67.742 Additive Inverse :

The additive inverse of 67.742 is -67.742.

This means that when we add 67.742 and -67.742, the result is zero:

67.742 + (-67.742) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 67.742
  • Additive inverse: -67.742

To verify: 67.742 + (-67.742) = 0

Extended Mathematical Exploration of 67.742

Let's explore various mathematical operations and concepts related to 67.742 and its additive inverse -67.742.

Basic Operations and Properties

  • Square of 67.742: 4588.978564
  • Cube of 67.742: 310866.58588249
  • Square root of |67.742|: 8.2305528368391
  • Reciprocal of 67.742: 0.014761890702961
  • Double of 67.742: 135.484
  • Half of 67.742: 33.871
  • Absolute value of 67.742: 67.742

Trigonometric Functions

  • Sine of 67.742: -0.98050954117707
  • Cosine of 67.742: 0.19647147289299
  • Tangent of 67.742: -4.9905949537576

Exponential and Logarithmic Functions

  • e^67.742: 2.6301274449531E+29
  • Natural log of 67.742: 4.2157063716069

Floor and Ceiling Functions

  • Floor of 67.742: 67
  • Ceiling of 67.742: 68

Interesting Properties and Relationships

  • The sum of 67.742 and its additive inverse (-67.742) is always 0.
  • The product of 67.742 and its additive inverse is: -4588.978564
  • The average of 67.742 and its additive inverse is always 0.
  • The distance between 67.742 and its additive inverse on a number line is: 135.484

Applications in Algebra

Consider the equation: x + 67.742 = 0

The solution to this equation is x = -67.742, which is the additive inverse of 67.742.

Graphical Representation

On a coordinate plane:

  • The point (67.742, 0) is reflected across the y-axis to (-67.742, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 67.742 and Its Additive Inverse

Consider the alternating series: 67.742 + (-67.742) + 67.742 + (-67.742) + ...

The sum of this series oscillates between 0 and 67.742, never converging unless 67.742 is 0.

In Number Theory

For integer values:

  • If 67.742 is even, its additive inverse is also even.
  • If 67.742 is odd, its additive inverse is also odd.
  • The sum of the digits of 67.742 and its additive inverse may or may not be the same.

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