Developmental Mathematics (9th Edition)
Developmental Mathematics (9th Edition)
9th Edition
ISBN: 9780321997173
Author: Marvin L. Bittinger, Judith A. Beecher
Publisher: PEARSON
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Chapter 7.2, Problem 77ES
To determine

To calculate: The order of following numbers from least to the greatest 23, 17, 13, 27, 23, 25, 13, 25 and 98.

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Write a Regression summary explaining significance of mode, explaining regression coefficients, significance of the independent variables, R and R square. Premiums earned Net income Dividends Underwriting Gain/ Loss 30.2 1.6 0.6 0.1 47.2 0.6 0.7 -3.6 92.8 8.4 1.8 -1.5 95.4 7.6 2 -4 100.4 6.3 2.2 -8.1 104.9 6.3 2.4 -10.8 113.2 2.2 2.3 -18.2 130.3 3.0 2.4 -21.4 161.9 13.5 2.3 -12.8 182.5 14.9 2.9 -5.9 193.3 11.7 2.9 -7.6
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).
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