21 Additive Inverse :
The additive inverse of 21 is -21.
This means that when we add 21 and -21, the result is zero:
21 + (-21) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 21
- Additive inverse: -21
To verify: 21 + (-21) = 0
Extended Mathematical Exploration of 21
Let's explore various mathematical operations and concepts related to 21 and its additive inverse -21.
Basic Operations and Properties
- Square of 21: 441
- Cube of 21: 9261
- Square root of |21|: 4.5825756949558
- Reciprocal of 21: 0.047619047619048
- Double of 21: 42
- Half of 21: 10.5
- Absolute value of 21: 21
Trigonometric Functions
- Sine of 21: 0.83665563853606
- Cosine of 21: -0.54772926022427
- Tangent of 21: -1.5274985276366
Exponential and Logarithmic Functions
- e^21: 1318815734.4832
- Natural log of 21: 3.0445224377234
Floor and Ceiling Functions
- Floor of 21: 21
- Ceiling of 21: 21
Interesting Properties and Relationships
- The sum of 21 and its additive inverse (-21) is always 0.
- The product of 21 and its additive inverse is: -441
- The average of 21 and its additive inverse is always 0.
- The distance between 21 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21 = 0
The solution to this equation is x = -21, which is the additive inverse of 21.
Graphical Representation
On a coordinate plane:
- The point (21, 0) is reflected across the y-axis to (-21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21 and Its Additive Inverse
Consider the alternating series: 21 + (-21) + 21 + (-21) + ...
The sum of this series oscillates between 0 and 21, never converging unless 21 is 0.
In Number Theory
For integer values:
- If 21 is even, its additive inverse is also even.
- If 21 is odd, its additive inverse is also odd.
- The sum of the digits of 21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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