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# Solutions for Chapter 7.3: OPERATIONAL PROPERTIES

## Full solutions for A First Course in Differential Equations with Modeling Applications | 10th Edition

ISBN: 9781111827052

Solutions for Chapter 7.3: OPERATIONAL PROPERTIES

Solutions for Chapter 7.3
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##### ISBN: 9781111827052

This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.3: OPERATIONAL PROPERTIES includes 83 full step-by-step solutions. Since 83 problems in chapter 7.3: OPERATIONAL PROPERTIES have been answered, more than 116246 students have viewed full step-by-step solutions from this chapter. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a complex number

The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

• Complex plane

A coordinate plane used to represent the complex numbers. The x-axis of the complex plane is called the real axis and the y-axis is the imaginary axis

• Components of a vector

See Component form of a vector.

• Equivalent arrows

Arrows that have the same magnitude and direction.

• Horizontal asymptote

The line is a horizontal asymptote of the graph of a function ƒ if lim x:- q ƒ(x) = or lim x: q ƒ(x) = b

• Imaginary part of a complex number

See Complex number.

• Independent events

Events A and B such that P(A and B) = P(A)P(B)

• Inverse tangent function

The function y = tan-1 x

• Negative association

A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

• Positive linear correlation

See Linear correlation.

• Projectile motion

The movement of an object that is subject only to the force of gravity

• Quotient identities

tan ?= sin ?cos ?and cot ?= cos ? sin ?

• Reduced row echelon form

A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.

• Reflection across the y-axis

x, y and (-x,y) are reflections of each other across the y-axis.

• Second-degree equation in two variables

Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.

• Shrink of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.

• Spiral of Archimedes

The graph of the polar curve.

• Triangular number

A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

• Xmax

The x-value of the right side of the viewing window,.

• Zoom out

A procedure of a graphing utility used to view more of the coordinate plane (used, for example, to find theend behavior of a function).