7.5 Additive Inverse :
The additive inverse of 7.5 is -7.5.
This means that when we add 7.5 and -7.5, the result is zero:
7.5 + (-7.5) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 7.5
- Additive inverse: -7.5
To verify: 7.5 + (-7.5) = 0
Extended Mathematical Exploration of 7.5
Let's explore various mathematical operations and concepts related to 7.5 and its additive inverse -7.5.
Basic Operations and Properties
- Square of 7.5: 56.25
- Cube of 7.5: 421.875
- Square root of |7.5|: 2.7386127875258
- Reciprocal of 7.5: 0.13333333333333
- Double of 7.5: 15
- Half of 7.5: 3.75
- Absolute value of 7.5: 7.5
Trigonometric Functions
- Sine of 7.5: 0.93799997677474
- Cosine of 7.5: 0.34663531783503
- Tangent of 7.5: 2.7060138667727
Exponential and Logarithmic Functions
- e^7.5: 1808.0424144561
- Natural log of 7.5: 2.0149030205423
Floor and Ceiling Functions
- Floor of 7.5: 7
- Ceiling of 7.5: 8
Interesting Properties and Relationships
- The sum of 7.5 and its additive inverse (-7.5) is always 0.
- The product of 7.5 and its additive inverse is: -56.25
- The average of 7.5 and its additive inverse is always 0.
- The distance between 7.5 and its additive inverse on a number line is: 15
Applications in Algebra
Consider the equation: x + 7.5 = 0
The solution to this equation is x = -7.5, which is the additive inverse of 7.5.
Graphical Representation
On a coordinate plane:
- The point (7.5, 0) is reflected across the y-axis to (-7.5, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 7.5 and Its Additive Inverse
Consider the alternating series: 7.5 + (-7.5) + 7.5 + (-7.5) + ...
The sum of this series oscillates between 0 and 7.5, never converging unless 7.5 is 0.
In Number Theory
For integer values:
- If 7.5 is even, its additive inverse is also even.
- If 7.5 is odd, its additive inverse is also odd.
- The sum of the digits of 7.5 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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