2. LINEAR MOTION In this experiment you will study the motion of an object in one dimension from a number of points of view. You will demonstrate how the variables of motion are related by differentiation and integration and investigate the relationship between potential and kinetic energy. Theory Why Study Motion? Motion is everywhere in the universe. Only at a temperature of absolute zero is the motion in any body truly absent. If motion exists then so also does energy. To the delight of
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2011‚ one US dollar was equivalent to 0.7749 Euros. A linear equation of a function‚ E‚ which converts US dollars (D) to Euros (E) would be E = 0.7749D You would just put the number of dollars in for "D" and multiply by 0.7749 and this will give you the number of Euros you would get for your US dollars. This is a "real world application" of a linear function. Cell Phones Just about everyone has a cell phone‚ and most rate plans are a linear function of some kind. Let’s take a look at a basic example
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The linear probability model‚ ctd. When Y is binary‚ the linear regression model Yi = β0 + β1Xi + ui is called the linear probability model. • The predicted value is a probability: • E(Y|X=x) = Pr(Y=1|X=x) = prob. that Y = 1 given x • Yˆ = the predicted probability that Yi = 1‚ given X • β1 = change in probability that Y = 1 for a given ∆x: Pr(Y = 1 | X = x + ∆x ) − Pr(Y = 1 | X = x ) β1 = ∆x 5 Example: linear probability model‚ HMDA data Mortgage denial v. ratio of debt payments to income (P/I
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Linear Thermal Expansion The term thermal expansion refers to the increase in size of an object as that object is heated. With relatively few exceptions‚ all objects expand when they are heated and contract when they are cooled. Perhaps the most important exception to this rule is water. Water contracts as it cools from its boiling point to about 39.2°F (4°C). At that point‚ it begins to expand as it cools further to its freezing point. This unusual effect explains the fact that ice is less dense
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Specification of an "Innovation Opportunities Explorer" Loet Leydesdorff‚ Daniele Rotolo‚ Wouter de Nooy (Submitted on 28 Feb 2012 (v1)‚ last revised 29 Jan 2013 (this version‚ v2)) The process of innovation follows non-linear patterns across the domains of science‚ technology‚ and the economy. Novel bibliometric mapping techniques can be used to investigate and represent distinctive‚ but complementary perspectives on the innovation process (e.g.‚ "demand" and "supply") as well as the interactions
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Newton’s Laws‚ linear momentum‚ and kinetic energy. Principles In this experiment you will study a collision where a moving object strikes and sticks to an initially motionless object. When the colliding objects stick together the collision is said to be completely inelastic. The net momentum of the system should not change‚ but the net kinetic energy of the system will decrease. The amount of kinetic energy left after the collision can be predicted using conservation of momentum. Linear momentum
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Activity 3.3Making Linear Measurements Purpose How thick is one of the hairs on your head? Could it be measured accurately with a standard inch scale? If the smallest increment on an inch scale is 1/16 inch‚ then 20 average size human hairs could fit within the space of a 1/16 inch gap. The required degree of accuracy needed is dependent on the application. If you were to build a home‚ a standard inch scale is perfect for laying out walls and locating window openings.A dial caliper is a precision
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SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES Solve the following systems: 1. x y 8 x y 2 by graphing by substitution by elimination by Cramer’s rule 2. 2 x 5 y 9 0 x 3y 1 0 by graphing by substitution by elimination by Cramer’s rule 3. 4 x 5 y 7 0 2 x 3 y 11 0 by graphing by substitution by elimination by Cramer’s rule CASE 1: intersecting lines independent & consistent m1m2 CASE 2: parallel lines
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Mr. Brajesh Mishra Roll- 32024 ________________________________________________________________ LINEAR BLOCK CODES A systematic (n‚k) linear block code is a mapping from a k-dimensional message vector to an ndimensional codeword in such a way that part of the sequence generated coincides with the k message digits. The difference (n − k) represents the parity bits. A systematic linear block will have a [k × n] generator matrix [G] of the form G=[P IK ] Then the code is
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Due in class Feb 6 UCI ID_____________________________ MultipleChoice Questions (Choose the best answer‚ and briefly explain your reasoning.) 1. Assume we have a simple linear regression model: . Given a random sample from the population‚ which of the following statement is true? a. OLS estimators are biased when BMI do not vary much in the sample. b. OLS estimators are biased when the sample size is small (say 20 observations)
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