10.4 Additive Inverse :
The additive inverse of 10.4 is -10.4.
This means that when we add 10.4 and -10.4, the result is zero:
10.4 + (-10.4) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 10.4
- Additive inverse: -10.4
To verify: 10.4 + (-10.4) = 0
Extended Mathematical Exploration of 10.4
Let's explore various mathematical operations and concepts related to 10.4 and its additive inverse -10.4.
Basic Operations and Properties
- Square of 10.4: 108.16
- Cube of 10.4: 1124.864
- Square root of |10.4|: 3.2249030993194
- Reciprocal of 10.4: 0.096153846153846
- Double of 10.4: 20.8
- Half of 10.4: 5.2
- Absolute value of 10.4: 10.4
Trigonometric Functions
- Sine of 10.4: -0.82782646908565
- Cosine of 10.4: -0.56098425742723
- Tangent of 10.4: 1.4756679142517
Exponential and Logarithmic Functions
- e^10.4: 32859.625674443
- Natural log of 10.4: 2.3418058061473
Floor and Ceiling Functions
- Floor of 10.4: 10
- Ceiling of 10.4: 11
Interesting Properties and Relationships
- The sum of 10.4 and its additive inverse (-10.4) is always 0.
- The product of 10.4 and its additive inverse is: -108.16
- The average of 10.4 and its additive inverse is always 0.
- The distance between 10.4 and its additive inverse on a number line is: 20.8
Applications in Algebra
Consider the equation: x + 10.4 = 0
The solution to this equation is x = -10.4, which is the additive inverse of 10.4.
Graphical Representation
On a coordinate plane:
- The point (10.4, 0) is reflected across the y-axis to (-10.4, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10.4 and Its Additive Inverse
Consider the alternating series: 10.4 + (-10.4) + 10.4 + (-10.4) + ...
The sum of this series oscillates between 0 and 10.4, never converging unless 10.4 is 0.
In Number Theory
For integer values:
- If 10.4 is even, its additive inverse is also even.
- If 10.4 is odd, its additive inverse is also odd.
- The sum of the digits of 10.4 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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