davidfarley7171
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take notes on 3 algebra concepts a ...
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davidfarley7171 commits to:
take notes on 3 algebra concepts a day
from https://www.mathsisfun.com/algebra/index-college.html Or until I get a job
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My Commitment Journal
 davidfarley7171
May 31, 2020, 11:48 PM
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| took notes on the quadratic equation today | |
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davidfarley7171
May 26, 2020, 7:25 PM
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Having a super hard time posting updates on this because my notes have characters that I cant have in this text input. but I got about half way through polynomials |
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davidfarley7171
May 19, 2020, 6:42 PM
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# letter conventions Start of the alphabet: a, b, c, ... constants (fixed values) From i to n: i, j, k, l, m, n positive integers (for counting) End of the alphabet: ... x, y, z variables (unknowns) Those are not rules, but they are often used that way. ... elipses mean infinity after a set # factors are the values on either side of a multiplication # Counting numbers are positive numbers after 0 # Whole numbers are regular numbers but include 0, may also be refered to as natural numbers. # Integers are numbers that are positive or negative. # Rational Numbers Any number that can be written as a fraction is called a Rational Number. Most numbers can be written this way except when dividing by 0. So this includes all integers and decimals. # square root The sqare root symbol looks like a checkmark with a bend. its called a Radical. The square root can be negative, but we only give the positive result by convention. Perfect squares are square roots that are not decimals. # calculate the square root a) start with a guess (let's guess 4 is the square root of 10) around b) divide by the guess (10/4 = 2.5) c) add that to the guess (4 + 2.5 = 6.5) d) then divide that result by 2, in other words halve it. (6.5/2 = 3.25) e) now, set that as the new guess, and start at b) again Our first attempt got us from 4 to 3.25 Going again (b to e) gets us: 3.163 Going again (b to e) gets us: 3.1623 And so, after 3 times around the answer is 3.1623, which is pretty good, because: 3.1623 x 3.1623 = 10.00014 What if we have to guess the square root for a difficult number such as "82,163" ... ? In that case we could think "82,163" has 5 digits, so the square root might have 3 digits (100x100=10,000), and the square root of 8 (the first digit) is about 3 (3x3=9), so 300 is a good start. # Irrational Numbers So, the square root of 2 (√2) is an irrational number. It is called irrational because it is not rational (can't be made using a simple ratio of integers). It isn't crazy or anything, just not rational. And we know there are many more irrational numbers. Pi (π) is a famous one. # Real Numbers Includes both rational and irrational numbers. Any number anywhere on the number line. # imaginary Numbers A number whose square is a negative Real Number. Let us just imagine that the square root of minus one exists. We can even give it a special symbol: the letter i And we can use it to answer questions: Example: what is the square root of −9 ? !-- Answer: √(−9) = √(9 × −1) = √(9) × √(−1) = 3 × √(−1) = 3i -- OK, the answer still involves i, but it gives a sensible and consistent answer. And i (the square root of −1) times any Real Number is an Imaginary Number. 3i, -6i, 0.05i, and pie i are all imaginary numbers. There are also many applications for Imaginary Numbers, for example in the fields of electricity and electronics. # Complex Numbers Yes, if we put a Real Number and an Imaginary Number together we get a new type of number called a Complex Number A Complex Number has a Real Part and an Imaginary Part, but either one could be zero So a Real Number is also a Complex Number (with an imaginary part of 0): and likewise an Imaginary Number is also a Complex Number (with a real part of 0): So the Complex Numbers include all Real Numbers and all Imaginary Numbers, and all combinations of them. # prime number a whole number that cannot be made by multiplying other whole numbers 1 is not Prime and also not Composite. # composite number Is a positive integer that has at least one divisor other than 1 and itself. Or it can be devided by some other number cleanly. # The Fundamental Theorem of Arithmetic Any integer greater than 1 is either a prime number, or can be written as a unique product of prime numbers (ignoring the order). It is like the Prime Numbers are the basic building blocks of all numbers. unique product of prime numbers" means there is only one (unique!) set of prime numbers that will work Its ok to repeat a prime number. Example: 12 is made by multiplying the prime numbers 2, 2 and 3 together. |
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