75/89 Additive Inverse :
The additive inverse of 75/89 is -75/89.
This means that when we add 75/89 and -75/89, the result is zero:
75/89 + (-75/89) = 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: 75/89
- Additive inverse: -75/89
To verify: 75/89 + (-75/89) = 0
Extended Mathematical Exploration of 75/89
Let's explore various mathematical operations and concepts related to 75/89 and its additive inverse -75/89.
Basic Operations and Properties
- Square of 75/89: 0.71013760888777
- Cube of 75/89: 0.59843056928744
- Square root of |75/89|: 0.91798509204316
- Reciprocal of 75/89: 1.1866666666667
- Double of 75/89: 1.685393258427
- Half of 75/89: 0.42134831460674
- Absolute value of 75/89: 0.84269662921348
Trigonometric Functions
- Sine of 75/89: 0.74644031009484
- Cosine of 75/89: 0.66545237505438
- Tangent of 75/89: 1.1217035780116
Exponential and Logarithmic Functions
- e^75/89: 2.3226217893046
- Natural log of 75/89: -0.17114825619583
Floor and Ceiling Functions
- Floor of 75/89: 0
- Ceiling of 75/89: 1
Interesting Properties and Relationships
- The sum of 75/89 and its additive inverse (-75/89) is always 0.
- The product of 75/89 and its additive inverse is: -5625
- The average of 75/89 and its additive inverse is always 0.
- The distance between 75/89 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/89 = 0
The solution to this equation is x = -75/89, which is the additive inverse of 75/89.
Graphical Representation
On a coordinate plane:
- The point (75/89, 0) is reflected across the y-axis to (-75/89, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/89 and Its Additive Inverse
Consider the alternating series: 75/89 + (-75/89) + 75/89 + (-75/89) + ...
The sum of this series oscillates between 0 and 75/89, never converging unless 75/89 is 0.
In Number Theory
For integer values:
- If 75/89 is even, its additive inverse is also even.
- If 75/89 is odd, its additive inverse is also odd.
- The sum of the digits of 75/89 and its additive inverse may or may not be the same.
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