71.75 Additive Inverse :

The additive inverse of 71.75 is -71.75.

This means that when we add 71.75 and -71.75, the result is zero:

71.75 + (-71.75) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 71.75
  • Additive inverse: -71.75

To verify: 71.75 + (-71.75) = 0

Extended Mathematical Exploration of 71.75

Let's explore various mathematical operations and concepts related to 71.75 and its additive inverse -71.75.

Basic Operations and Properties

  • Square of 71.75: 5148.0625
  • Cube of 71.75: 369373.484375
  • Square root of |71.75|: 8.4705371730487
  • Reciprocal of 71.75: 0.013937282229965
  • Double of 71.75: 143.5
  • Half of 71.75: 35.875
  • Absolute value of 71.75: 71.75

Trigonometric Functions

  • Sine of 71.75: 0.48523423423073
  • Cosine of 71.75: -0.87438420498687
  • Tangent of 71.75: -0.5549439610909

Exponential and Logarithmic Functions

  • e^71.75: 1.4475350107E+31
  • Natural log of 71.75: 4.2731878546397

Floor and Ceiling Functions

  • Floor of 71.75: 71
  • Ceiling of 71.75: 72

Interesting Properties and Relationships

  • The sum of 71.75 and its additive inverse (-71.75) is always 0.
  • The product of 71.75 and its additive inverse is: -5148.0625
  • The average of 71.75 and its additive inverse is always 0.
  • The distance between 71.75 and its additive inverse on a number line is: 143.5

Applications in Algebra

Consider the equation: x + 71.75 = 0

The solution to this equation is x = -71.75, which is the additive inverse of 71.75.

Graphical Representation

On a coordinate plane:

  • The point (71.75, 0) is reflected across the y-axis to (-71.75, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 71.75 and Its Additive Inverse

Consider the alternating series: 71.75 + (-71.75) + 71.75 + (-71.75) + ...

The sum of this series oscillates between 0 and 71.75, never converging unless 71.75 is 0.

In Number Theory

For integer values:

  • If 71.75 is even, its additive inverse is also even.
  • If 71.75 is odd, its additive inverse is also odd.
  • The sum of the digits of 71.75 and its additive inverse may or may not be the same.

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