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Chapter 10: Q. 45 (page 790)

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

Short Answer

Expert verified

The surface graph is shown 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:

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

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

Explanation.

The surface graph is shown below.

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

Find a vector in the direction of $<- 1, 2, 3>$ with magnitude 3.

Find $u + v$ and $u - v$ . Also sketch $u, v, u + v$ and $u - v$ .

role="math" localid="1649578020551" $u = (3, - 4) a n d v = (- 1, 5)$

Find the norm of the vector. $v = (\frac{1}{3}, \frac{1}{3}, - \frac{1}{3})$

In Exercises 24-27, find ${comp}_{u} v, {proj}_{u} v$ and the component of v orthogonal tou.

$u = <3, - 1, 2>, v = <- 4, - 6, 3>$

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

Short Answer

Step by step solution

Introduction.

Given Information.

Explanation.

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Most popular questions from this chapter

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Theoretical and Mathematical Physics

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Graph the quadric surfaces given by the equationsz=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

Theoretical and Mathematical Physics

Mechanics Maths

Decision Maths

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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