2704 Additive Inverse :

The additive inverse of 2704 is -2704.

This means that when we add 2704 and -2704, the result is zero:

2704 + (-2704) = 0

Additive Inverse of a Whole Number

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

  • Original number: 2704
  • Additive inverse: -2704

To verify: 2704 + (-2704) = 0

Extended Mathematical Exploration of 2704

Let's explore various mathematical operations and concepts related to 2704 and its additive inverse -2704.

Basic Operations and Properties

  • Square of 2704: 7311616
  • Cube of 2704: 19770609664
  • Square root of |2704|: 52
  • Reciprocal of 2704: 0.0003698224852071
  • Double of 2704: 5408
  • Half of 2704: 1352
  • Absolute value of 2704: 2704

Trigonometric Functions

  • Sine of 2704: 0.79028546477557
  • Cosine of 2704: -0.61273883846583
  • Tangent of 2704: -1.289759054207

Exponential and Logarithmic Functions

  • e^2704: INF
  • Natural log of 2704: 7.9024874371629

Floor and Ceiling Functions

  • Floor of 2704: 2704
  • Ceiling of 2704: 2704

Interesting Properties and Relationships

  • The sum of 2704 and its additive inverse (-2704) is always 0.
  • The product of 2704 and its additive inverse is: -7311616
  • The average of 2704 and its additive inverse is always 0.
  • The distance between 2704 and its additive inverse on a number line is: 5408

Applications in Algebra

Consider the equation: x + 2704 = 0

The solution to this equation is x = -2704, which is the additive inverse of 2704.

Graphical Representation

On a coordinate plane:

  • The point (2704, 0) is reflected across the y-axis to (-2704, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 2704 and Its Additive Inverse

Consider the alternating series: 2704 + (-2704) + 2704 + (-2704) + ...

The sum of this series oscillates between 0 and 2704, never converging unless 2704 is 0.

In Number Theory

For integer values:

  • If 2704 is even, its additive inverse is also even.
  • If 2704 is odd, its additive inverse is also odd.
  • The sum of the digits of 2704 and its additive inverse may or may not be the same.

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