1. Factor a trinomial whose leading coefficient is 1. Pick any one of the problems and solve the trinomial. If the trinomial is prime, state this and explain why. a. x2+8x+15 b. x2–4x –5 c. x2–14x+45 2.
Wow, I am glad we use the shorter version of π =3.14 to solve our math problems but what is π really used for in today’s world? The obvious answer is π is used in almost every branch of math. If you want to find the circumference of a circle, the surface area of a cylinder, the area of a sector of a circle, any measurement of a circle, cylinder, or sphere it involves π since π was used to make the circle. So with that in mind, I thought I had a good handle on where π is used in the real world today. It is used by architects, contractors, draftsmen, building and bridge designers, engineers, or just about any job that uses shapes.
For example. 127 is less than 128 so I cannot be subtracted. So you will put a zero and move that number over. Since 127 is greater than 64, you will subtract 64 from 128 and put a 1 for that value. Carry it over to the right.
Then I chose different types of numbers to test. For example: prime and composite numbers, and odd and even numbers. I found that when an even number was picked as the starting number (n), it can automatically be reduced to an odd number by subtracting one. When I figured that out my friend told me that all natural numbers have a common divisor which is one. Representations: If you want to win the game, you should start with an even number.
It means a number that is more than one and I can only divide it by one, and has no remaining numbers. It is also becomes equal, when using prime factors. I divided starting with the small number, and then I finished until it was equal, a perfect square. I used the formula x^a X x^b=x 2x2x23 2x2x2x2x3x193 The prime factor is
Assignment #2 1) Improve the result from problem 4 of the previous assignment by showing that for every e> 0, no matter how small, given n real numbers x1,...,xn where each xi is a real number in the interval [0, 1], there exists an algorithm that runs in linear time and that will output a permutation of the numbers, say y1, ...., yn, such that ∑ ni=2 |yi - yi-1| < 1 + e. (Hint: use buckets of size smaller than 1/n; you might also need the solution to problem 3 from the first assignment!) 2) To evaluate FFT(a0,a1,a2,a3,a4,a5,a6,a7) we apply recursively FFT and obtain FFT( a0,a2,a4,a6) and FFT(a1,a3,a5,a7). Proceeding further with recursion, we obtain FFT(a0,a4) and FFT(a2,a6) as well as FFT(a1,a5) and FFT(a3,a7). Thus, from bottom up, FFT(a0,a1,a2,a3,a4,a5,a6,a7)
Radicals Tips 1. Make sure that one of the two factors of the radicand (expression under the radical) is the largest perfect square: Example: Simplify 72 Correct 72 = 36 ∙ 2 = 62 Incorrect 72 = 9 ∙ 8 = 38 2. To be able to add or subtract radicals, the radicands must be the same. Example 1: Add 32 + 52 Answer: Since radicands are the same, (3 + 5)2 = 82 Example 2: Subtract 73 - 3 Answer: (7 – 1)3 = 63 Example 3: 318 - 52 (Must simplify first) 39 2 - 52 3 ∙ 3 ∙ 2 - 52 92 - 520 Answer: 42
Unit 3 – Algebra Basics Module 3C Sections 10.3 – 10.8 3C Addition of Real Numbers Addition on the Number Line To do the addition a + b on the number line, start at 0, move to a, and then move according to b. a) If b is positive, move from a to the right. b) If b is negative, move from a to the left. c) If b is 0, stay at a. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 2 3C Addition of Real Numbers Add real numbers without using the number line. Add: –4 + 9.
The first section in the book is about factors and multiples. In this section McKellar discusses prime numbers and prime factorization. She covers the definition of a factor, a prime number, and a prime factor. She also shows two techniques for factoring factor trees and EZ divisibility tricks. EZ divisibility tricks were something that was new to me so, I was really interested in them they are ways to test numbers to see what their factors may be.
Name ___________________ Date ____________ Period ___________ The Curious Incident of the Dog in the Night-time By Mark Haddon The rule for working out prime numbers is really simple, but no one has ever worked out a simple formula for telling you whether a very big number is a prime number or what the next one will be. If a number is really, really big, it can take a computer years to work out whether it is a prime number. Prime numbers are useful for writing codes and in America they are classed as Military Material and if you find one over 100 digits long you have to tell the CIA and they buy it off you for $10,000. But it would not be a very good way of making a living. Prime numbers are what is left when you have taken a Prime numbers are what is left when you have taken all the patterns away.