84/89 Additive Inverse :

The additive inverse of 84/89 is -84/89.

This means that when we add 84/89 and -84/89, the result is zero:

84/89 + (-84/89) = 0

Additive Inverse of a Fraction

For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:

  • Original fraction: 84/89
  • Additive inverse: -84/89

To verify: 84/89 + (-84/89) = 0

Extended Mathematical Exploration of 84/89

Let's explore various mathematical operations and concepts related to 84/89 and its additive inverse -84/89.

Basic Operations and Properties

  • Square of 84/89: 0.89079661658881
  • Cube of 84/89: 0.84075186284787
  • Square root of |84/89|: 0.97150410432437
  • Reciprocal of 84/89: 1.0595238095238
  • Double of 84/89: 1.8876404494382
  • Half of 84/89: 0.47191011235955
  • Absolute value of 84/89: 0.9438202247191

Trigonometric Functions

  • Sine of 84/89: 0.80980532492549
  • Cosine of 84/89: 0.58669867540529
  • Tangent of 84/89: 1.380274677399

Exponential and Logarithmic Functions

  • e^84/89: 2.5697798267685
  • Natural log of 84/89: -0.057819570888826

Floor and Ceiling Functions

  • Floor of 84/89: 0
  • Ceiling of 84/89: 1

Interesting Properties and Relationships

  • The sum of 84/89 and its additive inverse (-84/89) is always 0.
  • The product of 84/89 and its additive inverse is: -7056
  • The average of 84/89 and its additive inverse is always 0.
  • The distance between 84/89 and its additive inverse on a number line is: 168

Applications in Algebra

Consider the equation: x + 84/89 = 0

The solution to this equation is x = -84/89, which is the additive inverse of 84/89.

Graphical Representation

On a coordinate plane:

  • The point (84/89, 0) is reflected across the y-axis to (-84/89, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 84/89 and Its Additive Inverse

Consider the alternating series: 84/89 + (-84/89) + 84/89 + (-84/89) + ...

The sum of this series oscillates between 0 and 84/89, never converging unless 84/89 is 0.

In Number Theory

For integer values:

  • If 84/89 is even, its additive inverse is also even.
  • If 84/89 is odd, its additive inverse is also odd.
  • The sum of the digits of 84/89 and its additive inverse may or may not be the same.

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