67 Additive Inverse :
The additive inverse of 67 is -67.
This means that when we add 67 and -67, the result is zero:
67 + (-67) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 67
- Additive inverse: -67
To verify: 67 + (-67) = 0
Extended Mathematical Exploration of 67
Let's explore various mathematical operations and concepts related to 67 and its additive inverse -67.
Basic Operations and Properties
- Square of 67: 4489
- Cube of 67: 300763
- Square root of |67|: 8.1853527718725
- Reciprocal of 67: 0.014925373134328
- Double of 67: 134
- Half of 67: 33.5
- Absolute value of 67: 67
Trigonometric Functions
- Sine of 67: -0.85551997897532
- Cosine of 67: -0.51776979978951
- Tangent of 67: 1.6523172640102
Exponential and Logarithmic Functions
- e^67: 1.2523631708422E+29
- Natural log of 67: 4.204692619391
Floor and Ceiling Functions
- Floor of 67: 67
- Ceiling of 67: 67
Interesting Properties and Relationships
- The sum of 67 and its additive inverse (-67) is always 0.
- The product of 67 and its additive inverse is: -4489
- The average of 67 and its additive inverse is always 0.
- The distance between 67 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67 = 0
The solution to this equation is x = -67, which is the additive inverse of 67.
Graphical Representation
On a coordinate plane:
- The point (67, 0) is reflected across the y-axis to (-67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67 and Its Additive Inverse
Consider the alternating series: 67 + (-67) + 67 + (-67) + ...
The sum of this series oscillates between 0 and 67, never converging unless 67 is 0.
In Number Theory
For integer values:
- If 67 is even, its additive inverse is also even.
- If 67 is odd, its additive inverse is also odd.
- The sum of the digits of 67 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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