13.675 Additive Inverse :

The additive inverse of 13.675 is -13.675.

This means that when we add 13.675 and -13.675, the result is zero:

13.675 + (-13.675) = 0

Additive Inverse of a Decimal Number

For decimal numbers, we simply change the sign of the number:

  • Original number: 13.675
  • Additive inverse: -13.675

To verify: 13.675 + (-13.675) = 0

Extended Mathematical Exploration of 13.675

Let's explore various mathematical operations and concepts related to 13.675 and its additive inverse -13.675.

Basic Operations and Properties

  • Square of 13.675: 187.005625
  • Cube of 13.675: 2557.301921875
  • Square root of |13.675|: 3.6979724174201
  • Reciprocal of 13.675: 0.073126142595978
  • Double of 13.675: 27.35
  • Half of 13.675: 6.8375
  • Absolute value of 13.675: 13.675

Trigonometric Functions

  • Sine of 13.675: 0.8950883850887
  • Cosine of 13.675: 0.44588875617054
  • Tangent of 13.675: 2.0074253335654

Exponential and Logarithmic Functions

  • e^13.675: 868914.4909162
  • Natural log of 13.675: 2.615569348308

Floor and Ceiling Functions

  • Floor of 13.675: 13
  • Ceiling of 13.675: 14

Interesting Properties and Relationships

  • The sum of 13.675 and its additive inverse (-13.675) is always 0.
  • The product of 13.675 and its additive inverse is: -187.005625
  • The average of 13.675 and its additive inverse is always 0.
  • The distance between 13.675 and its additive inverse on a number line is: 27.35

Applications in Algebra

Consider the equation: x + 13.675 = 0

The solution to this equation is x = -13.675, which is the additive inverse of 13.675.

Graphical Representation

On a coordinate plane:

  • The point (13.675, 0) is reflected across the y-axis to (-13.675, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 13.675 and Its Additive Inverse

Consider the alternating series: 13.675 + (-13.675) + 13.675 + (-13.675) + ...

The sum of this series oscillates between 0 and 13.675, never converging unless 13.675 is 0.

In Number Theory

For integer values:

  • If 13.675 is even, its additive inverse is also even.
  • If 13.675 is odd, its additive inverse is also odd.
  • The sum of the digits of 13.675 and its additive inverse may or may not be the same.

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