(a) C is the intersection of the surfaces. x 2 + y 2 = z 2 , y = z 2 (a)Parameterize each of the two part to x ≥ 0 and x ≤ 0 taking t = z the parameter.

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Answer 1

Question

Chapter 14.1, Problem 31E

To determine

(a)

C is the intersection of the surfaces.

$x^{2} + y^{2} = z^{2}, y = z^{2}$

(a)Parameterize each of the two part to $x \geq 0$ and $x \leq 0$ taking $t = z$ the parameter.

To determine

(b)

Describe the projection of c onto the xy-plane

$(t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

$(- t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

To determine

(c)

Show that C lies on the sphere of radius $1$ with its center $(0, 1, 0)$ . This curve looks like a figure light lying on a sphere.

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Answer 2

Question

Chapter 14.1, Problem 31E

To determine

(a)

C is the intersection of the surfaces.

$x^{2} + y^{2} = z^{2}, y = z^{2}$

(a)Parameterize each of the two part to $x \geq 0$ and $x \leq 0$ taking $t = z$ the parameter.

To determine

(b)

Describe the projection of c onto the xy-plane

$(t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

$(- t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

To determine

(c)

Show that C lies on the sphere of radius $1$ with its center $(0, 1, 0)$ . This curve looks like a figure light lying on a sphere.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 14.1, Problem 31E

To determine

(a)

C is the intersection of the surfaces.

$x^{2} + y^{2} = z^{2}, y = z^{2}$

(a)Parameterize each of the two part to $x \geq 0$ and $x \leq 0$ taking $t = z$ the parameter.

To determine

(b)

Describe the projection of c onto the xy-plane

$(t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

$(- t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

To determine

(c)

Show that C lies on the sphere of radius $1$ with its center $(0, 1, 0)$ . This curve looks like a figure light lying on a sphere.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 14.1, Problem 31E

To determine

(a)

C is the intersection of the surfaces.

$x^{2} + y^{2} = z^{2}, y = z^{2}$

(a)Parameterize each of the two part to $x \geq 0$ and $x \leq 0$ taking $t = z$ the parameter.

To determine

(b)

Describe the projection of c onto the xy-plane

$(t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

$(- t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

To determine

(c)

Show that C lies on the sphere of radius $1$ with its center $(0, 1, 0)$ . This curve looks like a figure light lying on a sphere.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 14.1, Problem 31E

To determine

(a)

C is the intersection of the surfaces.

$x^{2} + y^{2} = z^{2}, y = z^{2}$

(a)Parameterize each of the two part to $x \geq 0$ and $x \leq 0$ taking $t = z$ the parameter.

To determine

(b)

Describe the projection of c onto the xy-plane

$(t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

$(- t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

To determine

(c)

Show that C lies on the sphere of radius $1$ with its center $(0, 1, 0)$ . This curve looks like a figure light lying on a sphere.

Answer 6

Chapter 14.1, Problem 31E

To determine

(a)

C is the intersection of the surfaces.

$x^{2} + y^{2} = z^{2}, y = z^{2}$

(a)Parameterize each of the two part to $x \geq 0$ and $x \leq 0$ taking $t = z$ the parameter.

Answer 7

Chapter 14.1, Problem 31E

To determine

(a)

C is the intersection of the surfaces.

$x^{2} + y^{2} = z^{2}, y = z^{2}$

(a)Parameterize each of the two part to $x \geq 0$ and $x \leq 0$ taking $t = z$ the parameter.

Answer 8

To determine

(b)

Describe the projection of c onto the xy-plane

$(t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

$(- t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

Answer 9

To determine

(b)

Describe the projection of c onto the xy-plane

$(t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

$(- t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

Answer 10

To determine

(c)

Show that C lies on the sphere of radius $1$ with its center $(0, 1, 0)$ . This curve looks like a figure light lying on a sphere.

Answer 11

To determine

(c)

Show that C lies on the sphere of radius $1$ with its center $(0, 1, 0)$ . This curve looks like a figure light lying on a sphere.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

(a) C is the intersection of the surfaces. x 2 + y 2 = z 2 , y = z 2 (a)Parameterize each of the two part to x ≥ 0 and x ≤ 0 taking t = z the parameter.

Solution Summary: The author explains that C is the intersection of the surfaces.

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(a)

C is the intersection of the surfaces.

$x^{2} + y^{2} = z^{2}, y = z^{2}$

(a)Parameterize each of the two part to $x \geq 0$ and $x \leq 0$ taking $t = z$ the parameter.

(b)

Describe the projection of c onto the xy-plane

$(t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

$(- t \sqrt{1 - t^{2}}, t^{2}, t),$ For $0 \leq t \leq 1$

(c)

Show that C lies on the sphere of radius $1$ with its center $(0, 1, 0)$ . This curve looks like a figure light lying on a sphere.

Want to see the full answer?

Chapter 14 Solutions

(a) C is the intersection of the surfaces. x 2 + y 2 = z 2 , y = z 2 (a)Parameterize each of the two part to x ≥ 0 and x ≤ 0 taking t = z the parameter.

Solution Summary: The author explains that C is the intersection of the surfaces.

Videos