(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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Students have asked these similar questions

Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

Find both parametric and rectangular representations for the plane tangent to r(u,v)=u2i+ucos(v)j+usin(v)kr(u,v)=u2i+ucos⁡(v)j+usin⁡(v)k at the point P(4,−2,0)P(4,−2,0).One possible parametric representation has the form⟨4−4u⟨4−4u , , 4v⟩4v⟩(Note that parametric representations are not unique. If your first and third components look different than the ones presented here, you will need to adjust your parameters so that they do match, and then the other components should match the ones expected here as well.)The equation for this plane in rectangular coordinates has the form x+x+ y+y+ z+z+ =0

Find the parametric equations of the line tangent to the curve of intersection of the surfaces x² + y² = z and x² + y² = 4 at the point (√2, √2,4).

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