Let 3.27<<5.89 represent an interval on the number line. Find the value that is in the middle of the interval.
1 answer:
Answer:
The middle value of the interval is 4.58
Step-by-step explanation:
Consider the provided interval.
We need to find the value that is in the middle of the interval.
We can find the middle value of the interval by adding the upper and lower limit and divide the sum of the upper and lower limits by 2.
Here the upper limit is 3.27 and lower limit is 5.89.
Hence, the middle value of the interval is 4.58
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Answer:
Step-by-step explanation:
The <em>Richter scale</em>, the standard measure of earthquake intensity, is a <em>logarithmic scale</em>, specifically logarithmic <em>base 10</em>. This means that every time you go up 1 on the Richter scale, you get an earthquake that's 10 times as powerful (a 2.0 is 10x stronger than a 1.0, a 3.0 is 10x stronger than a 2.0, etc.).
How do we compare two earthquake's intensities then? As a measure of raw intensity, let's call a "standard earthquake" S. What's the magnitude of this earthquake? The magnitude is whatever <em>power of 10</em> S corresponds to; to write this relationship as an equation, we can say , which we can rewrite in logarithmic form as
.
We're looking for the magnitude M of an earthquake 100 times larger than S, so reflect this, we can simply replace S with 100S, giving us the equation
.
To check to see if this equation is right, let's say we have an earthquake measuring a 3.0 on the Richter scale, so . Since taking 100 times some intensity is the same as taking 10 times that intensity twice, we'd expect that more intense earthquake to be a 5.0. We can expand the equation
using the product rule for logarithms to get the equation
And using the fact that and our assumption that
, we see that
as we wanted.