400 Additive Inverse :
The additive inverse of 400 is -400.
This means that when we add 400 and -400, the result is zero:
400 + (-400) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 400
- Additive inverse: -400
To verify: 400 + (-400) = 0
Extended Mathematical Exploration of 400
Let's explore various mathematical operations and concepts related to 400 and its additive inverse -400.
Basic Operations and Properties
- Square of 400: 160000
- Cube of 400: 64000000
- Square root of |400|: 20
- Reciprocal of 400: 0.0025
- Double of 400: 800
- Half of 400: 200
- Absolute value of 400: 400
Trigonometric Functions
- Sine of 400: -0.85091935963918
- Cosine of 400: -0.52529633864254
- Tangent of 400: 1.6198844291169
Exponential and Logarithmic Functions
- e^400: 5.2214696897641E+173
- Natural log of 400: 5.991464547108
Floor and Ceiling Functions
- Floor of 400: 400
- Ceiling of 400: 400
Interesting Properties and Relationships
- The sum of 400 and its additive inverse (-400) is always 0.
- The product of 400 and its additive inverse is: -160000
- The average of 400 and its additive inverse is always 0.
- The distance between 400 and its additive inverse on a number line is: 800
Applications in Algebra
Consider the equation: x + 400 = 0
The solution to this equation is x = -400, which is the additive inverse of 400.
Graphical Representation
On a coordinate plane:
- The point (400, 0) is reflected across the y-axis to (-400, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 400 and Its Additive Inverse
Consider the alternating series: 400 + (-400) + 400 + (-400) + ...
The sum of this series oscillates between 0 and 400, never converging unless 400 is 0.
In Number Theory
For integer values:
- If 400 is even, its additive inverse is also even.
- If 400 is odd, its additive inverse is also odd.
- The sum of the digits of 400 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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