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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

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

role="math" localid="1649693816584" $u = <3, 1, - 2>, v = <- 6, - 2, 4>$

What is meant by the triangle determined by vectors u and v in $ℝ^{3}$ ? How do you find the area of this triangle?

Prove the first part of Theorem $1.31$ (a): If $k > 0$ , then $\lim_{x \to \infty} x^{k} = \infty$ . (Hint: Given $M > 0$ , choose $N = M^{1 / k}$ . Then show that for $x > N$ it must follow that $x^{k} > M$ .)

Sketch the parallelogram determined by the two vectors $(1, 2)$ and $(3, - 1)$ . How can you use the cross product to find the area of this parallelogram?

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

$P (3, 1, 8), Q (0, 6, - 1), R (- 3, 5, - 3)$

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

Short Answer

Step by step solution

Introduction.

Given Information.

Explanation.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Decision Maths

Discrete Mathematics

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

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