484 Additive Inverse :

The additive inverse of 484 is -484.

This means that when we add 484 and -484, the result is zero:

484 + (-484) = 0

Additive Inverse of a Whole Number

For whole numbers, the additive inverse is the negative of that number:

  • Original number: 484
  • Additive inverse: -484

To verify: 484 + (-484) = 0

Extended Mathematical Exploration of 484

Let's explore various mathematical operations and concepts related to 484 and its additive inverse -484.

Basic Operations and Properties

  • Square of 484: 234256
  • Cube of 484: 113379904
  • Square root of |484|: 22
  • Reciprocal of 484: 0.0020661157024793
  • Double of 484: 968
  • Half of 484: 242
  • Absolute value of 484: 484

Trigonometric Functions

  • Sine of 484: 0.19350296674212
  • Cosine of 484: 0.98109969007334
  • Tangent of 484: 0.19723068786991

Exponential and Logarithmic Functions

  • e^484: 1.5795349547066E+210
  • Natural log of 484: 6.1820849067166

Floor and Ceiling Functions

  • Floor of 484: 484
  • Ceiling of 484: 484

Interesting Properties and Relationships

  • The sum of 484 and its additive inverse (-484) is always 0.
  • The product of 484 and its additive inverse is: -234256
  • The average of 484 and its additive inverse is always 0.
  • The distance between 484 and its additive inverse on a number line is: 968

Applications in Algebra

Consider the equation: x + 484 = 0

The solution to this equation is x = -484, which is the additive inverse of 484.

Graphical Representation

On a coordinate plane:

  • The point (484, 0) is reflected across the y-axis to (-484, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 484 and Its Additive Inverse

Consider the alternating series: 484 + (-484) + 484 + (-484) + ...

The sum of this series oscillates between 0 and 484, never converging unless 484 is 0.

In Number Theory

For integer values:

  • If 484 is even, its additive inverse is also even.
  • If 484 is odd, its additive inverse is also odd.
  • The sum of the digits of 484 and its additive inverse may or may not be the same.

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