70/72 Additive Inverse :
The additive inverse of 70/72 is -70/72.
This means that when we add 70/72 and -70/72, the result is zero:
70/72 + (-70/72) = 0
Additive Inverse of a Fraction
For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:
- Original fraction: 70/72
- Additive inverse: -70/72
To verify: 70/72 + (-70/72) = 0
Extended Mathematical Exploration of 70/72
Let's explore various mathematical operations and concepts related to 70/72 and its additive inverse -70/72.
Basic Operations and Properties
- Square of 70/72: 0.94521604938272
- Cube of 70/72: 0.91896004801097
- Square root of |70/72|: 0.98601329718327
- Reciprocal of 70/72: 1.0285714285714
- Double of 70/72: 1.9444444444444
- Half of 70/72: 0.48611111111111
- Absolute value of 70/72: 0.97222222222222
Trigonometric Functions
- Sine of 70/72: 0.82613989673087
- Cosine of 70/72: 0.56346505750535
- Tangent of 70/72: 1.4661776905714
Exponential and Logarithmic Functions
- e^70/72: 2.6438130764233
- Natural log of 70/72: -0.028170876966696
Floor and Ceiling Functions
- Floor of 70/72: 0
- Ceiling of 70/72: 1
Interesting Properties and Relationships
- The sum of 70/72 and its additive inverse (-70/72) is always 0.
- The product of 70/72 and its additive inverse is: -4900
- The average of 70/72 and its additive inverse is always 0.
- The distance between 70/72 and its additive inverse on a number line is: 140
Applications in Algebra
Consider the equation: x + 70/72 = 0
The solution to this equation is x = -70/72, which is the additive inverse of 70/72.
Graphical Representation
On a coordinate plane:
- The point (70/72, 0) is reflected across the y-axis to (-70/72, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 70/72 and Its Additive Inverse
Consider the alternating series: 70/72 + (-70/72) + 70/72 + (-70/72) + ...
The sum of this series oscillates between 0 and 70/72, never converging unless 70/72 is 0.
In Number Theory
For integer values:
- If 70/72 is even, its additive inverse is also even.
- If 70/72 is odd, its additive inverse is also odd.
- The sum of the digits of 70/72 and its additive inverse may or may not be the same.
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