125 Additive Inverse :
The additive inverse of 125 is -125.
This means that when we add 125 and -125, the result is zero:
125 + (-125) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 125
- Additive inverse: -125
To verify: 125 + (-125) = 0
Extended Mathematical Exploration of 125
Let's explore various mathematical operations and concepts related to 125 and its additive inverse -125.
Basic Operations and Properties
- Square of 125: 15625
- Cube of 125: 1953125
- Square root of |125|: 11.180339887499
- Reciprocal of 125: 0.008
- Double of 125: 250
- Half of 125: 62.5
- Absolute value of 125: 125
Trigonometric Functions
- Sine of 125: -0.61604045918866
- Cosine of 125: 0.78771451214423
- Tangent of 125: -0.7820605685069
Exponential and Logarithmic Functions
- e^125: 1.9355760420357E+54
- Natural log of 125: 4.8283137373023
Floor and Ceiling Functions
- Floor of 125: 125
- Ceiling of 125: 125
Interesting Properties and Relationships
- The sum of 125 and its additive inverse (-125) is always 0.
- The product of 125 and its additive inverse is: -15625
- The average of 125 and its additive inverse is always 0.
- The distance between 125 and its additive inverse on a number line is: 250
Applications in Algebra
Consider the equation: x + 125 = 0
The solution to this equation is x = -125, which is the additive inverse of 125.
Graphical Representation
On a coordinate plane:
- The point (125, 0) is reflected across the y-axis to (-125, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 125 and Its Additive Inverse
Consider the alternating series: 125 + (-125) + 125 + (-125) + ...
The sum of this series oscillates between 0 and 125, never converging unless 125 is 0.
In Number Theory
For integer values:
- If 125 is even, its additive inverse is also even.
- If 125 is odd, its additive inverse is also odd.
- The sum of the digits of 125 and its additive inverse may or may not be the same.
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