a. Using regression, find a quartic function, y = a x 4 + b x 3 + c x 2 + d x + e , that fits the data. y = 0.000002 x 4 − 0.00023 x 3 + 0.0098 x 2 − 0.067 x + 0.558 b. Graph the quartic function. c. Use the quartic function to predict the average price of a movie ticket in 2015 and in 2020. Do these estimates appear reasonable? d. Use the function to predict the year when the average price of a ticket will reach $20. Does this estimate seem reasonable?
a. Using regression, find a quartic function, y = a x 4 + b x 3 + c x 2 + d x + e , that fits the data. y = 0.000002 x 4 − 0.00023 x 3 + 0.0098 x 2 − 0.067 x + 0.558 b. Graph the quartic function. c. Use the quartic function to predict the average price of a movie ticket in 2015 and in 2020. Do these estimates appear reasonable? d. Use the function to predict the year when the average price of a ticket will reach $20. Does this estimate seem reasonable?
Solution Summary: The author explains how to determine the quartile function using regression for the provided data.
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.
Elementary Statistics: Picturing the World (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY