(a) To show: The vector equation ( r − u ) ⋅ ( r − v ) = 0 represents a sphere.

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Answer 1

Question

Chapter 9.4, Problem 51E

To determine

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

To determine

(b)

To find:

The center and radius of the sphere.

To determine

(c)

To interpret:

The result of part(a) geometrically.

To determine

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

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************* ********************************* Q.1) Classify the following statements as a true or false statements: a. If M is a module, then every proper submodule of M is contained in a maximal submodule of M. b. The sum of a finite family of small submodules of a module M is small in M. c. Zz is directly indecomposable. d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M. e. The Z-module has two composition series. Z 6Z f. Zz does not have a composition series. g. Any finitely generated module is a free module. h. If O→A MW→ 0 is short exact sequence then f is epimorphism. i. If f is a homomorphism then f-1 is also a homomorphism. Maximal C≤A if and only if is simple. Sup Q.4) Give an example and explain your claim in each case: Monomorphism not split. b) A finite free module. c) Semisimple module. d) A small submodule A of a module N and a homomorphism op: MN, but (A) is not small in M.

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T. Determine the least common denominator and the domain for the 2x-3 10 problem: + x²+6x+8 x²+x-12 3 2x 2. Add: + Simplify and 5x+10 x²-2x-8 state the domain. 7 3. Add/Subtract: x+2 1 + x+6 2x+2 4 Simplify and state the domain. x+1 4 4. Subtract: - Simplify 3x-3 x²-3x+2 and state the domain. 1 15 3x-5 5. Add/Subtract: + 2 2x-14 x²-7x Simplify and state the domain.

Answer 2

Question

Chapter 9.4, Problem 51E

To determine

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

To determine

(b)

To find:

The center and radius of the sphere.

To determine

(c)

To interpret:

The result of part(a) geometrically.

To determine

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

Expert Solution & Answer

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Answer 3

Question

Chapter 9.4, Problem 51E

To determine

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

To determine

(b)

To find:

The center and radius of the sphere.

To determine

(c)

To interpret:

The result of part(a) geometrically.

To determine

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 9.4, Problem 51E

To determine

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

To determine

(b)

To find:

The center and radius of the sphere.

To determine

(c)

To interpret:

The result of part(a) geometrically.

To determine

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

Expert Solution & Answer

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See solution

Answer 5

Chapter 9.4, Problem 51E

To determine

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

To determine

(b)

To find:

The center and radius of the sphere.

To determine

(c)

To interpret:

The result of part(a) geometrically.

To determine

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

Answer 6

Chapter 9.4, Problem 51E

To determine

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

Answer 7

Chapter 9.4, Problem 51E

To determine

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

Answer 8

To determine

(b)

To find:

The center and radius of the sphere.

Answer 9

To determine

(b)

To find:

The center and radius of the sphere.

Answer 10

To determine

(c)

To interpret:

The result of part(a) geometrically.

Answer 11

To determine

(c)

To interpret:

The result of part(a) geometrically.

Answer 12

To determine

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

Answer 13

To determine

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 9.1 - Prob. 1E Ch. 9.1 - CONCEPTS 2. a The length of a vector w=a1,a2 is...Ch. 9.1 - 38 Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - SKILLS 3-8 Sketching Vectors Sketch the vector...Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

(a) To show: The vector equation ( r − u ) ⋅ ( r − v ) = 0 represents a sphere.

Solution Summary: The author explains that the vector equation (r-u)cdot

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

(b)

To find:

The center and radius of the sphere.

(c)

To interpret:

The result of part(a) geometrically.

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

Want to see the full answer?

Chapter 9 Solutions

(a) To show: The vector equation ( r − u ) ⋅ ( r − v ) = 0 represents a sphere.

Solution Summary: The author explains that the vector equation (r-u)cdot

(a) To show: The vector equation (r−u)⋅(r−v)=0 represents a sphere.

(b) To find: The center and radius of the sphere.

(c) To interpret: The result of part(a) geometrically.

(d) To find: A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.

Want to see the full answer?

Chapter 9 Solutions

(a)

To show:

The vector equation (r−u)⋅(r−v)=0 represents a sphere.

(b)

To find:

The center and radius of the sphere.

(c)

To interpret:

The result of part(a) geometrically.

(d)

To find:

A vector equation for the sphere in which the points (0,1,3) and (2,−1,4) form the endpoints of a diameter and simplify the vector equation to obtain an algebraic equation for the sphere. Also find the center and radius of the sphere.