Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1.10 Direct Variation and Inverse Variation Direct Variation y varies directly as x y is directly proportional to x y = kx k is the constant of proportionality Inverse Variation y varies inversely as x y is inversely proportional to x k y x Ex. Find a mathematical model representing the statement. Find k. F is jointly proportional to x and the square root of y and inversely proportional to the cube of z. (F = 6 when x = 2, y = 9, and z = 3) kx y F 3 Z k 2 9 6 3 3 Solve for k. k 6 6 27 27 x y F 3 z k = 27 Now find F if x = 4, y = 16, and z = 4. 27 4 16 F 3 4 27 F 4 Finding a Least Squares Regression Line The amount p (in millions of dollars) of total annual prize money awarded at the Indianapolis 500 race from 1995 to 2004 are shown in the table. Construct a scatter plot that represents the data and find the least squares regression line for the data. Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Prize $, p 8.06 8.11 8.61 8.72 9.05 9.48 9.61 10.03 10.15 10.25 12 10 8 6 Prize $ 4 2 0 0 5 10 15 Year (5 = 1995) Come up with an equation that represents the points by hand and by a graphing utility. y - 8.6 = .243(x - 5) or y = .243x + 6.785 y = .268t + 6.66 TI-86 Linear Regression To input points STAT F2 (EDIT) Type in data There must be a one in the FSTAT column Quit a = y-int To get best fit line b = slope STAT Corr = corr F1 (CALC) coefficient F3 (linR) n = # of Enter ordered pairs Gives you equation of best fit line TI - 84 press STAT arrow to calc #4 LinReg(ax + b) Press enter twice a = slope b = y-int