Mass of small element of the rod of length dx is

{eq}dm=\rho(x) dx {/eq}

{eq}dm=\fr...

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Law of Averages: Definition & Formula

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Chapter 5 / Lesson 8
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In this lesson, you will learn about the law of averages and how it compares to the law of large numbers. You will also learn the formula for the law of averages. Following this lesson will be a brief quiz to test your new knowledge.


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