71 Additive Inverse :
The additive inverse of 71 is -71.
This means that when we add 71 and -71, the result is zero:
71 + (-71) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 71
- Additive inverse: -71
To verify: 71 + (-71) = 0
Extended Mathematical Exploration of 71
Let's explore various mathematical operations and concepts related to 71 and its additive inverse -71.
Basic Operations and Properties
- Square of 71: 5041
- Cube of 71: 357911
- Square root of |71|: 8.4261497731764
- Reciprocal of 71: 0.014084507042254
- Double of 71: 142
- Half of 71: 35.5
- Absolute value of 71: 71
Trigonometric Functions
- Sine of 71: 0.95105465325437
- Cosine of 71: -0.30902272816607
- Tangent of 71: -3.0776204031934
Exponential and Logarithmic Functions
- e^71: 6.8376712297627E+30
- Natural log of 71: 4.2626798770413
Floor and Ceiling Functions
- Floor of 71: 71
- Ceiling of 71: 71
Interesting Properties and Relationships
- The sum of 71 and its additive inverse (-71) is always 0.
- The product of 71 and its additive inverse is: -5041
- The average of 71 and its additive inverse is always 0.
- The distance between 71 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71 = 0
The solution to this equation is x = -71, which is the additive inverse of 71.
Graphical Representation
On a coordinate plane:
- The point (71, 0) is reflected across the y-axis to (-71, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71 and Its Additive Inverse
Consider the alternating series: 71 + (-71) + 71 + (-71) + ...
The sum of this series oscillates between 0 and 71, never converging unless 71 is 0.
In Number Theory
For integer values:
- If 71 is even, its additive inverse is also even.
- If 71 is odd, its additive inverse is also odd.
- The sum of the digits of 71 and its additive inverse may or may not be the same.
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