EBK PRECALCULUS: MATHEMATICS FOR CALCUL
7th Edition
ISBN: 9781337431125
Author: Watson
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 11.4, Problem 46E
To determine
To find: The equation of parabola that passes through the point
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4. Find the inverse Laplace Transform Show all of your work:
a. F(s) =
=
2s-3
(s²-10s+61)(5-3)
se-2s
b. G(s) =
(s+2)²
1. Consider the differential equation, show all of your work:
dy
=(y2)(y+1)
dx
a. Determine the equilibrium solutions for the differential equation.
b. Where is the differential equation increasing or decreasing?
c. Where are the changes in concavity?
d. Suppose that y(0)=0, what is the value of y as t goes to infinity?
2. Suppose a LC circuit has the following differential equation:
q'+4q=6etcos 4t, q(0) = 1
a. Find the function for q(t), use any method that we have studied in the course.
b. What is the transient and the steady-state of the circuit?
Chapter 11 Solutions
EBK PRECALCULUS: MATHEMATICS FOR CALCUL
Ch. 11.1 - A parabola is the set of all points in the plane...Ch. 11.1 - The graph of the equation x2 = 4py is a parabola...Ch. 11.1 - The graph of the equation y2 = 4px is a parabola...Ch. 11.1 - Label the focus, directrix, and vertex on the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 6ECh. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 8ECh. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...
Ch. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 12ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Graphing Parabolas An equation of a parabola is...Ch. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 50ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 54ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Finding the Equation of a Parabola Find an...Ch. 11.1 - Prob. 59ECh. 11.1 - Families of Parabolas (a) Find equations for the...Ch. 11.1 - Parabolic Reflector A lamp with a parabolic...Ch. 11.1 - Satellite Dish A reflector for a satellite dish is...Ch. 11.1 - Suspension Bridge In a suspension bridge the shape...Ch. 11.1 - Reflecting Telescope The Hale telescope at the...Ch. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.2 - An ellipse is the set of all points in the plane...Ch. 11.2 - The graph of the equation x2a2+y2b2=1 with a b 0...Ch. 11.2 - The graph of the equation x2b2+y2a2=1 with a b 0...Ch. 11.2 - Label the vertices and foci on the graphs given...Ch. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Prob. 6ECh. 11.2 - Graphs of Ellipses Match the equation with the...Ch. 11.2 - Prob. 8ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 13ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 18ECh. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Graphing Ellipses An equation of an ellipse is...Ch. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 32ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 51ECh. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Finding the Equation of an Ellipse Find an...Ch. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - Prob. 57ECh. 11.2 - Intersecting Ellipses Find the intersection points...Ch. 11.2 - Prob. 59ECh. 11.2 - Prob. 60ECh. 11.2 - Ancillary Circle The ancillary circle of an...Ch. 11.2 - Prob. 62ECh. 11.2 - Family of Ellipses If k 0, the following equation...Ch. 11.2 - How Wide Is an Ellipse at a Focus? A latus rectum...Ch. 11.2 - Perihelion and Aphelion The planets move around...Ch. 11.2 - The Orbit of Pluto With an eccentricity of 0.25,...Ch. 11.2 - Lunar Orbit For an object in an elliptical orbit...Ch. 11.2 - Plywood Ellipse A carpenter wishes to construct an...Ch. 11.2 - Sunburst Window A sunburst window above a doorway...Ch. 11.2 - DISCUSS: Drawing an Ellipse on a Blackboard Try...Ch. 11.2 - DISCUSS: Light Cone from a Flashlight A flashlight...Ch. 11.2 - DISCUSS: Is It an Ellipse? A piece of paper is...Ch. 11.3 - A hyperbola is the set of all points in the plane...Ch. 11.3 - The graph of the equation x2a2y2b2=1 with a 0, b ...Ch. 11.3 - Prob. 3ECh. 11.3 - Label the vertices, foci, and asymptotes on the...Ch. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Prob. 6ECh. 11.3 - Graphs of Hyperbolas Match the equation with the...Ch. 11.3 - Prob. 8ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 10ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Graphing Hyperbolas An equation of a hyperbola is...Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Finding an Equation of a Hyperbola Find the...Ch. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 38ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 40ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Finding the Equation of a Hyperbola Find an...Ch. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Perpendicular Asymptotes (a) Show that the...Ch. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Prob. 55ECh. 11.3 - Navigation In the figure on the next page, the...Ch. 11.3 - Comet Trajectories Some comets, such as Halleys...Ch. 11.3 - Ripples in Pool Two stones are dropped...Ch. 11.3 - Prob. 59ECh. 11.3 - DISCUSS: Light from a Lamp The light from a lamp...Ch. 11.4 - Prob. 1ECh. 11.4 - The graphs of x2 = 12y and (x 3)2 = 12(y 1) are...Ch. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Graphing Shifted Ellipses An equation of an...Ch. 11.4 - Prob. 12ECh. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Graphing Shifted Parabolas An equation of a...Ch. 11.4 - Prob. 20ECh. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Graphing Shifted Hyperbolas An equation of a...Ch. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Finding the Equation of a Shifted Conic Find an...Ch. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 50ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 52ECh. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Graphing Shifted Conics Complete the square to...Ch. 11.4 - Prob. 55ECh. 11.4 - Prob. 56ECh. 11.4 - Prob. 57ECh. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.4 - Prob. 62ECh. 11.4 - Prob. 63ECh. 11.4 - Prob. 64ECh. 11.4 - Prob. 65ECh. 11.4 - Path of a Cannonball A cannon fires a cannonball...Ch. 11.4 - Orbit of a Satellite A satellite is in an...Ch. 11.4 - Prob. 68ECh. 11.5 - Suppose the x- and y-axes are rotated through an...Ch. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Rotation of Axes Determine the XY-coordinates of...Ch. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 18ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Prob. 23ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 26ECh. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Graphing a Rotated Conic (a) Use the discriminant...Ch. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - Identifying a Hyperbola Using Rotation of Axes (a)...Ch. 11.5 - Prob. 34ECh. 11.5 - Prob. 35ECh. 11.5 - Prob. 36ECh. 11.5 - Prob. 37ECh. 11.5 - Prob. 38ECh. 11.5 - DISCOVER PROVE: Geometric Invariants Do you...Ch. 11.6 - Prob. 1ECh. 11.6 - Prob. 2ECh. 11.6 - Prob. 3ECh. 11.6 - Prob. 4ECh. 11.6 - Prob. 5ECh. 11.6 - Prob. 6ECh. 11.6 - Prob. 7ECh. 11.6 - Prob. 8ECh. 11.6 - Prob. 9ECh. 11.6 - Prob. 10ECh. 11.6 - Prob. 11ECh. 11.6 - Prob. 12ECh. 11.6 - Prob. 13ECh. 11.6 - Prob. 14ECh. 11.6 - Prob. 15ECh. 11.6 - Prob. 16ECh. 11.6 - Prob. 17ECh. 11.6 - Prob. 18ECh. 11.6 - Prob. 19ECh. 11.6 - Prob. 20ECh. 11.6 - Prob. 21ECh. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Prob. 25ECh. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Prob. 29ECh. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Prob. 37ECh. 11.6 - Prob. 38ECh. 11.6 - Prob. 39ECh. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Perihelion and Aphelion The planets move around...Ch. 11.6 - Prob. 45ECh. 11.6 - Prob. 46ECh. 11.6 - Prob. 47ECh. 11 - (a) Give the geometric definition of a parabola....Ch. 11 - Prob. 2RCCCh. 11 - (a) Give the geometric definition of a hyperbola....Ch. 11 - Prob. 4RCCCh. 11 - Prob. 5RCCCh. 11 - Prob. 6RCCCh. 11 - Prob. 7RCCCh. 11 - Prob. 8RCCCh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Identifying and Graphing a Conic Determine whether...Ch. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Prob. 56RECh. 11 - Prob. 57RECh. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - Prob. 60RECh. 11 - Finding the Equation of a Conic Find an equation...Ch. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Prob. 64RECh. 11 - Path of the Earth The path of the earth around the...Ch. 11 - LORAN A ship is located 40 mi from a straight...Ch. 11 - Prob. 67RECh. 11 - Prob. 68RECh. 11 - Prob. 69RECh. 11 - Prob. 70RECh. 11 - Prob. 71RECh. 11 - Prob. 72RECh. 11 - Prob. 73RECh. 11 - Prob. 74RECh. 11 - Prob. 75RECh. 11 - Prob. 76RECh. 11 - Prob. 77RECh. 11 - Prob. 78RECh. 11 - Prob. 79RECh. 11 - Prob. 80RECh. 11 - Find the focus and directrix of the parabola x2 =...Ch. 11 - Prob. 2TCh. 11 - Find the vertices, foci, and asymptotes of the...Ch. 11 - Prob. 4TCh. 11 - Prob. 5TCh. 11 - Prob. 6TCh. 11 - Prob. 7TCh. 11 - Prob. 8TCh. 11 - Prob. 9TCh. 11 - Determine whether the equation represents an...Ch. 11 - Determine whether the equation represents an...Ch. 11 - Prob. 12TCh. 11 - Prob. 13TCh. 11 - Find an equation for the parabola with focus (2,...Ch. 11 - A parabolic reflector for a car headlight forms a...Ch. 11 - (a) Use the discriminant to determine whether the...Ch. 11 - Prob. 17TCh. 11 - Conics in Architecture The photographs on page 836...Ch. 11 - Constructing a Hyperbola In this problem we...Ch. 11 - Prob. 3PCh. 11 - Prob. 4PCh. 11 - Tangent Lines to a Parabola In this problem we...Ch. 11 - Prob. 6P
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