5 Additive Inverse :
The additive inverse of 5 is -5.
This means that when we add 5 and -5, the result is zero:
5 + (-5) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 5
- Additive inverse: -5
To verify: 5 + (-5) = 0
Extended Mathematical Exploration of 5
Let's explore various mathematical operations and concepts related to 5 and its additive inverse -5.
Basic Operations and Properties
- Square of 5: 25
- Cube of 5: 125
- Square root of |5|: 2.2360679774998
- Reciprocal of 5: 0.2
- Double of 5: 10
- Half of 5: 2.5
- Absolute value of 5: 5
Trigonometric Functions
- Sine of 5: -0.95892427466314
- Cosine of 5: 0.28366218546323
- Tangent of 5: -3.3805150062466
Exponential and Logarithmic Functions
- e^5: 148.41315910258
- Natural log of 5: 1.6094379124341
Floor and Ceiling Functions
- Floor of 5: 5
- Ceiling of 5: 5
Interesting Properties and Relationships
- The sum of 5 and its additive inverse (-5) is always 0.
- The product of 5 and its additive inverse is: -25
- The average of 5 and its additive inverse is always 0.
- The distance between 5 and its additive inverse on a number line is: 10
Applications in Algebra
Consider the equation: x + 5 = 0
The solution to this equation is x = -5, which is the additive inverse of 5.
Graphical Representation
On a coordinate plane:
- The point (5, 0) is reflected across the y-axis to (-5, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 5 and Its Additive Inverse
Consider the alternating series: 5 + (-5) + 5 + (-5) + ...
The sum of this series oscillates between 0 and 5, never converging unless 5 is 0.
In Number Theory
For integer values:
- If 5 is even, its additive inverse is also even.
- If 5 is odd, its additive inverse is also odd.
- The sum of the digits of 5 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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