34 Additive Inverse :
The additive inverse of 34 is -34.
This means that when we add 34 and -34, the result is zero:
34 + (-34) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 34
- Additive inverse: -34
To verify: 34 + (-34) = 0
Extended Mathematical Exploration of 34
Let's explore various mathematical operations and concepts related to 34 and its additive inverse -34.
Basic Operations and Properties
- Square of 34: 1156
- Cube of 34: 39304
- Square root of |34|: 5.8309518948453
- Reciprocal of 34: 0.029411764705882
- Double of 34: 68
- Half of 34: 17
- Absolute value of 34: 34
Trigonometric Functions
- Sine of 34: 0.52908268612002
- Cosine of 34: -0.84857027478461
- Tangent of 34: -0.62349896271623
Exponential and Logarithmic Functions
- e^34: 5.8346174252745E+14
- Natural log of 34: 3.5263605246162
Floor and Ceiling Functions
- Floor of 34: 34
- Ceiling of 34: 34
Interesting Properties and Relationships
- The sum of 34 and its additive inverse (-34) is always 0.
- The product of 34 and its additive inverse is: -1156
- The average of 34 and its additive inverse is always 0.
- The distance between 34 and its additive inverse on a number line is: 68
Applications in Algebra
Consider the equation: x + 34 = 0
The solution to this equation is x = -34, which is the additive inverse of 34.
Graphical Representation
On a coordinate plane:
- The point (34, 0) is reflected across the y-axis to (-34, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 34 and Its Additive Inverse
Consider the alternating series: 34 + (-34) + 34 + (-34) + ...
The sum of this series oscillates between 0 and 34, never converging unless 34 is 0.
In Number Theory
For integer values:
- If 34 is even, its additive inverse is also even.
- If 34 is odd, its additive inverse is also odd.
- The sum of the digits of 34 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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