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Chapter 2: Problem 22

Find a function \(M\) such that \(M(m)\) is the number of miles in \(m\) meters.

Short Answer

Expert verified
The short answer is: Given the conversion factor 1 mile = 1609.34 meters, the function \(M(m)\) that converts \(m\) meters to miles is given by \(M(m) = \frac{m}{1609.34}\, miles\).

Step by step solution

01

Understand the relationship between miles and meters

We need to find a function that can convert meters to miles. To do that, we should be aware of the conversion factor between the two units: 1 mile = 1609.34 meters.
02

Set up the conversion factor as a fraction

In order to find the function M(m), we will set up the conversion factor as a fraction, where miles will be in the numerator and meters in the denominator: \(\frac{1 \, mile}{1609.34 \, meters}\).
03

Using the conversion factor to create the function M(m)

Now, we will write the function \(M(m)\) such that \(M(m)\) is the number of miles in the given meters \(m\). To do this, we should multiply \(m\) meters by the conversion factor. This will convert the unit of meters into miles, as needed. Thus, the function \(M(m)\) becomes: \[ M(m) = m * \frac{1 \, mile}{1609.34 \, meters} \]
04

Simplify the function M(m)

The function \(M(m)\) is already in its simplest form. Hence, this function will convert any number of meters \(m\) to its equivalent value in miles: \[ M(m) = \frac{m}{1609.34} \, miles \] So, use this function to convert any given number of meters to miles.

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