9 Additive Inverse :
The additive inverse of 9 is -9.
This means that when we add 9 and -9, the result is zero:
9 + (-9) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 9
- Additive inverse: -9
To verify: 9 + (-9) = 0
Extended Mathematical Exploration of 9
Let's explore various mathematical operations and concepts related to 9 and its additive inverse -9.
Basic Operations and Properties
- Square of 9: 81
- Cube of 9: 729
- Square root of |9|: 3
- Reciprocal of 9: 0.11111111111111
- Double of 9: 18
- Half of 9: 4.5
- Absolute value of 9: 9
Trigonometric Functions
- Sine of 9: 0.41211848524176
- Cosine of 9: -0.91113026188468
- Tangent of 9: -0.45231565944181
Exponential and Logarithmic Functions
- e^9: 8103.0839275754
- Natural log of 9: 2.1972245773362
Floor and Ceiling Functions
- Floor of 9: 9
- Ceiling of 9: 9
Interesting Properties and Relationships
- The sum of 9 and its additive inverse (-9) is always 0.
- The product of 9 and its additive inverse is: -81
- The average of 9 and its additive inverse is always 0.
- The distance between 9 and its additive inverse on a number line is: 18
Applications in Algebra
Consider the equation: x + 9 = 0
The solution to this equation is x = -9, which is the additive inverse of 9.
Graphical Representation
On a coordinate plane:
- The point (9, 0) is reflected across the y-axis to (-9, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 9 and Its Additive Inverse
Consider the alternating series: 9 + (-9) + 9 + (-9) + ...
The sum of this series oscillates between 0 and 9, never converging unless 9 is 0.
In Number Theory
For integer values:
- If 9 is even, its additive inverse is also even.
- If 9 is odd, its additive inverse is also odd.
- The sum of the digits of 9 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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