67.409 Additive Inverse :

The additive inverse of 67.409 is -67.409.

This means that when we add 67.409 and -67.409, the result is zero:

67.409 + (-67.409) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 67.409
  • Additive inverse: -67.409

To verify: 67.409 + (-67.409) = 0

Extended Mathematical Exploration of 67.409

Let's explore various mathematical operations and concepts related to 67.409 and its additive inverse -67.409.

Basic Operations and Properties

  • Square of 67.409: 4543.973281
  • Cube of 67.409: 306304.69489893
  • Square root of |67.409|: 8.2102984111419
  • Reciprocal of 67.409: 0.014834814342299
  • Double of 67.409: 134.818
  • Half of 67.409: 33.7045
  • Absolute value of 67.409: 67.409

Trigonometric Functions

  • Sine of 67.409: -0.99086872429852
  • Cosine of 67.409: -0.13483015689016
  • Tangent of 67.409: 7.3490141015392

Exponential and Logarithmic Functions

  • e^67.409: 1.8851969593733E+29
  • Natural log of 67.409: 4.210778540161

Floor and Ceiling Functions

  • Floor of 67.409: 67
  • Ceiling of 67.409: 68

Interesting Properties and Relationships

  • The sum of 67.409 and its additive inverse (-67.409) is always 0.
  • The product of 67.409 and its additive inverse is: -4543.973281
  • The average of 67.409 and its additive inverse is always 0.
  • The distance between 67.409 and its additive inverse on a number line is: 134.818

Applications in Algebra

Consider the equation: x + 67.409 = 0

The solution to this equation is x = -67.409, which is the additive inverse of 67.409.

Graphical Representation

On a coordinate plane:

  • The point (67.409, 0) is reflected across the y-axis to (-67.409, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 67.409 and Its Additive Inverse

Consider the alternating series: 67.409 + (-67.409) + 67.409 + (-67.409) + ...

The sum of this series oscillates between 0 and 67.409, never converging unless 67.409 is 0.

In Number Theory

For integer values:

  • If 67.409 is even, its additive inverse is also even.
  • If 67.409 is odd, its additive inverse is also odd.
  • The sum of the digits of 67.409 and its additive inverse may or may not be the same.

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