Open In App

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 10: Q. 42 (page 790)

Graph the quadric surfaces given by the equations
$z^{2} = \frac{x^{2}}{9} + \frac{y^{2}}{25}$

Short Answer

Expert verified

The surface graph is a cone, as illustrated below.

Step by step solution

Introduction.

Quadric surfaces are described in two dimensions by quadratic equations. Quadrics include spheres and cones.

Given Information.

Consider the following formula:

$z^{2} = \frac{x^{2}}{9} + \frac{y^{2}}{25}$

The goal is to create a graph of the quadric surface.

Explanation.

The surface graph is a cone, as illustrated below.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is $k = 1$ .

(b) True or False: $\sum_{k = 0}^{n} \frac{1}{k + 1} + \sum_{k = 1}^{n} k^{2}$ is equal to $\sum_{k = 0}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(c) True or False: $\sum_{k = 1}^{n} \frac{1}{k + 1} + \sum_{k = 0}^{n} k^{2}$ is equal to $\sum_{k = 1}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(d) True or False: $(\sum_{k = 1}^{n} \frac{1}{k + 1}) (\sum_{k = 1}^{n} k^{2})$ is equal to $\sum_{k = 1}^{n} \frac{k^{2}}{k + 1}$ .

(e) True or False: $\sum_{k = 0}^{m} \sqrt{k} + \sum_{k = m}^{n} \sqrt{k}$ is equal to $\sum_{k = 0}^{n} \sqrt{k}$ .

(f) True or False: $\sum_{k = 0}^{n} a_{k} = - a_{0} - a_{n} + \sum_{k = 1}^{n - 1} a_{k}$ .

(g) True or False: ${(\sum_{k = 1}^{10} a_{k})}^{2} = \sum_{k = 1}^{10} a_{k}^{2}$ .

(h) True or False: $\sum_{k = 1}^{n} {(e^{x})}^{2} = \frac{e^{x} (e^{x} + 1) (2 e^{x} + 1)}{6}$ .

what it means, in terms of limits, for a function to have a removable discontinuity, a jump discontinuity, or an infinite discontinuity at x = c

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

$u \times v and v \times u$

Fill in the blanks to complete each of the following theorem statements:

For $ε > 0, f (x) \in (L - ε, L + ε)$ if and only if $< ε .$

In Exercises 37–42, find $||v||$ and find the unit vector in the direction of v.

$v = <2, 1, - 5>$

See all solutions

Recommended explanations on Math Textbooks

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

Graph the quadric surfaces given by the equations
$z^{2} = \frac{x^{2}}{9} + \frac{y^{2}}{25}$

Short Answer

Step by step solution

Introduction.

Given Information.

Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Decision Maths

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Company

Product

Help

Graph the quadric surfaces given by the equationsz2=x29+y225

Short Answer

Step by step solution

Introduction.

Given Information.

Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Decision Maths

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Graph the quadric surfaces given by the equations
$z^{2} = \frac{x^{2}}{9} + \frac{y^{2}}{25}$