17th Edition

ISBN: 9780998625713

Author: Lynn Marecek, MaryAnne Anthony-Smith

Publisher: OpenStax - Rice University

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A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

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Textbook Question

Chapter 4.6, Problem 4.129TI

Find an equation of a line parallel to the line y = 3 x + 1 that contains the point ( 4 , 2 ) . Write the equation in slope−intercept form.

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Chapter 4.6, Problem 4.128TI

Chapter 4.6, Problem 4.130TI

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(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0

4. In a study of how students give directions, forty volunteers were given the task ofexplaining to another person how to reach a destination. Researchers measured thefollowing five aspects of the subjects’ direction-giving behavior:• whether a map was available or if directions were given from memory without a map,• the gender of the direction-giver,• the distances given as part of the directions,• the number of times directions such as “north” or “left” were used,• the frequency of errors in directions.a) Identify each of the variables in this study, and whether each is quantitative orqualitative. For each quantitative variable, state whether it is discrete or continuousb) Was this an observational study or an experimental study? Explain your answer

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Chapter 4 Solutions

Elementary Algebra

Ch. 4.1 - Plot each point in a rectangular coordinate system...Ch. 4.1 - Plot each point in a rectangular coordinate system...Ch. 4.1 - Plot each point: (a) (4,0) (b) (2,0) (c) (0,0) (d)...Ch. 4.1 - Plot each point: (a) (5,0) (b) (3,0) (c) (0,0) (d)...Ch. 4.1 - Name the ordered pair of each point shown in the...Ch. 4.1 - Name the ordered pair of each point shown in the...Ch. 4.1 - Which of the following ordered pairs are solutions...Ch. 4.1 - Which of the following ordered pairs are solutions...Ch. 4.1 - Which of the following ordered pairs are solutions...Ch. 4.1 - Which of the following ordered pairs are solutions...

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