67.164 Additive Inverse :

The additive inverse of 67.164 is -67.164.

This means that when we add 67.164 and -67.164, the result is zero:

67.164 + (-67.164) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 67.164
  • Additive inverse: -67.164

To verify: 67.164 + (-67.164) = 0

Extended Mathematical Exploration of 67.164

Let's explore various mathematical operations and concepts related to 67.164 and its additive inverse -67.164.

Basic Operations and Properties

  • Square of 67.164: 4511.002896
  • Cube of 67.164: 302976.99850694
  • Square root of |67.164|: 8.1953645434477
  • Reciprocal of 67.164: 0.014888928592698
  • Double of 67.164: 134.328
  • Half of 67.164: 33.582
  • Absolute value of 67.164: 67.164

Trigonometric Functions

  • Sine of 67.164: -0.92857482626407
  • Cosine of 67.164: -0.37114524384485
  • Tangent of 67.164: 2.5019176229892

Exponential and Logarithmic Functions

  • e^67.164: 1.4755522155812E+29
  • Natural log of 67.164: 4.2071373896972

Floor and Ceiling Functions

  • Floor of 67.164: 67
  • Ceiling of 67.164: 68

Interesting Properties and Relationships

  • The sum of 67.164 and its additive inverse (-67.164) is always 0.
  • The product of 67.164 and its additive inverse is: -4511.002896
  • The average of 67.164 and its additive inverse is always 0.
  • The distance between 67.164 and its additive inverse on a number line is: 134.328

Applications in Algebra

Consider the equation: x + 67.164 = 0

The solution to this equation is x = -67.164, which is the additive inverse of 67.164.

Graphical Representation

On a coordinate plane:

  • The point (67.164, 0) is reflected across the y-axis to (-67.164, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 67.164 and Its Additive Inverse

Consider the alternating series: 67.164 + (-67.164) + 67.164 + (-67.164) + ...

The sum of this series oscillates between 0 and 67.164, never converging unless 67.164 is 0.

In Number Theory

For integer values:

  • If 67.164 is even, its additive inverse is also even.
  • If 67.164 is odd, its additive inverse is also odd.
  • The sum of the digits of 67.164 and its additive inverse may or may not be the same.

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