20 Additive Inverse :
The additive inverse of 20 is -20.
This means that when we add 20 and -20, the result is zero:
20 + (-20) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 20
- Additive inverse: -20
To verify: 20 + (-20) = 0
Extended Mathematical Exploration of 20
Let's explore various mathematical operations and concepts related to 20 and its additive inverse -20.
Basic Operations and Properties
- Square of 20: 400
- Cube of 20: 8000
- Square root of |20|: 4.4721359549996
- Reciprocal of 20: 0.05
- Double of 20: 40
- Half of 20: 10
- Absolute value of 20: 20
Trigonometric Functions
- Sine of 20: 0.91294525072763
- Cosine of 20: 0.40808206181339
- Tangent of 20: 2.2371609442247
Exponential and Logarithmic Functions
- e^20: 485165195.40979
- Natural log of 20: 2.995732273554
Floor and Ceiling Functions
- Floor of 20: 20
- Ceiling of 20: 20
Interesting Properties and Relationships
- The sum of 20 and its additive inverse (-20) is always 0.
- The product of 20 and its additive inverse is: -400
- The average of 20 and its additive inverse is always 0.
- The distance between 20 and its additive inverse on a number line is: 40
Applications in Algebra
Consider the equation: x + 20 = 0
The solution to this equation is x = -20, which is the additive inverse of 20.
Graphical Representation
On a coordinate plane:
- The point (20, 0) is reflected across the y-axis to (-20, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 20 and Its Additive Inverse
Consider the alternating series: 20 + (-20) + 20 + (-20) + ...
The sum of this series oscillates between 0 and 20, never converging unless 20 is 0.
In Number Theory
For integer values:
- If 20 is even, its additive inverse is also even.
- If 20 is odd, its additive inverse is also odd.
- The sum of the digits of 20 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: