The equation f ( x ) = − x 2 + 4 and g ( x ) = − x − 2 . a. f ( x ) = 0

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Answer 1

Question

Chapter 4.5, Problem 28MP

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

a. $f (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

b. $g (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

c. $f (x) = g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

d. $f (x) > 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

e. $g (x) \leq 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

f. $f (x) > g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

g. $f (x) \geq 1$

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Question 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]

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Answer 2

Question

Chapter 4.5, Problem 28MP

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

a. $f (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

b. $g (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

c. $f (x) = g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

d. $f (x) > 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

e. $g (x) \leq 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

f. $f (x) > g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

g. $f (x) \geq 1$

Expert Solution & Answer

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Answer 3

Question

Chapter 4.5, Problem 28MP

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

a. $f (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

b. $g (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

c. $f (x) = g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

d. $f (x) > 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

e. $g (x) \leq 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

f. $f (x) > g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

g. $f (x) \geq 1$

Expert Solution & Answer

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Answer 4

Question

Chapter 4.5, Problem 28MP

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

a. $f (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

b. $g (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

c. $f (x) = g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

d. $f (x) > 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

e. $g (x) \leq 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

f. $f (x) > g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

g. $f (x) \geq 1$

Expert Solution & Answer

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Answer 5

Chapter 4.5, Problem 28MP

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

a. $f (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

b. $g (x) = 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

c. $f (x) = g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

d. $f (x) > 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

e. $g (x) \leq 0$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

f. $f (x) > g (x)$

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

g. $f (x) \geq 1$

Answer 6

Chapter 4.5, Problem 28MP

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

a. $f (x) = 0$

Answer 7

Chapter 4.5, Problem 28MP

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

a. $f (x) = 0$

Answer 8

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

b. $g (x) = 0$

Answer 9

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

b. $g (x) = 0$

Answer 10

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

c. $f (x) = g (x)$

Answer 11

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

c. $f (x) = g (x)$

Answer 12

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

d. $f (x) > 0$

Answer 13

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

d. $f (x) > 0$

Answer 14

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

e. $g (x) \leq 0$

Answer 15

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

e. $g (x) \leq 0$

Answer 16

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

f. $f (x) > g (x)$

Answer 17

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

f. $f (x) > g (x)$

Answer 18

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

g. $f (x) \geq 1$

Answer 19

To determine

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

g. $f (x) \geq 1$

Answer 20

Expert Solution & Answer

Answer 21

Expert Solution & Answer

Answer 22

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Answer 23

Ch. 4.1 - Prob. 1AYP Ch. 4.1 - Prob. 2AYP Ch. 4.1 - Prob. 3AYP Ch. 4.1 - Prob. 4AYP Ch. 4.1 - Prob. 5AYP Ch. 4.1 - Prob. 6AYP Ch. 4.1 - Prob. 7CV Ch. 4.1 - Prob. 8CV Ch. 4.1 - Prob. 9CV Ch. 4.1 - Prob. 10CV

The equation f ( x ) = − x 2 + 4 and g ( x ) = − x − 2 . a. f ( x ) = 0

To find: The equation f( x ) = − x 2 + 4 and g( x ) = −x − 2 . a. f( x ) = 0

To find: The equation f( x ) = − x 2 + 4 and g( x ) = −x − 2 . b. g( x ) = 0

To find: The equation f( x ) = − x 2 + 4 and g( x ) = −x − 2 . c. f( x ) = g( x )

To find: The equation f( x ) = − x 2 + 4 and g( x ) = −x − 2 . d. f( x ) > 0

To find: The equation f( x ) = − x 2 + 4 and g( x ) = −x − 2 . e. g( x ) ≤ 0

To find: The equation f( x ) = − x 2 + 4 and g( x ) = −x − 2 . f. f( x ) > g( x )

To find: The equation f( x ) = − x 2 + 4 and g( x ) = −x − 2 . g. f( x ) ≥ 1

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Chapter 4 Solutions

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

a. $f (x) = 0$

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

b. $g (x) = 0$

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

c. $f (x) = g (x)$

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

d. $f (x) > 0$

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

e. $g (x) \leq 0$

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

f. $f (x) > g (x)$

To find: The equation $f (x) = - x^{2} + 4$ and $g (x) = - x - 2$ .

g. $f (x) \geq 1$