Course Notes Linear Math & Matrices PSB – Dr. H. Schellinx Linear equations As we have seen‚ a linear equation with n different variables‚ say x1‚ x2 ‚ x3‚...‚ xn ‚ can always be written in the equivalent standard form a1 x1 + a2 x2 + a3 x3 +... + an xn = c ‚ where c is a constant‚ the xi are the unknowns and the ci are coefficients. Here are
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(2-2i)(9+i) (-7+5i) - (6-8i) (3+i)^2 2) Solve the following equation by factoring x^2 - 6x = 0 3) A bank loaned $17‚000‚ part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled at $2‚000‚ how much was loaned at 8%? 4) Find the real solutions of the equation √2x-7 = 0 5) Solve the inequality 5 < 7 - ½x < 9 6) Decide whether the following equations are parallel‚ perpendicular‚ or neither. y= 4x+6 y= -¼x + ¼
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References: ▪ http://www.coe.uncc.edu/~jraja/megr6181/pdf/Flatness_Straightness.pdf ▪ http://www.weibull.com/AccelTestWeb/least_squares_method.htm ▪ Nitin Maheshwari‚ A Thesis “On the Selection of CMM based Inspection Methodology for Circularity Toleran”‚ Division of Research and Advanced Studies of the University of Cincinnati (2001) 9. Appendices 9.1 Appendix A-Procedure 9.2 Appendix B-Certificates of calibration
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Jasmine Chai Grade 10 196298501 Patterns within systems of linear equations Systems of linear equations are a collection of linear equations that are related by having one solution‚ no solution or many solutions. A solution is the point of intersection between the two or more lines that are described by the linear equation. Consider the following equations: x + 2y = 3 and 2x – y = -4. These equations are an example of a 2x2 system due to the two unknown variables (x and y) it has. In one of
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The relationship between an object’s position and time if it travels in a straight line at a constant speed‚ as well as the relationship between the same object’s speed and time‚ will both result in a linear model. This hypothesis will be tested by using a model car‚ a spark timer‚ and timer tape. Procedure 1.Obtain a model car‚ spark timer‚ half a meter of timer tape. 2.Tape the length of timer tape to the back of the model car. 3.Feed the timer tape through the spark timer‚ setting the
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Forum #2: Linear Equations in Real Life Pick one of the following problems. Show how you would solve it using a system of linear equations. 1) John spent $201 shirts and pants for work. Shirts cost $27 and pants cost $22. If he bought a total of 8 articles of clothing‚ then how many of each kind did he buy? 2) A school dance has 228 students. There are 63 fewer girls than twice as many boys. How many boys and girls attended the dance? 3) There are 15 animals in the barn. Some are ducks and some
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Thus I assumed an asymptote at 23°C. 1st equation: An equation for an exponentially decaying graph is in the form of: y = a + b (e –m x) Where: a= Vertical Translations (Ambient Temperature)‚ b= Dilations‚ m= Gradient x= Time (t)‚ y= Temperature (T (t)) From the data‚ we know that the value of ‘a’ is always equal to 23 °C. The original equation is equal to: T (t) = 23 + b (e –m t) This part of the investigation had some issues. I had formed the equation but was confused on how to solve it. Later
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two main kinds of graphs in kinematics: 1. Displacement – Time Graphs ● Sometimes called d-t graphs‚ or position – time graphs. 2. Velocity – Time Graphs ● Sometimes called v-t graphs. Displacement - Time (d-t) Graphs This type of graph is based on the most basic things we need to know about the motion of an object (position and time). ● Typically you will be given a table of values that show the displacement of the object over a particular period of time. ● If the graph shows complex
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direct proportion. The equation for the trend line is Y = 20.788 X - 0.0093 ; R ² = 0.9675. This equation will be used to calculate the unknown concentration of Methylene Blue solution. Figure 2: Standard curve of Average light absorbance by ten different concentration of Methlene Blue. The data is collected from all the groups in the class. All the points in the graph represent the means of all the groups. The figure shows a direct proportion. Its equation for trend line is Y = 23
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straight line the linear density‚ ‚ of the string (show procedure and calculations). Comment. Y – axis X – axis Frequency (Hz) N 78 1 151.8 2 234 3 320.8 4 397.9 5 Using the calculator we perform linear regression to obtain the slope B as 80.08 while A = -4.54 Which is nothing but To obtain the error on the slope: αB Where N = 5 The error αμ is: Hence the linear density is 1.1x103
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