13 Additive Inverse :
The additive inverse of 13 is -13.
This means that when we add 13 and -13, the result is zero:
13 + (-13) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 13
- Additive inverse: -13
To verify: 13 + (-13) = 0
Extended Mathematical Exploration of 13
Let's explore various mathematical operations and concepts related to 13 and its additive inverse -13.
Basic Operations and Properties
- Square of 13: 169
- Cube of 13: 2197
- Square root of |13|: 3.605551275464
- Reciprocal of 13: 0.076923076923077
- Double of 13: 26
- Half of 13: 6.5
- Absolute value of 13: 13
Trigonometric Functions
- Sine of 13: 0.42016703682664
- Cosine of 13: 0.9074467814502
- Tangent of 13: 0.46302113293649
Exponential and Logarithmic Functions
- e^13: 442413.39200892
- Natural log of 13: 2.5649493574615
Floor and Ceiling Functions
- Floor of 13: 13
- Ceiling of 13: 13
Interesting Properties and Relationships
- The sum of 13 and its additive inverse (-13) is always 0.
- The product of 13 and its additive inverse is: -169
- The average of 13 and its additive inverse is always 0.
- The distance between 13 and its additive inverse on a number line is: 26
Applications in Algebra
Consider the equation: x + 13 = 0
The solution to this equation is x = -13, which is the additive inverse of 13.
Graphical Representation
On a coordinate plane:
- The point (13, 0) is reflected across the y-axis to (-13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 13 and Its Additive Inverse
Consider the alternating series: 13 + (-13) + 13 + (-13) + ...
The sum of this series oscillates between 0 and 13, never converging unless 13 is 0.
In Number Theory
For integer values:
- If 13 is even, its additive inverse is also even.
- If 13 is odd, its additive inverse is also odd.
- The sum of the digits of 13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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