Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and m x represents the gas mileage (in mpg). a. Use regression to find a quadratic function to model the data. b. At what speed is the gas mileage the greatest? Round to the neatest mile per hour. c. What is the maximum gas mileage? Round to the nearest mile per gallon.
Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and m x represents the gas mileage (in mpg). a. Use regression to find a quadratic function to model the data. b. At what speed is the gas mileage the greatest? Round to the neatest mile per hour. c. What is the maximum gas mileage? Round to the nearest mile per gallon.
Solution Summary: The author explains how to determine the quadratic function of the following data using Ti-83 graphing calculator.
Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and
m
x
represents the gas mileage (in mpg).
a. Use regression to find a quadratic function to model the data.
b. At what speed is the gas mileage the greatest? Round to the neatest mile per hour.
c. What is the maximum gas mileage? Round to the nearest mile per gallon.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
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