Amani has Magical Powers

FOUR IS COSMOS! What does that mean?  Well, the game goes like this: Person A says any number to "any" other number. (Like 18 to 8) Person B tries guessing the pattern, and also doing what Person A did. For example, Person A could say: 19 to 8 8 to 5 5 to 4 4 is COSMOS! That sounds like utter nonsense, right?  It actually makes perfect sense. Look at how many letters these numbers have. 19 has 8 letters in its name (N-I-N-E-T-E-E-N) 8 has 5 letters in its name (E-I-G-H-T) 5 has 4 letters in its name (F-I-V-E) 4 has 4 letters in its name, they're the same number which is why it's COSMOS! HAVE FUN PLAYING THIS GAME!

Why are these two very different things grouped together? That's because they both use the same style charts as one of the most effective strategies.  MIXTURE PROBLEMS: Y ou have to create a chart that has THREE columns and rows. Top Row: Prices/Percentages Middle Row:   Volumes: (x,  y and the total number) Bottom row: Multiply everything from the top and down, and put the result in the appropriate box. It sounds very confusing, which is why I will provide a drawing for the example problem right now. Example Problem: Apple Jack has wants to have a 34 gallon apple cider batch. Blend 1 has 3% pure apple juice, and Blend 2 has 58% pure apple juice. She wants her final batch to have 36% pure apple juice. How much should she use? Chart: IMPORTANT: "Equation 1" is just: x + y = 34 "Equation 2" is just: 0.03x + 0.58y = 12.24       Now solve for x and y using system of linear equations: 0.03x + 0.58y = 12.24  x + y = 34 ...Let's...

GENERAL EXPONENTIAL FUNCTIONS: These are used to show the growth/decay of a value over time using exponents and the initial value.  Formula:  f(x) = a ⋅ bˣ    a = the value you start with x = amount of time b = the growth/decay factor EXPONENTIAL GROWTH: In here, b will ALWAYS be GREATER than 0.   Key words on identifying exponential growth problems: Tripled ==> b = 3 Doubled ==> b = 2 Example Problem: Minnie Mouse had  70  bows. Over the course of 4 years, the amount of bows kept tripling  each year. How much does she have now?  As you can probably see, I have put key words/numbers in bold.  a = 70 (starting amount) x = 4 (amount of years) b = 3 (growth factor) Now just set up the formula! f(x) = 70 ⋅ 3⁴ 3⁴ = 81  70 ⋅ 81 = 5,670 In total, Minnie Mouse has 5,670 bows now.  EXPONENTIAL DECAY:   In here, b will ALWAYS be BETWEEN 0 and 1. Key words on identifying exponential decay problems: Halv...

What are radicals? Just a fancy word for roots. (√) What if the number under the radical isn't a perfect square? It's going to be irrational, but as mathematicians, we must ALWAYS  simplify.  SIMPLIFYING IRRATIONAL RADICALS WITHOUT VARIABLES:   √50 = ? 1. Find the greatest factor and a perfect square of 50! The only perfect square that's a factor of 50 is  25 .   2. Take the square root of that exact factor! √25 = 5 3. Put the "unchanged" number inside , and the "square rooted number"  outside! 5√2 = √50   EXPANDING RADICALS! 5√2 = ? 1. Square the number outside of the radical! 5² = 25 2. Multiply the result with the number  inside  the radical!     25 x 2 = 50  How can I tell if I've simplified enough? Ask yourself , does the number inside the radical have any factors you can get the square root of? If it doesn't (like having factors such as 7 or 5), then you have simplified enough!  SIMPLIFYING RADICALS WITH VARIA...

Quadratic: ax ² + bx + c = 0 When a = 1: You find two numbers that add up to "b" which also multiply to equate to "c". For example: x ² + 8x + 15 = 0 Factors of 15: 1, 15, 3, and 5. You HAVE to find factors BEFORE you find addends!  Which pair adds up to 8? 3 and 5 Therefore, your factored form will be: (x+3)(x+5) = 0 What happens when a doesn't equal 0?  You still have to find two numbers that add up to "b", but also multiplies to equal to "ac". For example:  12x ² - 13x + 3 ac:  Multiply 12 and 3 = 36  b: NEGATIVE   13 (signs matter!) Factors of 36: 1, 36, 2, 18, 3, 12, 4, 9, 6, 6,   Hmm... I can't seem to find anything. Let me check the signs in the original equation. If b is negative but c is positive...that means our two numbers HAVE to be negative.  That's because adding negative numbers gives us a negative number (b). But multiply two negative numbers gives us a POSITIVE number (c).  So... I can just make any pair...

 A Question There was once a question,  One she shoved into the back of her mind, And thrown into the depths of a bottomless ocean. The golden star student, The master violinist, The embodiment of obsession with perfection, She was so confused, So completely lost, She was getting wasted and used. Days spent sitting on the empty ground,  Her eyes searching for the truth, But she knew would never be found.  The question was trivial, Yet her days were spent trying to answer it, Or even deciphering the question.  Maybe she knew what the question was, Maybe she did have an answer, She had just ignored it, and always would.