42 Additive Inverse :
The additive inverse of 42 is -42.
This means that when we add 42 and -42, the result is zero:
42 + (-42) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 42
- Additive inverse: -42
To verify: 42 + (-42) = 0
Extended Mathematical Exploration of 42
Let's explore various mathematical operations and concepts related to 42 and its additive inverse -42.
Basic Operations and Properties
- Square of 42: 1764
- Cube of 42: 74088
- Square root of |42|: 6.4807406984079
- Reciprocal of 42: 0.023809523809524
- Double of 42: 84
- Half of 42: 21
- Absolute value of 42: 42
Trigonometric Functions
- Sine of 42: -0.91652154791563
- Cosine of 42: -0.39998531498835
- Tangent of 42: 2.2913879924375
Exponential and Logarithmic Functions
- e^42: 1.7392749415205E+18
- Natural log of 42: 3.7376696182834
Floor and Ceiling Functions
- Floor of 42: 42
- Ceiling of 42: 42
Interesting Properties and Relationships
- The sum of 42 and its additive inverse (-42) is always 0.
- The product of 42 and its additive inverse is: -1764
- The average of 42 and its additive inverse is always 0.
- The distance between 42 and its additive inverse on a number line is: 84
Applications in Algebra
Consider the equation: x + 42 = 0
The solution to this equation is x = -42, which is the additive inverse of 42.
Graphical Representation
On a coordinate plane:
- The point (42, 0) is reflected across the y-axis to (-42, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 42 and Its Additive Inverse
Consider the alternating series: 42 + (-42) + 42 + (-42) + ...
The sum of this series oscillates between 0 and 42, never converging unless 42 is 0.
In Number Theory
For integer values:
- If 42 is even, its additive inverse is also even.
- If 42 is odd, its additive inverse is also odd.
- The sum of the digits of 42 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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