67.75 Additive Inverse :

The additive inverse of 67.75 is -67.75.

This means that when we add 67.75 and -67.75, the result is zero:

67.75 + (-67.75) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 67.75
  • Additive inverse: -67.75

To verify: 67.75 + (-67.75) = 0

Extended Mathematical Exploration of 67.75

Let's explore various mathematical operations and concepts related to 67.75 and its additive inverse -67.75.

Basic Operations and Properties

  • Square of 67.75: 4590.0625
  • Cube of 67.75: 310976.734375
  • Square root of |67.75|: 8.2310388165772
  • Reciprocal of 67.75: 0.014760147601476
  • Double of 67.75: 135.5
  • Half of 67.75: 33.875
  • Absolute value of 67.75: 67.75

Trigonometric Functions

  • Sine of 67.75: -0.97890641002146
  • Cosine of 67.75: 0.20430917849892
  • Tangent of 67.75: -4.7912992319463

Exponential and Logarithmic Functions

  • e^67.75: 2.6512528534781E+29
  • Natural log of 67.75: 4.2158244597598

Floor and Ceiling Functions

  • Floor of 67.75: 67
  • Ceiling of 67.75: 68

Interesting Properties and Relationships

  • The sum of 67.75 and its additive inverse (-67.75) is always 0.
  • The product of 67.75 and its additive inverse is: -4590.0625
  • The average of 67.75 and its additive inverse is always 0.
  • The distance between 67.75 and its additive inverse on a number line is: 135.5

Applications in Algebra

Consider the equation: x + 67.75 = 0

The solution to this equation is x = -67.75, which is the additive inverse of 67.75.

Graphical Representation

On a coordinate plane:

  • The point (67.75, 0) is reflected across the y-axis to (-67.75, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 67.75 and Its Additive Inverse

Consider the alternating series: 67.75 + (-67.75) + 67.75 + (-67.75) + ...

The sum of this series oscillates between 0 and 67.75, never converging unless 67.75 is 0.

In Number Theory

For integer values:

  • If 67.75 is even, its additive inverse is also even.
  • If 67.75 is odd, its additive inverse is also odd.
  • The sum of the digits of 67.75 and its additive inverse may or may not be the same.

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