84 Additive Inverse :
The additive inverse of 84 is -84.
This means that when we add 84 and -84, the result is zero:
84 + (-84) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 84
- Additive inverse: -84
To verify: 84 + (-84) = 0
Extended Mathematical Exploration of 84
Let's explore various mathematical operations and concepts related to 84 and its additive inverse -84.
Basic Operations and Properties
- Square of 84: 7056
- Cube of 84: 592704
- Square root of |84|: 9.1651513899117
- Reciprocal of 84: 0.011904761904762
- Double of 84: 168
- Half of 84: 42
- Absolute value of 84: 84
Trigonometric Functions
- Sine of 84: 0.73319032007329
- Cosine of 84: -0.68002349558734
- Tangent of 84: -1.078183805164
Exponential and Logarithmic Functions
- e^84: 3.0250773222011E+36
- Natural log of 84: 4.4308167988433
Floor and Ceiling Functions
- Floor of 84: 84
- Ceiling of 84: 84
Interesting Properties and Relationships
- The sum of 84 and its additive inverse (-84) is always 0.
- The product of 84 and its additive inverse is: -7056
- The average of 84 and its additive inverse is always 0.
- The distance between 84 and its additive inverse on a number line is: 168
Applications in Algebra
Consider the equation: x + 84 = 0
The solution to this equation is x = -84, which is the additive inverse of 84.
Graphical Representation
On a coordinate plane:
- The point (84, 0) is reflected across the y-axis to (-84, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 84 and Its Additive Inverse
Consider the alternating series: 84 + (-84) + 84 + (-84) + ...
The sum of this series oscillates between 0 and 84, never converging unless 84 is 0.
In Number Theory
For integer values:
- If 84 is even, its additive inverse is also even.
- If 84 is odd, its additive inverse is also odd.
- The sum of the digits of 84 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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