Gaussians An important function in statistics is the Gaussian (or normal distribution, or bell-shaped curve), ƒ(x) = e¯ªx². a. Graph the Gaussian for a b. Given that -ax² dx = = 0.5, 1, and 2. TT a 9 compute the area under the curves in part (a). c. Complete the square to evaluate a> 0, b, and c are real numbers. 8 So e-(ax²+bx+c) dx, where e-(x²+bx+c)

aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line between (a,f(a)) and (b,f(b)).

Planetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1AU astronomical unit is the mean distance from Earth to the sun, abut 93 million miles. Planet d=distance AU v=velocity km/sec Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1.00 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. a Use power regression to express velocity as a power function of distance from the sun. b Plot the data along with the regression equation. c An asteroid orbits at a mean distance of 3AU from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?