67.134 Additive Inverse :

The additive inverse of 67.134 is -67.134.

This means that when we add 67.134 and -67.134, the result is zero:

67.134 + (-67.134) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 67.134
  • Additive inverse: -67.134

To verify: 67.134 + (-67.134) = 0

Extended Mathematical Exploration of 67.134

Let's explore various mathematical operations and concepts related to 67.134 and its additive inverse -67.134.

Basic Operations and Properties

  • Square of 67.134: 4506.973956
  • Cube of 67.134: 302571.1895621
  • Square root of |67.134|: 8.1935340360555
  • Reciprocal of 67.134: 0.014895581970388
  • Double of 67.134: 134.268
  • Half of 67.134: 33.567
  • Absolute value of 67.134: 67.134

Trigonometric Functions

  • Sine of 67.134: -0.91702431169381
  • Cosine of 67.134: -0.39883130740014
  • Tangent of 67.134: 2.2992786541047

Exponential and Logarithmic Functions

  • e^67.134: 1.4319430571284E+29
  • Natural log of 67.134: 4.2066906220536

Floor and Ceiling Functions

  • Floor of 67.134: 67
  • Ceiling of 67.134: 68

Interesting Properties and Relationships

  • The sum of 67.134 and its additive inverse (-67.134) is always 0.
  • The product of 67.134 and its additive inverse is: -4506.973956
  • The average of 67.134 and its additive inverse is always 0.
  • The distance between 67.134 and its additive inverse on a number line is: 134.268

Applications in Algebra

Consider the equation: x + 67.134 = 0

The solution to this equation is x = -67.134, which is the additive inverse of 67.134.

Graphical Representation

On a coordinate plane:

  • The point (67.134, 0) is reflected across the y-axis to (-67.134, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 67.134 and Its Additive Inverse

Consider the alternating series: 67.134 + (-67.134) + 67.134 + (-67.134) + ...

The sum of this series oscillates between 0 and 67.134, never converging unless 67.134 is 0.

In Number Theory

For integer values:

  • If 67.134 is even, its additive inverse is also even.
  • If 67.134 is odd, its additive inverse is also odd.
  • The sum of the digits of 67.134 and its additive inverse may or may not be the same.

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