87 Additive Inverse :
The additive inverse of 87 is -87.
This means that when we add 87 and -87, the result is zero:
87 + (-87) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 87
- Additive inverse: -87
To verify: 87 + (-87) = 0
Extended Mathematical Exploration of 87
Let's explore various mathematical operations and concepts related to 87 and its additive inverse -87.
Basic Operations and Properties
- Square of 87: 7569
- Cube of 87: 658503
- Square root of |87|: 9.3273790530888
- Reciprocal of 87: 0.011494252873563
- Double of 87: 174
- Half of 87: 43.5
- Absolute value of 87: 87
Trigonometric Functions
- Sine of 87: -0.82181783663082
- Cosine of 87: 0.56975033426531
- Tangent of 87: -1.4424174716642
Exponential and Logarithmic Functions
- e^87: 6.0760302250569E+37
- Natural log of 87: 4.4659081186546
Floor and Ceiling Functions
- Floor of 87: 87
- Ceiling of 87: 87
Interesting Properties and Relationships
- The sum of 87 and its additive inverse (-87) is always 0.
- The product of 87 and its additive inverse is: -7569
- The average of 87 and its additive inverse is always 0.
- The distance between 87 and its additive inverse on a number line is: 174
Applications in Algebra
Consider the equation: x + 87 = 0
The solution to this equation is x = -87, which is the additive inverse of 87.
Graphical Representation
On a coordinate plane:
- The point (87, 0) is reflected across the y-axis to (-87, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 87 and Its Additive Inverse
Consider the alternating series: 87 + (-87) + 87 + (-87) + ...
The sum of this series oscillates between 0 and 87, never converging unless 87 is 0.
In Number Theory
For integer values:
- If 87 is even, its additive inverse is also even.
- If 87 is odd, its additive inverse is also odd.
- The sum of the digits of 87 and its additive inverse may or may not be the same.
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