11 Additive Inverse :
The additive inverse of 11 is -11.
This means that when we add 11 and -11, the result is zero:
11 + (-11) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 11
- Additive inverse: -11
To verify: 11 + (-11) = 0
Extended Mathematical Exploration of 11
Let's explore various mathematical operations and concepts related to 11 and its additive inverse -11.
Basic Operations and Properties
- Square of 11: 121
- Cube of 11: 1331
- Square root of |11|: 3.3166247903554
- Reciprocal of 11: 0.090909090909091
- Double of 11: 22
- Half of 11: 5.5
- Absolute value of 11: 11
Trigonometric Functions
- Sine of 11: -0.9999902065507
- Cosine of 11: 0.0044256979880508
- Tangent of 11: -225.9508464542
Exponential and Logarithmic Functions
- e^11: 59874.141715198
- Natural log of 11: 2.3978952727984
Floor and Ceiling Functions
- Floor of 11: 11
- Ceiling of 11: 11
Interesting Properties and Relationships
- The sum of 11 and its additive inverse (-11) is always 0.
- The product of 11 and its additive inverse is: -121
- The average of 11 and its additive inverse is always 0.
- The distance between 11 and its additive inverse on a number line is: 22
Applications in Algebra
Consider the equation: x + 11 = 0
The solution to this equation is x = -11, which is the additive inverse of 11.
Graphical Representation
On a coordinate plane:
- The point (11, 0) is reflected across the y-axis to (-11, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 11 and Its Additive Inverse
Consider the alternating series: 11 + (-11) + 11 + (-11) + ...
The sum of this series oscillates between 0 and 11, never converging unless 11 is 0.
In Number Theory
For integer values:
- If 11 is even, its additive inverse is also even.
- If 11 is odd, its additive inverse is also odd.
- The sum of the digits of 11 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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