# Math Notes

- Author:
- lmusleh403350

## Open Top Box Deconstruction Notes

Laila Musleh
1/1/17
Period: 5
Math Notes

**Open Top Box deconstruction notes **

- Map of the Open Top Box with
*A = 1152* - The box end is:

*¼ b x ¼ h*- The box width
**=***w - 2 (¼)*

**= w - ½ h**- V = w x h x d =
*(w -½ h) (¼ h) (¼ h)* - In order to fold into a box, w-½ must be positive
*w-½ h > 0 or w ½ h* - If
, the “w”*A = 1152***w*h/w = 1152/w** - V = w x h x d
*=(w-½ h) (¼ h) (¼ h)* *V = (w-½ * 1152/w) (¼*1152/w) (¼*1152/w)**= (w -576/w) (288/w) (288/w)*

Review: The Number System

- We know that these sets of numbers exist, because we can ask questions that require them. If an operation never requires a new set of numbers, then we say the set is “closed”, or completely self-contained, under that operation

- “The set of natural numbers is closed with respect to addition.”
- The first blank is the name of a set of numbers. The second blank is the name of an operation.
- This means that if you pick any two natural numbers and add them, you will get a new natural number. “The set of natural numbers is NOT closed under subtraction.” Because 1 – 2 gives an answer that is NOT a natural number (-1 is not a natural number)

- The sets of natural and whole numbers are closed under addition and multiplication.
- The set of integers is closed under addition, subtraction, and multiplication
- The set of rational numbers is closed under addition, subtraction,multiplication*, and division*
- The set of real numbers is closed under addition, subtraction, multiplication*, and division*, but NOT exponents

- Given: y = ax2 + bx + c where a, b, and c are all real numbers
- Solve this equation: 0 = x2 + 1
- - 1 = x2
- X = +- square root -1
- X = ???

- For the set to be closed, the answer must be a number in the set
- So, what is that number?
- What is square root -1 ?
- Square root -1 = the thing that when you square it, you get -1
- There is NO such real number!
- So, we define square root -1 = i, or equivalently - 1 = i2
- This is the imaginary number
- If a number is some multiple of ݅, we call it an imaginary number:
- Each of these is an example of an imaginary number
- If a number is a combination of a real number and some multiple of ݅, we call it a complex number:
- Each of these is an example of a complex number