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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