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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285741550

Chapter 12.6, Problem 14E

Textbook Problem

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Use traces to sketch and identify the surface.

z^{2} − 4*x*^{2} − *y*^{2} = 4

To determine

**To identify**: The given surface equation and sketch it.

**Given data:**

Surface equation is

**Formula used:**

Consider the standard equation of hyperboloid of two sheets.

Consider the given surface equation.

Rearrange the equation.

By comparing equation (2) with (1), the computed expression satisfies the equation of hyperboloid of two sheets.

Thus, the surface equation

**Case i:**

Let

Substitute *k* for *x* in equation (2),

The trace of this expression in

**Case ii:**

Let

Substitute *k* for *y* in equation (2),

The trace of this expression in

**Case iii:**

Let

Calculus: Early Transcendentals

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How do you find...Ch. 12 - Write equations in standard form of the six types...Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - Determine whether the statement is true or false....Ch. 12 - (a) Find an equation of the sphere that passes...Ch. 12 - Copy the vectors in the figure and use them to...Ch. 12 - If u and v are the vectors shown in the figure,...Ch. 12 - Calculate the given quantity if a = i + j 2k b =...Ch. 12 - Find the values of x such that the vectors 3, 2, x...Ch. 12 - Find two unit vectors that are orthogonal to both...Ch. 12 - Suppose that u (v w) = 2. 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Plotting Points in the Cartesian Plane In Exercises 1 and 2, plot the points in the Cartesian plane. See Exampl...

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Sketching a Line in the Plane In Exercises 35-42, sketch the graph of the equation. y1=3(x+4)

Calculus: Early Transcendental Functions

Solve the equations in Exercises 126. x43x3=0

Finite Mathematics and Applied Calculus (MindTap Course List)

The following scores are the ages for a random sample of n = 32 drivers who were issued parking tickets in Chic...

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Professional athletes are threatening to strike because they claim that they are underpaid. The team owners hav...

Essentials Of Statistics

21-47 Differentiate. y=ln(1x)+1lnx

Calculus (MindTap Course List)

Solve the equations in Exercises 126. (x+1)2(2x+3)(x+1)(2x+3)2=0

Applied Calculus

A population has a mean of µ = 50 and a standard deviation of s = 10. If 3 points were added to every score in ...

Statistics for The Behavioral Sciences (MindTap Course List)

Book Design A book designer has decided that the pages of a book should have 1-in. margins at the top and botto...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval...

Single Variable Calculus

Sketch the graphs of the equations in Exercises 512. yx=1

Finite Mathematics

Compute the following binomial probabilities directly from the formula for b(x, n, p): a. b(3; 8, .35) b. b(5; ...

Probability and Statistics for Engineering and the Sciences

Myers-Briggs: Marriage Counseling Isabel Myers was a pioneer in the study of personality types. She identified ...

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One of the angles of an isosceles triangle measures 96. What is the measure of the largest angles of the triang...

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Solve the following word problems. Round dollars to the nearest cent and percents to the nearest tenth of a per...

Contemporary Mathematics for Business & Consumers

Simplify the algebraic expressions in Problems 1-14 by com- bining similar terms. Objective 1 7x+11x

Intermediate Algebra

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Mathematical Excursions (MindTap Course List)

Find each product: (z11)2

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67. Heat index During a particular summer, Dallas, Texas, endured 29 consecutive days on which the temperature ...

Mathematical Applications for the Management, Life, and Social Sciences

Finding an Inverse Function In Exercises 63-68, (a) sketch a graph of the function f, {b) determine an interval...

Calculus: Early Transcendental Functions (MindTap Course List)

Deduce the following laws of logarithms from (15): (a) logb(xy) = logb x + logb y (b) logb(x/y) = logb x logb ...

Single Variable Calculus: Early Transcendentals

Finding a Particular Solution In Exercises 17-24, find the particular solution of the first-order linear differ...

Calculus of a Single Variable

As increases from 0 to 90, the value of sin tends toward what number?

Trigonometry (MindTap Course List)

2. List all common divisors of each of the following pair a.30,28 b.42,45 c.24,32 d.210,40 e.40,24 f.30,50

Elements Of Modern Algebra

If the interval [1, 3] is divided into n subintervals of length x, then the shaded area at the right is a) limn...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

The equation of the plane partially drawn in the figure is:
x = 3
y = 3
z = 3
x + y = 3

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 21 to 30, use the drawings, where provided, to solve each problem, Angle measures should be found ...

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In Exercises 14, write the augmented matrix corresponding to each system of equations. 3x+7y8z=5 x+3z=24x3y=7

Finite Mathematics for the Managerial, Life, and Social Sciences

CONCEPT CHECK Surface Integral Explain how to set up a surface integral given that you will project the surface...

Multivariable Calculus

Graphical Reasoning An electronically controlled thermostat is programmed to lower the temperature during the n...

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Evaluating a Definite Integral In Exercises 5966, evaluate the definite integral. 0/3sec3/2xtanxdx

Calculus

Describe a distribution of scores that has a mean of M = 30 and a standard deviation of SD = 6. (Where are the ...

Research Methods for the Behavioral Sciences (MindTap Course List)

The following crosstabulation shows household income by educational level of the head of household (Statistical...

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Wave propagation Stones dropped into a calm pond at points A and B create ripples that propagate in widening ci...

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Consider the following time series data. a. Construct a time series plot. What type of pattern exists in the da...

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Identify the options for reducing or controlling the variance within treatment condition and explain how each o...

Research Methods for the Behavioral Sciences (MindTap Course List)

The city council in a large city has become concerned about the trend toward exclusion of renters with children...

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Identify each of the following angles as acute. obtuse, right, straight, or reflex. (a)BAC,(b)BAD , and (a)CAD.

Mathematics For Machine Technology