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Chapter 2: Problem 19

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

Short Answer

Expert verified
The function \(f(m)\) that converts miles to inches is: \(f(m) = 63360 m\).

Step by step solution

01

Understand the relationship between miles, feet, and inches

There are 5280 feet in one mile and 12 inches in one foot. Let \(m\) be the number of miles and \(f(m)\) be the number of inches. We need to convert \(m\) miles into inches.
02

Convert miles to feet

To convert \(m\) miles to feet, we multiply \(m\) by the number of feet in one mile: $$ \text{Feet}(m) = m \times 5280 $$
03

Convert feet to inches

To convert the number of feet obtained in the previous step to inches, we multiply the result by the number of inches in one foot: $$ f(m) = \text{Feet}(m) \times 12 $$
04

Substitute the expression for Feet\((m)\)

We can now substitute the expression for Feet\((m)\) from Step 2 into the equation in Step 3: $$ f(m) = (m \times 5280) \times 12 $$
05

Simplify the expression

Simplify the expression by multiplying the constants: $$ f(m) = m \times (5280 \times 12) $$ $$ f(m) = m \times 63360 $$
06

Write the final function

The function \(f(m)\) that converts miles to inches is: $$ f(m) = 63360 m $$

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