The coast-down time y for a car as it drops 10 mph from an initial speed x depends on several factors, such as average drag, tire pressure, and whether the transmission is in neutral. The table gives coast-down time in seconds for a car under standard conditions for selected speeds.
initial speed (mph) coast down time (seconds) intial speed (mph) coast down time(seconds)
30 30 50 18
27 55 16
35 23 60 15
40 20 65 13
45
g(x)=___x^2- ___x+___
To find the equation for the coast-down time, you can use the method of least squares to fit a quadratic equation to the given data points.
Using the first three data points (30, 30), (35, 23), and (40, 20), we can form the following system of equations:
30^2a + 30b + c = 30
35^2a + 35b + c = 23
40^2a + 40b + c = 20
Simplifying these equations, we get:
900a + 30b + c = 30
1225a + 35b + c = 23
1600a + 40b + c = 20
To solve this system of equations, you can either use matrix methods or solve it by substitution or elimination. Once you find the values of a, b, and c, you can write the equation for g(x) as:
g(x) = ax^2 + bx + c