80.74 Additive Inverse :

The additive inverse of 80.74 is -80.74.

This means that when we add 80.74 and -80.74, the result is zero:

80.74 + (-80.74) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 80.74
  • Additive inverse: -80.74

To verify: 80.74 + (-80.74) = 0

Extended Mathematical Exploration of 80.74

Let's explore various mathematical operations and concepts related to 80.74 and its additive inverse -80.74.

Basic Operations and Properties

  • Square of 80.74: 6518.9476
  • Cube of 80.74: 526339.829224
  • Square root of |80.74|: 8.9855439456941
  • Reciprocal of 80.74: 0.012385434728759
  • Double of 80.74: 161.48
  • Half of 80.74: 40.37
  • Absolute value of 80.74: 80.74

Trigonometric Functions

  • Sine of 80.74: -0.80838830591911
  • Cosine of 80.74: 0.58864959598494
  • Tangent of 80.74: -1.3732928917865

Exponential and Logarithmic Functions

  • e^80.74: 1.1612787227853E+35
  • Natural log of 80.74: 4.3912341154248

Floor and Ceiling Functions

  • Floor of 80.74: 80
  • Ceiling of 80.74: 81

Interesting Properties and Relationships

  • The sum of 80.74 and its additive inverse (-80.74) is always 0.
  • The product of 80.74 and its additive inverse is: -6518.9476
  • The average of 80.74 and its additive inverse is always 0.
  • The distance between 80.74 and its additive inverse on a number line is: 161.48

Applications in Algebra

Consider the equation: x + 80.74 = 0

The solution to this equation is x = -80.74, which is the additive inverse of 80.74.

Graphical Representation

On a coordinate plane:

  • The point (80.74, 0) is reflected across the y-axis to (-80.74, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 80.74 and Its Additive Inverse

Consider the alternating series: 80.74 + (-80.74) + 80.74 + (-80.74) + ...

The sum of this series oscillates between 0 and 80.74, never converging unless 80.74 is 0.

In Number Theory

For integer values:

  • If 80.74 is even, its additive inverse is also even.
  • If 80.74 is odd, its additive inverse is also odd.
  • The sum of the digits of 80.74 and its additive inverse may or may not be the same.

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