31 Additive Inverse :
The additive inverse of 31 is -31.
This means that when we add 31 and -31, the result is zero:
31 + (-31) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 31
- Additive inverse: -31
To verify: 31 + (-31) = 0
Extended Mathematical Exploration of 31
Let's explore various mathematical operations and concepts related to 31 and its additive inverse -31.
Basic Operations and Properties
- Square of 31: 961
- Cube of 31: 29791
- Square root of |31|: 5.56776436283
- Reciprocal of 31: 0.032258064516129
- Double of 31: 62
- Half of 31: 15.5
- Absolute value of 31: 31
Trigonometric Functions
- Sine of 31: -0.40403764532307
- Cosine of 31: 0.91474235780453
- Tangent of 31: -0.4416955680207
Exponential and Logarithmic Functions
- e^31: 29048849665247
- Natural log of 31: 3.4339872044851
Floor and Ceiling Functions
- Floor of 31: 31
- Ceiling of 31: 31
Interesting Properties and Relationships
- The sum of 31 and its additive inverse (-31) is always 0.
- The product of 31 and its additive inverse is: -961
- The average of 31 and its additive inverse is always 0.
- The distance between 31 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31 = 0
The solution to this equation is x = -31, which is the additive inverse of 31.
Graphical Representation
On a coordinate plane:
- The point (31, 0) is reflected across the y-axis to (-31, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31 and Its Additive Inverse
Consider the alternating series: 31 + (-31) + 31 + (-31) + ...
The sum of this series oscillates between 0 and 31, never converging unless 31 is 0.
In Number Theory
For integer values:
- If 31 is even, its additive inverse is also even.
- If 31 is odd, its additive inverse is also odd.
- The sum of the digits of 31 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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