42.474 Additive Inverse :

The additive inverse of 42.474 is -42.474.

This means that when we add 42.474 and -42.474, the result is zero:

42.474 + (-42.474) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 42.474
  • Additive inverse: -42.474

To verify: 42.474 + (-42.474) = 0

Extended Mathematical Exploration of 42.474

Let's explore various mathematical operations and concepts related to 42.474 and its additive inverse -42.474.

Basic Operations and Properties

  • Square of 42.474: 1804.040676
  • Cube of 42.474: 76624.823672424
  • Square root of |42.474|: 6.5172079911569
  • Reciprocal of 42.474: 0.023543815039789
  • Double of 42.474: 84.948
  • Half of 42.474: 21.237
  • Absolute value of 42.474: 42.474

Trigonometric Functions

  • Sine of 42.474: -0.99804756213265
  • Cosine of 42.474: 0.062458495987948
  • Tangent of 42.474: -15.979372323106

Exponential and Logarithmic Functions

  • e^42.474: 2.7939834184203E+18
  • Natural log of 42.474: 3.7488921240201

Floor and Ceiling Functions

  • Floor of 42.474: 42
  • Ceiling of 42.474: 43

Interesting Properties and Relationships

  • The sum of 42.474 and its additive inverse (-42.474) is always 0.
  • The product of 42.474 and its additive inverse is: -1804.040676
  • The average of 42.474 and its additive inverse is always 0.
  • The distance between 42.474 and its additive inverse on a number line is: 84.948

Applications in Algebra

Consider the equation: x + 42.474 = 0

The solution to this equation is x = -42.474, which is the additive inverse of 42.474.

Graphical Representation

On a coordinate plane:

  • The point (42.474, 0) is reflected across the y-axis to (-42.474, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 42.474 and Its Additive Inverse

Consider the alternating series: 42.474 + (-42.474) + 42.474 + (-42.474) + ...

The sum of this series oscillates between 0 and 42.474, never converging unless 42.474 is 0.

In Number Theory

For integer values:

  • If 42.474 is even, its additive inverse is also even.
  • If 42.474 is odd, its additive inverse is also odd.
  • The sum of the digits of 42.474 and its additive inverse may or may not be the same.

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