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Chapter 10: Q. 44 (page 790)

Graph the quadric surfaces given by the equations
$x^{2} + y^{2} - z^{2} = 1$

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:

$x^{2} + y^{2} - z^{2} = 1$

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

If u and v are nonzero vectors in $ℝ^{3}$ , why do the equations role="math" localid="1649263352081" $u \cdot (u \times v) = 0$ and $v \cdot (u \times v) = 0$ tell us that the cross product is orthogonal to both u and v?

Consider the sequence of sums $\frac{1}{3}, \frac{1}{3} + \frac{1}{9}, \frac{1}{3} + \frac{1}{9} + \frac{1}{27}, \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81}, \dots$

(a) What happens to the terms of this sequence of sums as k gets larger and larger?

(b) Find a sufficiently large value of k which will guarantee that every term past the kth term of this sequence of sums is in the interval (0.49999, 0.5).

Find the mass of a 30-centimeter rod with square cross sections of side length 2 centimeters, given that the density of the rod x centimeters from the left end is ρ(x) = $10 \cdot 5 + 0 \cdot 01527 x^{2}$ grams per cubic centimeter.

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

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
$x^{2} + y^{2} - z^{2} = 1$

Short Answer

Step by step solution

Introduction.

Given Information.

Explanation.

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Graph the quadric surfaces given by the equationsx2+y2−z2=1

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

Discrete Mathematics

Pure Maths

Statistics

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Graph the quadric surfaces given by the equations
$x^{2} + y^{2} - z^{2} = 1$