1.1. Equations and Graphs In each of problems 1 - 4‚ find (a) an ordered pair that is a solution of the equation‚ (b) the intercepts of the graph‚ and (c) determine if the graph has symmetry. 1. 2. 3. 4. 5. Once a car is driven off of the dealership lot‚ it loses a significant amount of its resale value. The graph below shows the depreciated value of a BMW versus that of a Chevy after years. Which of the following statements is the best conclusion about the data? a. You should
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Differential Equations Second Order Differential Equations Introduction In the previous chapter we looked at first order differential equations. In this chapter we will move on to second order differential equations. Just as we did in the last chapter we will look at some special cases of second order differential equations that we can solve. Unlike the previous chapter however‚ we are going to have to be even more restrictive as to the kinds of differential equations that we’ll look at
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Quadratic equation In elementary algebra‚ a quadratic equation (from the Latin quadratus for "square") is any equation having the form where x represents an unknown‚ and a‚ b‚ and c represent known numbers such that a is not equal to 0. If a = 0‚ then the equation is linear‚ not quadratic. The numbers a‚ b‚ and c are the coefficients of the equation‚ and may be distinguished by calling them‚ the quadratic coefficient‚ the linear coefficient and the constant or free
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Coefficient of Linear Expansion Introduction With few exceptions materials expand somewhat when heated through a temperature range that does not produce a change in phase (i.e. melting‚ freezing‚ boiling etc.). The added heat increases the average amplitude of vibration of the atoms in the material‚ which increases the average separation between the atoms. Although this effect is small‚ it is very important in any application that involves using different materials in an environment where they
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Straight Line Equations and Inequalities A: Linear Equations - Straight lines Please remember that when you are drawing graphs you should always label your axes and that y is always shown on the vertical axis. A linear equation between two variables x and y can be represented by y = a + bx where “a” and “b” are any two constants. For example‚ suppose we wish to plot the straight line If x = -2‚ say‚ then y = 3 + 2(-2) = 3 - 4 = -1 If x= -2 -1 -1 1 0 3 1 5 2 7 As you can see‚ we have plotted the
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a project of your choice‚ either from your own work or as a hypothetical situation. Be sure that you stae your situation first‚ before you develpp the LP model Linear programming is a modeling technique that is used to help managers make logical and informed decisions. All date and input factors are known with certainty. Linear program models are developed in three different steps: Formulation Solution Interpretation The formulation step deals with displaying the problem in a mathematical
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Project 1: Linear Correlation and Regression Analysis Gross Revenue and TV advertising: Pfizer Inc‚ along with other pharmaceutical companies‚ has begun investing more promotion dollars into television advertising. Data collected over a two year period‚ shows the amount of money Pfizer spent on television advertising and the revenue generated‚ all on a monthly bases. |Month |TV advertising |Gross Revenue | |1 |17 |4.1 | |2
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This article considers the relationship between two variables in two ways: (1) by using regression analysis and (2) by computing the correlation coefficient. By using the regression model‚ we can evaluate the magnitude of change in one variable due to a certain change in another variable. For example‚ an economist can estimate the amount of change in food expenditure due to a certain change in the income of a household by using the regression model. A sociologist may want to estimate the increase
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RHA; same trend for LL and PL. The Linear Shrinkage (LS) decreases as the RHA content increases‚ enhancing the volume stability of the soil. The results obtained from the researches’ work are shown below in Figure 2.7. Figure 2.7: Variation of OMC‚ LL‚ PL‚ PI‚ and LS with RHA content Roy (2014) conducted a research on the soil stabilization using RHA and cement‚ using the soil sample from Burdwan‚ India by disturbed sampling method. The CBR value obtained from the experiment is to evaluate the
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1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12)‚ 19–22‚ and 25. For brevity‚ the symbols R1‚ R2‚…‚ stand for row 1 (or equation 1)‚ row 2 (or equation 2)‚ and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 −2 x1 − 7 x2 = −5 1 −2 5 −7 7 −5 x1 + 5 x2 = 7 Replace R2 by R2 + (2)R1 and obtain: 3x2 = 9 x1 + 5 x2 = 7 x2 = 3 x1 1 0 1 0 1 0 5 3 5 1 0 1 7 9 7 3 −8 3 Scale R2 by 1/3: Replace R1 by R1
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