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- 1.5 a) What is the equation of the line parallel to LM passing through N. b) Show that line in (a) passing through the point QP the midpoint KLSuppose A is changed to A' .How large a relative change can this change produce in the solution to Ax = b?The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.8 8.2 7 3.5 2.3 2.3 2.4 0.5 yy 13.8 11.1 10.1 6.9 6.1 6 6.2 4.5 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.83x+4.14. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 2.2 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 9.3 thousand automatic weapons?Answer = Round to 3 decimal places.
- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.3 6.9 3.9 2.7 2.4 2.1 0.7 yy 14.3 11.3 10 7.4 6.5 6.4 5.9 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.23. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.Use the equation with the values rounded to two decimal places to make your predictions.A) How many murders per 100,000 residents can be expected in a state with 5.5 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 3.9 thousand automatic weapons?Answer = Round to 3 decimal places.In Problems 7 & 8, Find an equation in point-slope form, y-y1=m(x-x1), of the line through the given points. 7. (2,7) and (4, -5) 8. (3, 20) and (-5,4) Can Explain to me Step by StepThe properties in Problem 83 provide us with another way to write the equation of a line parallel or perpendicular to a given line that contains a given point not on the line. For example, suppose that we want the equation of the line perpendicular to 3x + 4y = 6 that contains the point (1, 2). The form 4x - 3y = k, where k is a constant, represents a family of lines perpendicular to 3x + 4y = 6 because we have satisfied the condition AA' = -BB'. Therefore, to find what specific line of the family contains (1, 2), we substitute 1 for x and 2 for y to determine k.4x - 3y = k4(1) - 3(2) = k-2 = k Thus the equation of the desired line is 4x - 3y = -2. Use the properties from Problem 83 to help write the equation of each of the following lines.(a) Contains (1, 8) and is parallel to 2x + 3y = 6(b) Contains (-1, 4) and is parallel to x - 2y = 4(c) Contains (2, -7) and is perpendicular to 3x - 5y = 10(d) Contains (-1, -4) and is perpendicular to 2x + 5y = 12
- 7) Write an equation for Nas a function of K, that is, N is the dependent variable and K is the independent variable. Use the values for the initial number of Na and K ions given in problem 5. Interpret the slope of the equationSolve the following boundary-value problem: y'' - 2y' - 3y = 0, y(0) = 3, y'(0) = 1Q, 1: Environtech Engineering, a company that specializes in the construction of antipollution filtration devices, has recorded the following sales record over the last 9 years: Year 1987 1988 1989 1990 1991 1992 1993 1994 1995 Sales (x 100,000) 13 15 19 21 27 35 47 49 97 a) Plot these data with suitable scale and define shape. b) Develop the linear estimating equation that best describes these data, and plot this line on the graph from part (a). c) Develop the second-degree estimating equation that best describes these data, and plot this curve on the graph from part (a). d) Does the market to the best of your knowledge favor (b) or (c) as the more accurate estimating method?