12 Additive Inverse :
The additive inverse of 12 is -12.
This means that when we add 12 and -12, the result is zero:
12 + (-12) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 12
- Additive inverse: -12
To verify: 12 + (-12) = 0
Extended Mathematical Exploration of 12
Let's explore various mathematical operations and concepts related to 12 and its additive inverse -12.
Basic Operations and Properties
- Square of 12: 144
- Cube of 12: 1728
- Square root of |12|: 3.4641016151378
- Reciprocal of 12: 0.083333333333333
- Double of 12: 24
- Half of 12: 6
- Absolute value of 12: 12
Trigonometric Functions
- Sine of 12: -0.53657291800043
- Cosine of 12: 0.84385395873249
- Tangent of 12: -0.63585992866158
Exponential and Logarithmic Functions
- e^12: 162754.791419
- Natural log of 12: 2.484906649788
Floor and Ceiling Functions
- Floor of 12: 12
- Ceiling of 12: 12
Interesting Properties and Relationships
- The sum of 12 and its additive inverse (-12) is always 0.
- The product of 12 and its additive inverse is: -144
- The average of 12 and its additive inverse is always 0.
- The distance between 12 and its additive inverse on a number line is: 24
Applications in Algebra
Consider the equation: x + 12 = 0
The solution to this equation is x = -12, which is the additive inverse of 12.
Graphical Representation
On a coordinate plane:
- The point (12, 0) is reflected across the y-axis to (-12, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 12 and Its Additive Inverse
Consider the alternating series: 12 + (-12) + 12 + (-12) + ...
The sum of this series oscillates between 0 and 12, never converging unless 12 is 0.
In Number Theory
For integer values:
- If 12 is even, its additive inverse is also even.
- If 12 is odd, its additive inverse is also odd.
- The sum of the digits of 12 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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