The Language of Algebra. The language of Algebra uses numbers and variables. A variable is a symbol that can be replaced by any menber of a set of numbers or other objects. When numbers and variables are combibed using the operations of arithmetic, the result is called an algebraic expression, or simply an expression. The expression π r ^ 2 uses the variable r and the numbers π and 2.
November 1, 2013 Unit 3 homework 3 Short answer 5. Write a pseudo code statement that declares the variable cost so it can hold real numbers? long cost int total count=220 total=10+210 totalfee=total-downPayment 6. Write a pseudo code statement that declares the variable total so it can hold integers. Initialize the variable with the value 0.
6. What will the following pseudocode program display? Module Main() Declare Integer x = 1 Declare real y = 3.4 Display x, “ ”, Y Call changeUs (x, y) Display x, “ ”, y End Module Module changeUs(Integer a, Real b) Set a = 0 Set b = 0 Display a, “ “, b End Module 7. What will the following psudocode program display? Module main() Declare Integer x = 1
MAT221: Introduction to Algebra Week 5 Discussion Factoring According to what I calculated, the GCF of 92 and 64 is 4. I found this answer by : Divisor 92 divided by 4 equals 23 and 64 divided by 4 equals 16. I used the factor of numbers to help me. 92/4=23 1,2,4,23,46,92 2/24 2/12 2/6 3/3 64/4=16 1,2,4,8,76,32,64 24=2x2x2x3 Prime factors are also know as natural numbers. It means a number that is more than one and I can only divide it by one, and has no remaining numbers.
Randy Michael NT 1210 Lab 1.1 Professor Chibuzo Onukwufor 4/1/15 Lab 1.1 1: Convert the decimal value 127 to binary. Explain the process of conversion that you used. Decimal Number | Binary Number | Remainder | 127 - | 64 | 63 | 63 - | 32 | 31 | 31 - | 16 | 15 | 15 - | 8 | 7 | 7 - | 4 | 3 | 3 - | 2 | 1 | 1 - | 1 | 0 | Binary | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | Decimal | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | Conversion | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | I took the decimal and divided it by two giving 1 for the remainders and 0 if it did not have a remainder. 2: Explain why the values 102 and 00102 are equivalent. They are equivalent because they represent the powers of 10 3: Based on the breakdown of the decimal and binary systems in this lab, describe the available digit values and the first four digits of a base 5 numbering system.
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)
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. An example is, if the sum of the digits is divisible by 3, then 3 is a factor of that number. Another topic in this chapter is greatest common factor (GCF). For this topic McKellar gives a definition and three methods for the reader to try. The first method is the list method which is listing all the factors of both numbers and finding the ones they have in common.
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
Math Background Simplify the following expressions (ln is the natural logarithm): (a) ln (b) b − ln(ex ) (a) ln(a) + ln(b) (c) eln(a)+ln(b)−ln(c) (d) ln ea × eb × ec (e) ex × e−x (f) ex+y − ex × ey (g) eln(x) 1 (h) ln(x) + ln( x ) ( ) 2. Math Background Sketch functions with (a) a positive first derivative and a positive second derivative over the range x in (0, 1). (b) a negative first derivative and a negative second derivative over the range x in (0, 1). 3. Math Background Consider the following function: 1 f (K, L) = K 1/2 × L1/2 2 This
A mathematician from Baghdad, Alkhwarizimi, worked with π but it was Al-Khashi from Samarkand in 1430 AD that approximated π to 16 decimal places. Then came the European Renaissance with a whole new world of mathematicians. Viete in 1593 AD expressed π as an infinite product by using 2s and square roots. In 1610, Ludolph van Ceulen calculated π to 35 decimal places followed by Snell in 1630 to 39 decimal places. In 1655 Wallis showed the value of π/2=2/1x2/3x4/3x4/5x6/5x6/7x8/7x8/9...