42.907 Additive Inverse :

The additive inverse of 42.907 is -42.907.

This means that when we add 42.907 and -42.907, the result is zero:

42.907 + (-42.907) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 42.907
  • Additive inverse: -42.907

To verify: 42.907 + (-42.907) = 0

Extended Mathematical Exploration of 42.907

Let's explore various mathematical operations and concepts related to 42.907 and its additive inverse -42.907.

Basic Operations and Properties

  • Square of 42.907: 1841.010649
  • Cube of 42.907: 78992.243916643
  • Square root of |42.907|: 6.5503435024432
  • Reciprocal of 42.907: 0.023306220430233
  • Double of 42.907: 85.814
  • Half of 42.907: 21.4535
  • Absolute value of 42.907: 42.907

Trigonometric Functions

  • Sine of 42.907: -0.87973147555696
  • Cosine of 42.907: 0.47547085180312
  • Tangent of 42.907: -1.8502321903031

Exponential and Logarithmic Functions

  • e^42.907: 4.3079765938941E+18
  • Natural log of 42.907: 3.7590349827863

Floor and Ceiling Functions

  • Floor of 42.907: 42
  • Ceiling of 42.907: 43

Interesting Properties and Relationships

  • The sum of 42.907 and its additive inverse (-42.907) is always 0.
  • The product of 42.907 and its additive inverse is: -1841.010649
  • The average of 42.907 and its additive inverse is always 0.
  • The distance between 42.907 and its additive inverse on a number line is: 85.814

Applications in Algebra

Consider the equation: x + 42.907 = 0

The solution to this equation is x = -42.907, which is the additive inverse of 42.907.

Graphical Representation

On a coordinate plane:

  • The point (42.907, 0) is reflected across the y-axis to (-42.907, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 42.907 and Its Additive Inverse

Consider the alternating series: 42.907 + (-42.907) + 42.907 + (-42.907) + ...

The sum of this series oscillates between 0 and 42.907, never converging unless 42.907 is 0.

In Number Theory

For integer values:

  • If 42.907 is even, its additive inverse is also even.
  • If 42.907 is odd, its additive inverse is also odd.
  • The sum of the digits of 42.907 and its additive inverse may or may not be the same.

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