72.25 Additive Inverse :

The additive inverse of 72.25 is -72.25.

This means that when we add 72.25 and -72.25, the result is zero:

72.25 + (-72.25) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 72.25
  • Additive inverse: -72.25

To verify: 72.25 + (-72.25) = 0

Extended Mathematical Exploration of 72.25

Let's explore various mathematical operations and concepts related to 72.25 and its additive inverse -72.25.

Basic Operations and Properties

  • Square of 72.25: 5220.0625
  • Cube of 72.25: 377149.515625
  • Square root of |72.25|: 8.5
  • Reciprocal of 72.25: 0.013840830449827
  • Double of 72.25: 144.5
  • Half of 72.25: 36.125
  • Absolute value of 72.25: 72.25

Trigonometric Functions

  • Sine of 72.25: 0.0066309839702791
  • Cosine of 72.25: -0.99997801478412
  • Tangent of 72.25: -0.0066311297570984

Exponential and Logarithmic Functions

  • e^72.25: 2.3865817622242E+31
  • Natural log of 72.25: 4.2801323269925

Floor and Ceiling Functions

  • Floor of 72.25: 72
  • Ceiling of 72.25: 73

Interesting Properties and Relationships

  • The sum of 72.25 and its additive inverse (-72.25) is always 0.
  • The product of 72.25 and its additive inverse is: -5220.0625
  • The average of 72.25 and its additive inverse is always 0.
  • The distance between 72.25 and its additive inverse on a number line is: 144.5

Applications in Algebra

Consider the equation: x + 72.25 = 0

The solution to this equation is x = -72.25, which is the additive inverse of 72.25.

Graphical Representation

On a coordinate plane:

  • The point (72.25, 0) is reflected across the y-axis to (-72.25, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 72.25 and Its Additive Inverse

Consider the alternating series: 72.25 + (-72.25) + 72.25 + (-72.25) + ...

The sum of this series oscillates between 0 and 72.25, never converging unless 72.25 is 0.

In Number Theory

For integer values:

  • If 72.25 is even, its additive inverse is also even.
  • If 72.25 is odd, its additive inverse is also odd.
  • The sum of the digits of 72.25 and its additive inverse may or may not be the same.

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