72 Additive Inverse :
The additive inverse of 72 is -72.
This means that when we add 72 and -72, the result is zero:
72 + (-72) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 72
- Additive inverse: -72
To verify: 72 + (-72) = 0
Extended Mathematical Exploration of 72
Let's explore various mathematical operations and concepts related to 72 and its additive inverse -72.
Basic Operations and Properties
- Square of 72: 5184
- Cube of 72: 373248
- Square root of |72|: 8.4852813742386
- Reciprocal of 72: 0.013888888888889
- Double of 72: 144
- Half of 72: 36
- Absolute value of 72: 72
Trigonometric Functions
- Sine of 72: 0.25382336276204
- Cosine of 72: -0.96725058827388
- Tangent of 72: -0.26241737750194
Exponential and Logarithmic Functions
- e^72: 1.8586717452841E+31
- Natural log of 72: 4.2766661190161
Floor and Ceiling Functions
- Floor of 72: 72
- Ceiling of 72: 72
Interesting Properties and Relationships
- The sum of 72 and its additive inverse (-72) is always 0.
- The product of 72 and its additive inverse is: -5184
- The average of 72 and its additive inverse is always 0.
- The distance between 72 and its additive inverse on a number line is: 144
Applications in Algebra
Consider the equation: x + 72 = 0
The solution to this equation is x = -72, which is the additive inverse of 72.
Graphical Representation
On a coordinate plane:
- The point (72, 0) is reflected across the y-axis to (-72, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 72 and Its Additive Inverse
Consider the alternating series: 72 + (-72) + 72 + (-72) + ...
The sum of this series oscillates between 0 and 72, never converging unless 72 is 0.
In Number Theory
For integer values:
- If 72 is even, its additive inverse is also even.
- If 72 is odd, its additive inverse is also odd.
- The sum of the digits of 72 and its additive inverse may or may not be the same.
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