Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. -3.6 and -1.4

Question
Piecewise-Defined Functions
asked 2021-02-21
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.
-3.6 and -1.4

Answers (1)

2021-02-22
Step 1
Given:
The two numbers as -3.6 and -1.4
Step 2
Explanation:
Definition:
Distance between two numbers:
In terms of absolute value,
Let P and Q be any two real numbers
then,
\(\displaystyle{\left|{{P}-{Q}}\right|}=\) The distance between P and Q
Step 3
The given two numbers as -3.6 and -1.4
Therefore,
Consider D be the distance between -3.6 and -1.4,
\(\displaystyle{D}={\left|{-{3.6}-{\left(-{1.4}\right)}}\right|}\)
\(\displaystyle{D}={\left|{-{2.2}}\right|}\)
D=2.2
Or
\(\displaystyle{D}={\left|{-{1.4}-{\left(-{3.6}\right)}}\right|}\)
\(\displaystyle{D}={\left|{{2.2}}\right|}\)
D=2.2
Here the change in the order of numbers does not effect the answer
Since both are same.
Therefore,
Absolute value between -3.6 and -1.4 is 2.2.
Hence the solution.
0

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