75 Additive Inverse :
The additive inverse of 75 is -75.
This means that when we add 75 and -75, the result is zero:
75 + (-75) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 75
- Additive inverse: -75
To verify: 75 + (-75) = 0
Extended Mathematical Exploration of 75
Let's explore various mathematical operations and concepts related to 75 and its additive inverse -75.
Basic Operations and Properties
- Square of 75: 5625
- Cube of 75: 421875
- Square root of |75|: 8.6602540378444
- Reciprocal of 75: 0.013333333333333
- Double of 75: 150
- Half of 75: 37.5
- Absolute value of 75: 75
Trigonometric Functions
- Sine of 75: -0.38778163540943
- Cosine of 75: 0.92175126972475
- Tangent of 75: -0.42070095062112
Exponential and Logarithmic Functions
- e^75: 3.733241996799E+32
- Natural log of 75: 4.3174881135363
Floor and Ceiling Functions
- Floor of 75: 75
- Ceiling of 75: 75
Interesting Properties and Relationships
- The sum of 75 and its additive inverse (-75) is always 0.
- The product of 75 and its additive inverse is: -5625
- The average of 75 and its additive inverse is always 0.
- The distance between 75 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75 = 0
The solution to this equation is x = -75, which is the additive inverse of 75.
Graphical Representation
On a coordinate plane:
- The point (75, 0) is reflected across the y-axis to (-75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75 and Its Additive Inverse
Consider the alternating series: 75 + (-75) + 75 + (-75) + ...
The sum of this series oscillates between 0 and 75, never converging unless 75 is 0.
In Number Theory
For integer values:
- If 75 is even, its additive inverse is also even.
- If 75 is odd, its additive inverse is also odd.
- The sum of the digits of 75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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