73/84 Additive Inverse :

The additive inverse of 73/84 is -73/84.

This means that when we add 73/84 and -73/84, the result is zero:

73/84 + (-73/84) = 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: 73/84
  • Additive inverse: -73/84

To verify: 73/84 + (-73/84) = 0

Extended Mathematical Exploration of 73/84

Let's explore various mathematical operations and concepts related to 73/84 and its additive inverse -73/84.

Basic Operations and Properties

  • Square of 73/84: 0.75524376417234
  • Cube of 73/84: 0.65634279505453
  • Square root of |73/84|: 0.9322272357358
  • Reciprocal of 73/84: 1.1506849315068
  • Double of 73/84: 1.7380952380952
  • Half of 73/84: 0.43452380952381
  • Absolute value of 73/84: 0.86904761904762

Trigonometric Functions

  • Sine of 73/84: 0.76371446996275
  • Cosine of 73/84: 0.64555418701261
  • Tangent of 73/84: 1.1830369709117

Exponential and Logarithmic Functions

  • e^73/84: 2.384638687248
  • Natural log of 73/84: -0.14035735769492

Floor and Ceiling Functions

  • Floor of 73/84: 0
  • Ceiling of 73/84: 1

Interesting Properties and Relationships

  • The sum of 73/84 and its additive inverse (-73/84) is always 0.
  • The product of 73/84 and its additive inverse is: -5329
  • The average of 73/84 and its additive inverse is always 0.
  • The distance between 73/84 and its additive inverse on a number line is: 146

Applications in Algebra

Consider the equation: x + 73/84 = 0

The solution to this equation is x = -73/84, which is the additive inverse of 73/84.

Graphical Representation

On a coordinate plane:

  • The point (73/84, 0) is reflected across the y-axis to (-73/84, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 73/84 and Its Additive Inverse

Consider the alternating series: 73/84 + (-73/84) + 73/84 + (-73/84) + ...

The sum of this series oscillates between 0 and 73/84, never converging unless 73/84 is 0.

In Number Theory

For integer values:

  • If 73/84 is even, its additive inverse is also even.
  • If 73/84 is odd, its additive inverse is also odd.
  • The sum of the digits of 73/84 and its additive inverse may or may not be the same.

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