67.69 Additive Inverse :

The additive inverse of 67.69 is -67.69.

This means that when we add 67.69 and -67.69, the result is zero:

67.69 + (-67.69) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 67.69
  • Additive inverse: -67.69

To verify: 67.69 + (-67.69) = 0

Extended Mathematical Exploration of 67.69

Let's explore various mathematical operations and concepts related to 67.69 and its additive inverse -67.69.

Basic Operations and Properties

  • Square of 67.69: 4581.9361
  • Cube of 67.69: 310151.254609
  • Square root of |67.69|: 8.2273932688307
  • Reciprocal of 67.69: 0.014773230905599
  • Double of 67.69: 135.38
  • Half of 67.69: 33.845
  • Absolute value of 67.69: 67.69

Trigonometric Functions

  • Sine of 67.69: -0.98939610393277
  • Cosine of 67.69: 0.14524238197804
  • Tangent of 67.69: -6.8120344107435

Exponential and Logarithmic Functions

  • e^67.69: 2.4968559069697E+29
  • Natural log of 67.69: 4.2149384585205

Floor and Ceiling Functions

  • Floor of 67.69: 67
  • Ceiling of 67.69: 68

Interesting Properties and Relationships

  • The sum of 67.69 and its additive inverse (-67.69) is always 0.
  • The product of 67.69 and its additive inverse is: -4581.9361
  • The average of 67.69 and its additive inverse is always 0.
  • The distance between 67.69 and its additive inverse on a number line is: 135.38

Applications in Algebra

Consider the equation: x + 67.69 = 0

The solution to this equation is x = -67.69, which is the additive inverse of 67.69.

Graphical Representation

On a coordinate plane:

  • The point (67.69, 0) is reflected across the y-axis to (-67.69, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 67.69 and Its Additive Inverse

Consider the alternating series: 67.69 + (-67.69) + 67.69 + (-67.69) + ...

The sum of this series oscillates between 0 and 67.69, never converging unless 67.69 is 0.

In Number Theory

For integer values:

  • If 67.69 is even, its additive inverse is also even.
  • If 67.69 is odd, its additive inverse is also odd.
  • The sum of the digits of 67.69 and its additive inverse may or may not be the same.

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