42.426 Additive Inverse :

The additive inverse of 42.426 is -42.426.

This means that when we add 42.426 and -42.426, the result is zero:

42.426 + (-42.426) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 42.426
  • Additive inverse: -42.426

To verify: 42.426 + (-42.426) = 0

Extended Mathematical Exploration of 42.426

Let's explore various mathematical operations and concepts related to 42.426 and its additive inverse -42.426.

Basic Operations and Properties

  • Square of 42.426: 1799.965476
  • Cube of 42.426: 76365.335284776
  • Square root of |42.426|: 6.5135243916024
  • Reciprocal of 42.426: 0.023570452081271
  • Double of 42.426: 84.852
  • Half of 42.426: 21.213
  • Absolute value of 42.426: 42.426

Trigonometric Functions

  • Sine of 42.426: -0.99989488878131
  • Cosine of 42.426: 0.014498668525528
  • Tangent of 42.426: -68.964600923235

Exponential and Logarithmic Functions

  • e^42.426: 2.6630399966307E+18
  • Natural log of 42.426: 3.7477613818502

Floor and Ceiling Functions

  • Floor of 42.426: 42
  • Ceiling of 42.426: 43

Interesting Properties and Relationships

  • The sum of 42.426 and its additive inverse (-42.426) is always 0.
  • The product of 42.426 and its additive inverse is: -1799.965476
  • The average of 42.426 and its additive inverse is always 0.
  • The distance between 42.426 and its additive inverse on a number line is: 84.852

Applications in Algebra

Consider the equation: x + 42.426 = 0

The solution to this equation is x = -42.426, which is the additive inverse of 42.426.

Graphical Representation

On a coordinate plane:

  • The point (42.426, 0) is reflected across the y-axis to (-42.426, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 42.426 and Its Additive Inverse

Consider the alternating series: 42.426 + (-42.426) + 42.426 + (-42.426) + ...

The sum of this series oscillates between 0 and 42.426, never converging unless 42.426 is 0.

In Number Theory

For integer values:

  • If 42.426 is even, its additive inverse is also even.
  • If 42.426 is odd, its additive inverse is also odd.
  • The sum of the digits of 42.426 and its additive inverse may or may not be the same.

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