64 Additive Inverse :
The additive inverse of 64 is -64.
This means that when we add 64 and -64, the result is zero:
64 + (-64) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 64
- Additive inverse: -64
To verify: 64 + (-64) = 0
Extended Mathematical Exploration of 64
Let's explore various mathematical operations and concepts related to 64 and its additive inverse -64.
Basic Operations and Properties
- Square of 64: 4096
- Cube of 64: 262144
- Square root of |64|: 8
- Reciprocal of 64: 0.015625
- Double of 64: 128
- Half of 64: 32
- Absolute value of 64: 64
Trigonometric Functions
- Sine of 64: 0.92002603819679
- Cosine of 64: 0.39185723042955
- Tangent of 64: 2.3478603091954
Exponential and Logarithmic Functions
- e^64: 6.2351490808116E+27
- Natural log of 64: 4.1588830833597
Floor and Ceiling Functions
- Floor of 64: 64
- Ceiling of 64: 64
Interesting Properties and Relationships
- The sum of 64 and its additive inverse (-64) is always 0.
- The product of 64 and its additive inverse is: -4096
- The average of 64 and its additive inverse is always 0.
- The distance between 64 and its additive inverse on a number line is: 128
Applications in Algebra
Consider the equation: x + 64 = 0
The solution to this equation is x = -64, which is the additive inverse of 64.
Graphical Representation
On a coordinate plane:
- The point (64, 0) is reflected across the y-axis to (-64, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 64 and Its Additive Inverse
Consider the alternating series: 64 + (-64) + 64 + (-64) + ...
The sum of this series oscillates between 0 and 64, never converging unless 64 is 0.
In Number Theory
For integer values:
- If 64 is even, its additive inverse is also even.
- If 64 is odd, its additive inverse is also odd.
- The sum of the digits of 64 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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