... 6. Solve these equations for [pic] a. [pic] [4] b. [pic] [4] c. [pic] [3] Total 50 marks Topic Assessment Solutions 1. (i) [pic] Solutions are in the 1st and 4th quadrants. [pic] or [pic] [pic] (ii) [pic] Solutions are in the 3rd and 4th quadrants [pic] or [pic] [pic] (iii) [pic] Solutions are in 1st and 3rd quadrants. [pic] or [pic] [pic] 2. (i) [pic] Solutions are in 1st and 4th quadrants. [pic] or [pic] [pic] (ii) [pic] Solutions are in 1st and 2nd quadrants [pic] or [pic] [pic] (iii) [pic] Solutions are in 1st and 3rd quadrants [pic] or [pic] [pic] 3. (i) [pic] Solutions are in 1st and 2nd quadrants [pic] or [pic] [pic] (ii) [pic] Solutions are in 1st and 4th quadrants [pic] (iii) [pic] Solutions are in 2nd and 4th quadrants [pic] or [pic] [pic] 4. (i) [pic] [pic] has solutions in the 1st and 4th quadrants [pic] or [pic] [pic] has solutions in the 2nd and 4th quadrants [pic] or [pic] [pic] (ii) [pic] [pic] has...
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...Janurary 4th, 1969 Day one of Operation 69, located on the range of Vietnam to take down General Form, the leader of the upper bound Vietnam Army. General Form his right-hand man Master Quadrants are responsible for the relation of invading our domain and torturing many citizens with their quadratic functions of Leading Coefficient Test. I am Leuitenant Axis the leader of Alpha I. We are specialized in top secret missions, mostly assasination related. Our Cartesian plane arrived in Vietnam at 20 hundred hours at the lower bound of Vietnam in order to assure noone sees us. 2 hours of sleep, then we head on into the dark towards Descartes Rules of Signs, an underground market that will supply us with standard forms of desguises so we can have the element of surprise. Janurary 6th.1969 Day three and we have arrived to Descartes Rules of signs and have recieved our desguises have can head to the upper bound to achieve the solution of assasinating our targets. From what the test intervals show, there are many hideouts and many coordinates we would have to search, so I decided to take a risky independent variable in our mission. I decided to split my platoon into ordered pairs to increase our chances of assasinating these power functions. Sargeant Hays and Private Colt will be station on the right orgin of the upper bound, which is a HAM radio station to intercept any important information to keep us updated. Corpral James and Private Skychild will be stationed at the composition...
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...Ned’s Hermann’s Brains Quadrants Theory of G. Gnanalingam. Known as one of the influential marketing whiz of Malaysia, Tan Sri Datuk G. Gnanalingam started from a humble beginning. A decedent of Sri Lankan Tamil ancestry, he was born in Singapore and grew up in Port Dickson . Getting his early education from Royal Military College, he continued to further his studies in University Malaya and Harvard Business School, Boston. With a strong education background, he started his career in British American Tobacco. After years in the company, he was appointed into becoming the Marketing Director in an early age of 34. He continued expanding his potential as he established his own consulting firm and the firm being appointed to be responsible in handling commercial operations of RTM. He had done the impossible as he increases the revenue from RM 55 million to RM 350 in a period of 10 years. Currently, he is the Executive Chairman of Westport, one of the biggest port operator in Malaysia. Based from his past achievement, we can conclude exactly what is his most active quadrants in the Ned Hermann Brain Quadrants Theory. From the observation, his tendency is much more to quadrant C and quadrant D. His emotions towards the death of his father almost caused him to drop out from his university . It can be seen that his reaction to the situation is drastic and the placement of being emotional would be in the quadrant C. Being labelled as one of the most influential marketing guru in Malaysia...
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...If you have just started using smartphone or if you are new to LG G4, EasyHome is the answer t your problems. Your home screen is undoubtedly the very first thing you look at while you open your phone or even close it. When you tends to unlock your screen or press the home button, all of this procedure is done with the help of an app called a launcher. There are several kinds of launchers and LG LG4 has been using pretty standards one however EasyHome is definitely a step in right direction. EasyHome has been made simpler with huge icons so that it is easy to touch and load them. EasyHome is a consumer friendly launcher; let’s take a detailed look at this new innovative launcher. PHOTO 2 The launcher settings can be easily altered to EasyHome with the help of settings. The homescreen option is right under the display tab with all its highlighted specifications. When you select EasyHome, you will be directed to your new homescreen which will certainly have a lot different outlook from what you are accustomed of watching usually. Options offered by EasyHome: Following are several new options offered by EasyHome which will help in personalizing your home screen. • In EasyHome there is no smart widget it has been exchanged with a much simpler weather and time widget. Clicking on the weather will direct you to the weather app whereas tapping on time will take you to the clock. PHOTO 3 • Dock is also bit changed than usual, the usual for app and six dot bar that lead you to your...
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...the three forces on a diagram with a pair of x and y axes. Find the angle of each force with the x-axis. This angle is called the reference angle, and is the one used to calculate sines and cosines. Next compute the x- and y-components of the three forces, placing like components in columns. Place plus or minus signs on the various quantities according to whether an x-component is to the right or left of the origin, or whether a y-component is up or down relative to the origin. Add the columns with regard to sign (subtracting the minus quantities), and place the correct sign on each sum. The resulting quantities are the x- and y-components of the resultant. Since they are forces at right angles to each other, they are combined by the Pythagorean Theorem. The angle of the resultant is found by the fact that the ratio of the y-component to the x-component is the tangent of the angle of the resultant with the x-axis. Make a new drawing showing the two components of the resultant along the x- and...
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...Last Modified: 06/11/09 Pre-Algebra Practice Exam This test is designed to be used with a Scantron form. Please fill out the information section of the form with your name, subject, “Practice Final” for “Test No.,” date, and section number (in the box marked “Period”). Circle the letter on the test paper that corresponds to the correct answer and fill in the appropriate space on the Scantron form with a Number 2 pencil. Be sure to fill in only one answer per question and to fully erase any changes. Also, be sure that you are marking your answer next to the correct question number. Evaluate the expressions for the given values of the variables for problems 1 – 3. 1. [pic] When x = –2, y = 3, and z = –2 a) –6.5 b) 2.5 c) 4 d) –6 2. [pic] When r = 2, s = –3 , and t = –1 a) –32 b) –24 c) 32 d) 18 3. [pic] When d = 3, e = 7, and f = 10 a) 9 b) 27 c) 47 d) 12 Divide: 4. [pic] a)[pic] b)[pic][pic] c) [pic] d) [pic] Simplify problems 5-7: 5. [pic] a) [pic] b) [pic] c) [pic] d) [pic] 6. [pic] a) [pic] b) [pic] c) [pic] d)[pic] 7. [pic] a) [pic] b) [pic] c) [pic] d) [pic] Simplify problems 8 – 16: 8. [pic] a) 4 b) 8 c) –2 d) –8 9. [pic] a) 64 b) 3 c) –41 d)...
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...Philosophy 390M Thinking About Thinking What does it mean to think? This question may have a lot of different answers depending on who you ask You may get as simple of explanation as picturing a cat in your head. Or you could Google it and come up with the definition of “think” which is directing one’s attention toward something or to have a particular opinion idea or belief about someone or something. People in the science field may try to say that thinking is brain activity. Someone may have a answer completely different from any of these, but are these examples really thinking? I believe that true thinking is something far more than the simple idea of a cat or someone’s opinion of something. Before we can figure out what it means to think we have to look at what it is not. First of all, thinking is not remembering which is easily confused on a daily basis. When try to remember something we say that we are trying to think, but we are not. We are trying to recall something to our memory such as a past experience or the name of person you met last week You are not trying to think of that persons name because they already have one, you are simply trying to put a face and name together. Which brings me to my next point, thinking is not puzzle solving. Putting something together as simple as a four year olds puzzle or as complex as a car motor require the same amount of thinking, none. Each piece of the puzzle has only one way in which it will work. We may figure out how they fit...
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...Running head: Pythagorean Quadratic Pythagorean Quadratic Sharlee M. Walker MAT 221 Instructor Xiaolong Yao December 2, 2013 Pythagorean Quadratic Ahmed’s half of the map doesn’t indicate which direction the 2x + 6 paces should go, we can assume that his and Vanessa’s paces should end up in the same place. I did this out on scratch piece of paper and I saw that it forms a right triangle with 2x + 6 being the length of the hypotenuse, and x and 2x + 4 being the legs of the triangle. Now I know how I can use the Pythagorean Theorem to solve for x. The Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, these lengths have the formula of a2 + b2 = c2. Let a = x, and b = 2x + 4, so that c = 2x + 6. Then, by putting these measurements into the Theorem equation we have x2 + (2x + 4)2 = (2x + 6)2. The binomials into the Pythagorean Thermo x2 + 4x2 + 16x + 16 = 4x2 + 24x + 36 are the binomials squared. Then 4x2 on both sides of the equation which can be (-4x2 -4x2) subtracted out first leaving the equation to be x2 + 16x + 16 = 24x + 36. Next we should subtract 16x from both sides of equation, which then leaves us with: x2 +16 = 8x + 36. The next step would then be to subtract 36 from both sides to get a result of. x2 -20= 8x. Finally we need to subtract 8x from both sides to get x2 – 8x...
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...Buried Treasure Allen Raikes MAT 221 DR. Steven Flanders Ahmed and Vanessa has a treasure that needs to be located. It’s up to me and to help find it, I will do that by using the Pythagorean quadratic. On page 371 we learned that the Ahmed has a half of the map and Vanessa has the other half. Ahmed half in say the treasure is buried in the desert 2x+6 paces from Castle Rock and Vanessa half says that when she gets to Castle Rock to walk x paces to the north, and then walk 2x+4 paces to the east. So with all the information I have I need to find x. the Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, which have of a relationship of a2+b2=c2. In this problem I will let a=x, and b= 2x+4, and c=2x+6. So know it time to put the measurements into the Theorem equation; 1) X2+ (2x+4)2=(2x+6)2 this is the Pythagorean Theorem 2) X2+4x2+16x+16 = 4x2+ 24x+36 are the binomials squared 3) 4x2 & 4x2 on both sides can be subtracted out. 4) X2+16x+16 = 24x +36 subtract 16x from both sides 5) X2+16 = 8x+36 now subtract 36 from both sides 6) X2-20 = 8x 7) X2-8x-20=0 this is the quadratic equation to solve by factoring using the zero factor. 8) (x-)(x+) Since the coefficient of x2 is 1 we have to start with pair of () is the 20 in negative there will be one + and one – in the binomials. 9) -2, 10: -10,2: -5,4; -4, -5 10) Looks I’m going to use -10 and 2 is...
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...Assignment 5 1 Assignment 5 DeJuan Stanley MAT 221 Prof Timothy Kilgore June 2, 2014 MAT 221 Week 5 Assignment Buried treasure. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information then they can find x and save a lot of digging. What is x? The key to solving this equation is to use the Pythagorean Theorem which has a right angle in the equation with a & b equaling side c. Based on the example we know that we will have to use the formula A^2 + B^2 = C^2. What we know is that Ahmed’s half of the map is 2x + 6 = treasure, which would be how far he would need to walk, (A^2). Vanessa’s map needs to show her how to get to the North of Castle Rock, which is 2x + 4, (C^2). We are trying to solve for X (side B). Vanessa is forming a 90 degree angle from point B and walk (2x + 4) until she made it to C. The formula we would use to solve for X is the following: (2x + 6)^2 = x^2 + (2x + 4)^2 4x^2 + 24x + 36 = x^2 +4x^2 + 16x + 16 The next step would be to combine like terms, multiplying, adding, and subtracting. 24x + 36 = x^2 + 16x + 16 -24x -24x 36 = x^2 – 8x + 16 -36 -36 Now we have a quadratic...
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...5.0 x 10-27 kg, moves along the positive y-axis with a speed of 6.0 x 106 m/s. Another particle of mass 8.4 x 10-27 kg, moves along the positive x-axis with a speed of 4.0 x 106 m/s. Determine the third particle’s speed and direction of motion. (Assume that mass is conserved) Write down what you know mnucl = 17 x 10-27 kg m1 = 5.0 x 10-27 kg m2 = 8.4 x 10-27 kg m3 = mnucl – (m1 + m2) = 17 x 10-27 kg – (5.0 x 10-27 kg + 8.4 x 10-27 kg) = 3.6 x 10-27 kg vnuci = 0 m/s v1 = 6.0 x 106 m/s @ y-axis v2 = 4.0 x 106 m/s @ x-axis v3 = ? Draw a vector diagram of the momentum Solve for the momentum of the third particle and then find its velocity Right angled triangle so use Pythagorean Theorem P12 + P22 = P32 therefore: ( (P12 + P22) = P3 ( ((m1v1)2 + (m2v2)2) = P3 ( ((5.0 x 10 –27 kg)(6.0x106m/s))2 + (8.4 x 10-27kg)(4.0 x 106 m/s))2 = P3 ((2.0 x 10-39 kg2m2/s2) = 4.50 x 10-20 kgm/s = P3 v3 = P3 / m3 = 4.50 x 10-20 kgm/s / 3.6 x 10-27 kg = 12.5 x 106 m/s Use...
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...equations, radicals, roots, plane geometry, and verbal problems. | Course Objectives: | Upon successful completion of this course, the student should be able to: * perform basic functions with rational numbers, including integers; * simplify expressions containing exponents; * use the order of operations agreement; * read and interpret various graph formats; * calculate mean, median, and mode of data sets; * determine the probability of an event; * work with metric units; * evaluate and simplify variable expressions; * solve basic algebraic equations; * define and describe geometric concepts, including angles and plane figures; * calculate perimeter, area and volume of geometric figures and solids; * use the Pythagorean Theorem to solve for the unknown side of a right triangle; * interpret the rectangular coordinate system and graph basic linear equations and functions; * complete daily tasks in a timely manner; and * work...
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...History of Geometry Geometry was thoroughly organized in about 300 BC, when the Greek mathematician Euclid gathered what was known at the time, added original work of his own, and arranged 465 propositions into 13 books, called 'Elements'. The books covered not only plane and solid geometry but also much of what is now known as algebra, trigonometry, and advanced arithmetic. Through the ages, the propositions have been rearranged, and many of the proofs are different, but the basic idea presented in the 'Elements' has not changed. In the work facts are not just cataloged but are developed in a fashionable way. Even in 300 BC, geometry was recognized to be not just for mathematicians. Anyone can benefit from the basic learning of geometry, which is how to follow lines of reasoning, how to say precisely what is intended, and especially how to prove basic concepts by following these lines of reasoning. Taking a course in geometry is beneficial for all students, who will find that learning to reason and prove convincingly is necessary for every profession. It is true that not everyone must prove things, but everyone is exposed to proof. Politicians, advertisers, and many other people try to offer convincing arguments. Anyone who cannot tell a good proof from a bad one may easily be persuaded in the wrong direction. Geometry provides a simplified universe, where points and lines obey believable rules and where conclusions are easily verified. By first studying how to reason in...
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...Finite Element Method(FEM) for Two Dimensional Laplace Equation with Dirichlet Boundary Conditions April 9, 2007 1 Variational Formulation of the Laplace Equation The problem is to solve the Laplace equation rPu = 0 (1) in domain subject to Dirichlet boundary conditions on @ . We know from our study of the uniqueness of the solution of the Laplace equation that nding the solution is equivalent to nding u that minimizes 1 Z jjrujjPd W= (2) 2 subject to the same boundary conditions. Here the di erential d denotes the volume di erential and stands for dxdy for a plane region. W has interpretations such as stored energy or dissipated power in various problems. 2 Meshing First we approximate the boundary of by polygons. Then can be divided into small triangles called triangular elements. There is a great deal of exibility in this division process. The term meshing is used for this division. For the resulting FEM matrices to be well-conditioned it is important that the triangles produced by meshing should not have angles which are too small. At the end of the meshing process the following quantities are created. Nv : number of vertices or nodes. Nv ¢ 2 array of real numbers holding the x and y coordinates of the vertices. Ne: number of triangular elements. 1 Ne ¢ 3 array of integers holding the vertices of the triangular elements. Nvf : Number of vertices on which the u values are not...
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...Pythagorean Theorem: Finding Treasure Patricia Diggs MAT 221 Introduction to Algebra Instructor Bridget Simmons May 12, 2013 Pythagorean Theorem: Finding Treasure In this paper I will attempt to use the Pythagorean Theorem to solve the problem which reads Ahmed has half of a treasure map which indicates that the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x+4 paces to the east. If they share their information they can find x and save a lot of digging. What is x? The Pythagorean Theorem states that in every right triangle with legs the length a and b and hypotenuse c, these lengths have the relationship of a2 + b2=c2. a=x b=(2x+4)2 c=(2x+6)2 this is the binomials we will insert into our equation x2+(2x+4)2=(2x+6)2 the binomials into the Pythagorean Theorem x2+4x2+16x+16=24x36 the binomial squared. The 4x2can be subtracted out first x2+16x+16=24x+36 now subtract 24x from both sides x2+-8x+16=36 now subtract 36 from both sides x2-8x-20=0 this is a quadratic equation to solve by factoring and using the zero factor. (x- )(x+ ) the coefficient of x2 is one (1). We can start with a pair of parenthesis with an x each. We have to find...
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