7 Additive Inverse :
The additive inverse of 7 is -7.
This means that when we add 7 and -7, the result is zero:
7 + (-7) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 7
- Additive inverse: -7
To verify: 7 + (-7) = 0
Extended Mathematical Exploration of 7
Let's explore various mathematical operations and concepts related to 7 and its additive inverse -7.
Basic Operations and Properties
- Square of 7: 49
- Cube of 7: 343
- Square root of |7|: 2.6457513110646
- Reciprocal of 7: 0.14285714285714
- Double of 7: 14
- Half of 7: 3.5
- Absolute value of 7: 7
Trigonometric Functions
- Sine of 7: 0.65698659871879
- Cosine of 7: 0.7539022543433
- Tangent of 7: 0.87144798272432
Exponential and Logarithmic Functions
- e^7: 1096.6331584285
- Natural log of 7: 1.9459101490553
Floor and Ceiling Functions
- Floor of 7: 7
- Ceiling of 7: 7
Interesting Properties and Relationships
- The sum of 7 and its additive inverse (-7) is always 0.
- The product of 7 and its additive inverse is: -49
- The average of 7 and its additive inverse is always 0.
- The distance between 7 and its additive inverse on a number line is: 14
Applications in Algebra
Consider the equation: x + 7 = 0
The solution to this equation is x = -7, which is the additive inverse of 7.
Graphical Representation
On a coordinate plane:
- The point (7, 0) is reflected across the y-axis to (-7, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 7 and Its Additive Inverse
Consider the alternating series: 7 + (-7) + 7 + (-7) + ...
The sum of this series oscillates between 0 and 7, never converging unless 7 is 0.
In Number Theory
For integer values:
- If 7 is even, its additive inverse is also even.
- If 7 is odd, its additive inverse is also odd.
- The sum of the digits of 7 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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