10 Additive Inverse :
The additive inverse of 10 is -10.
This means that when we add 10 and -10, the result is zero:
10 + (-10) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 10
- Additive inverse: -10
To verify: 10 + (-10) = 0
Extended Mathematical Exploration of 10
Let's explore various mathematical operations and concepts related to 10 and its additive inverse -10.
Basic Operations and Properties
- Square of 10: 100
- Cube of 10: 1000
- Square root of |10|: 3.1622776601684
- Reciprocal of 10: 0.1
- Double of 10: 20
- Half of 10: 5
- Absolute value of 10: 10
Trigonometric Functions
- Sine of 10: -0.54402111088937
- Cosine of 10: -0.83907152907645
- Tangent of 10: 0.64836082745909
Exponential and Logarithmic Functions
- e^10: 22026.465794807
- Natural log of 10: 2.302585092994
Floor and Ceiling Functions
- Floor of 10: 10
- Ceiling of 10: 10
Interesting Properties and Relationships
- The sum of 10 and its additive inverse (-10) is always 0.
- The product of 10 and its additive inverse is: -100
- The average of 10 and its additive inverse is always 0.
- The distance between 10 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10 = 0
The solution to this equation is x = -10, which is the additive inverse of 10.
Graphical Representation
On a coordinate plane:
- The point (10, 0) is reflected across the y-axis to (-10, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10 and Its Additive Inverse
Consider the alternating series: 10 + (-10) + 10 + (-10) + ...
The sum of this series oscillates between 0 and 10, never converging unless 10 is 0.
In Number Theory
For integer values:
- If 10 is even, its additive inverse is also even.
- If 10 is odd, its additive inverse is also odd.
- The sum of the digits of 10 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: