74.007 Additive Inverse :

The additive inverse of 74.007 is -74.007.

This means that when we add 74.007 and -74.007, the result is zero:

74.007 + (-74.007) = 0

Additive Inverse of a Decimal Number

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

  • Original number: 74.007
  • Additive inverse: -74.007

To verify: 74.007 + (-74.007) = 0

Extended Mathematical Exploration of 74.007

Let's explore various mathematical operations and concepts related to 74.007 and its additive inverse -74.007.

Basic Operations and Properties

  • Square of 74.007: 5477.036049
  • Cube of 74.007: 405339.00687834
  • Square root of |74.007|: 8.6027321241568
  • Reciprocal of 74.007: 0.01351223532909
  • Double of 74.007: 148.014
  • Half of 74.007: 37.0035
  • Absolute value of 74.007: 74.007

Trigonometric Functions

  • Sine of 74.007: -0.98392011290709
  • Cosine of 74.007: 0.17860910227897
  • Tangent of 74.007: -5.5087904275465

Exponential and Logarithmic Functions

  • e^74.007: 1.3830303869293E+32
  • Natural log of 74.007: 4.304159683325

Floor and Ceiling Functions

  • Floor of 74.007: 74
  • Ceiling of 74.007: 75

Interesting Properties and Relationships

  • The sum of 74.007 and its additive inverse (-74.007) is always 0.
  • The product of 74.007 and its additive inverse is: -5477.036049
  • The average of 74.007 and its additive inverse is always 0.
  • The distance between 74.007 and its additive inverse on a number line is: 148.014

Applications in Algebra

Consider the equation: x + 74.007 = 0

The solution to this equation is x = -74.007, which is the additive inverse of 74.007.

Graphical Representation

On a coordinate plane:

  • The point (74.007, 0) is reflected across the y-axis to (-74.007, 0).
  • The midpoint between these two points is always (0, 0).

Series Involving 74.007 and Its Additive Inverse

Consider the alternating series: 74.007 + (-74.007) + 74.007 + (-74.007) + ...

The sum of this series oscillates between 0 and 74.007, never converging unless 74.007 is 0.

In Number Theory

For integer values:

  • If 74.007 is even, its additive inverse is also even.
  • If 74.007 is odd, its additive inverse is also odd.
  • The sum of the digits of 74.007 and its additive inverse may or may not be the same.

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