67.424 Additive Inverse :

The additive inverse of 67.424 is -67.424.

This means that when we add 67.424 and -67.424, the result is zero:

67.424 + (-67.424) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 67.424
  • Additive inverse: -67.424

To verify: 67.424 + (-67.424) = 0

Extended Mathematical Exploration of 67.424

Let's explore various mathematical operations and concepts related to 67.424 and its additive inverse -67.424.

Basic Operations and Properties

  • Square of 67.424: 4545.995776
  • Cube of 67.424: 306509.21920102
  • Square root of |67.424|: 8.2112118472245
  • Reciprocal of 67.424: 0.014831514000949
  • Double of 67.424: 134.848
  • Half of 67.424: 33.712
  • Absolute value of 67.424: 67.424

Trigonometric Functions

  • Sine of 67.424: -0.99277963016938
  • Cosine of 67.424: -0.11995251527482
  • Tangent of 67.424: 8.276438621523

Exponential and Logarithmic Functions

  • e^67.424: 1.9136880628336E+29
  • Natural log of 67.424: 4.2110010376218

Floor and Ceiling Functions

  • Floor of 67.424: 67
  • Ceiling of 67.424: 68

Interesting Properties and Relationships

  • The sum of 67.424 and its additive inverse (-67.424) is always 0.
  • The product of 67.424 and its additive inverse is: -4545.995776
  • The average of 67.424 and its additive inverse is always 0.
  • The distance between 67.424 and its additive inverse on a number line is: 134.848

Applications in Algebra

Consider the equation: x + 67.424 = 0

The solution to this equation is x = -67.424, which is the additive inverse of 67.424.

Graphical Representation

On a coordinate plane:

  • The point (67.424, 0) is reflected across the y-axis to (-67.424, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 67.424 and Its Additive Inverse

Consider the alternating series: 67.424 + (-67.424) + 67.424 + (-67.424) + ...

The sum of this series oscillates between 0 and 67.424, never converging unless 67.424 is 0.

In Number Theory

For integer values:

  • If 67.424 is even, its additive inverse is also even.
  • If 67.424 is odd, its additive inverse is also odd.
  • The sum of the digits of 67.424 and its additive inverse may or may not be the same.

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