Introduction
... (n – 5) = 0 when n = 5. = (n - 5)2 – (5)2 + 27 Furthermore, when n is 5, Un equals 2. = (n – 5)2 – 25 + 27 = (n -5)2 + 2 (n – 5)2 + 2 > 0 for all values of n. Therefore all terms of the sequence Un = n2 – 10n + 27 are positive. ...
... (n – 5) = 0 when n = 5. = (n - 5)2 – (5)2 + 27 Furthermore, when n is 5, Un equals 2. = (n – 5)2 – 25 + 27 = (n -5)2 + 2 (n – 5)2 + 2 > 0 for all values of n. Therefore all terms of the sequence Un = n2 – 10n + 27 are positive. ...
... This solution is always true because r can be replaced with any number and each side of the equation will always be true. Equations that are always true will show the same thing on each side throughout solving each step. In the second line of the equation 3r - 2 = 3r -2 is shown. At this step in sol ...
Linear Notes
... 1st: Find the vertex and write it in a table. 2nd: Move in the positive x direction one space, and find the y that goes with it. Put that point in the table. ...
... 1st: Find the vertex and write it in a table. 2nd: Move in the positive x direction one space, and find the y that goes with it. Put that point in the table. ...
REU 2006 · Discrete Math · Lecture 2
... Proof. First, let us observe the lower bound. We need to find c1 such that p(n) ≥ c1 . So we need to find some way of producing distinct partitions that gives about this many partitions. Imagine that we have a partition of n into k distinct terms which are greater than 2. So n = a1 + · · · + ak . To ...
... Proof. First, let us observe the lower bound. We need to find c1 such that p(n) ≥ c1 . So we need to find some way of producing distinct partitions that gives about this many partitions. Imagine that we have a partition of n into k distinct terms which are greater than 2. So n = a1 + · · · + ak . To ...
Engaging Students in Proof and Reasoning in High School Non
... them.##She#identified#student#work#that#had#the#potential#to#help#her#students#discover#and#make#sense# of#an#important#mathematics#concept.##Specifically,#when#Pretty#counted#on#from#the#larger#number,#the# teacher#understood#Pretty’s#strategy#was#based#on#the#commutative#property.##The#teacher#als ...
... them.##She#identified#student#work#that#had#the#potential#to#help#her#students#discover#and#make#sense# of#an#important#mathematics#concept.##Specifically,#when#Pretty#counted#on#from#the#larger#number,#the# teacher#understood#Pretty’s#strategy#was#based#on#the#commutative#property.##The#teacher#als ...
02 Notes
... What do you know about density? When you are writing about it, include an example of density using water and oil. ...
... What do you know about density? When you are writing about it, include an example of density using water and oil. ...
Chapter 9 Answers
... 28. Never. Sample answer: The whole numbers consist only of 0 and the positive integers. 29. Sometimes. Sample answer: For example, √(4/9) = 2/3 is rational, but √20 is irrational. 30. Sometimes. Sample answer: The real numbers consist of the rational numbers and the irrational numbers, which do no ...
... 28. Never. Sample answer: The whole numbers consist only of 0 and the positive integers. 29. Sometimes. Sample answer: For example, √(4/9) = 2/3 is rational, but √20 is irrational. 30. Sometimes. Sample answer: The real numbers consist of the rational numbers and the irrational numbers, which do no ...
over Chapter 1 - Hays High School
... Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the line shown. Notice that every real number is the x-coordinate of some point on the line. Also, every real number is the y-coordinate of some point on the line. Answer: The domain ...
... Since x can be any real number, there is an infinite number of ordered pairs that can be graphed. All of them lie on the line shown. Notice that every real number is the x-coordinate of some point on the line. Also, every real number is the y-coordinate of some point on the line. Answer: The domain ...
R input and output for authoring statistics problems in LON CAPA
... LON CAPA is a web based software for class management, exam or homework questions that can be taken online or printed for a paper test [1]. Questions for these tests can be created in the autho ...
... LON CAPA is a web based software for class management, exam or homework questions that can be taken online or printed for a paper test [1]. Questions for these tests can be created in the autho ...
MS-Word - Edward Bosworth, Ph.D.
... Note that the multiplication involves dropping the leading ones from the product terms, so that our products are 0.75, 1.5, 1.0, but we would multiply only the numbers 0.375, 0.75, 0.50, and (of course) 0.0. Another example: convert 0.71875 Number Product Binary 0.71875 x2 = 1.4375 ...
... Note that the multiplication involves dropping the leading ones from the product terms, so that our products are 0.75, 1.5, 1.0, but we would multiply only the numbers 0.375, 0.75, 0.50, and (of course) 0.0. Another example: convert 0.71875 Number Product Binary 0.71875 x2 = 1.4375 ...
3.5 Programming paradigms
... Reverse polish notation is simply polish notation written the other way around. So those examples would be AB+ and AB+2*. This can be read as ‘take the numbers A and B and add them together, then take the result and the number 2 and multiply them together.’ Reverse polish notation puts each op ...
... Reverse polish notation is simply polish notation written the other way around. So those examples would be AB+ and AB+2*. This can be read as ‘take the numbers A and B and add them together, then take the result and the number 2 and multiply them together.’ Reverse polish notation puts each op ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.