To answer: The questions related to the function, y = x 2 − 8 .

Question

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Answer 1

Question

Chapter 3.6, Problem 1AE

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

a. $d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

a. Distance $d$ as a function of $x$

Let, $P = (x, y)$ be the point on the graph of $y = x^{2} - 8$ . The distance from $O$ to $P$ is

$d = \sqrt{{(x - 0)}^{2} + {(y - 0)}^{2}}$

$= \sqrt{{(x)}^{2} + {(y)}^{2}}$

Substituting $y = x^{2} - 8$ for $y$ , then

$d (x) = \sqrt{{(x)}^{2} + {(x^{2} - 8)}^{2}}$

$d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

b. $d (0) = 8$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

b. Value of $d$ if $x = 0$

Substituting $x = 0$ , the distance $d$ is

$d (0) = \sqrt{0^{4} - 15 {(0)}^{2} + 64}$

$d (0) = 8$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

c. $d (1) = 7.07$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

c. Value of $d$ if $x = 1$

Substituting $x = 1$ , the distance $d$ is

$d (1) = \sqrt{1 - 15 + 64}$

$d (1) = \sqrt{50} ≅ 7.07$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 1

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

d. Graph

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 2

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

(e) $x = - 2.74$ or $x = 2.74$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

(e) Smallest $d$

The value of $d$ is smallest when $x = - 2.74$ or $x = 2.74$ .

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Answer 2

Question

Chapter 3.6, Problem 1AE

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

a. $d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

a. Distance $d$ as a function of $x$

Let, $P = (x, y)$ be the point on the graph of $y = x^{2} - 8$ . The distance from $O$ to $P$ is

$d = \sqrt{{(x - 0)}^{2} + {(y - 0)}^{2}}$

$= \sqrt{{(x)}^{2} + {(y)}^{2}}$

Substituting $y = x^{2} - 8$ for $y$ , then

$d (x) = \sqrt{{(x)}^{2} + {(x^{2} - 8)}^{2}}$

$d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

b. $d (0) = 8$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

b. Value of $d$ if $x = 0$

Substituting $x = 0$ , the distance $d$ is

$d (0) = \sqrt{0^{4} - 15 {(0)}^{2} + 64}$

$d (0) = 8$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

c. $d (1) = 7.07$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

c. Value of $d$ if $x = 1$

Substituting $x = 1$ , the distance $d$ is

$d (1) = \sqrt{1 - 15 + 64}$

$d (1) = \sqrt{50} ≅ 7.07$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 1

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

d. Graph

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 2

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

(e) $x = - 2.74$ or $x = 2.74$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

(e) Smallest $d$

The value of $d$ is smallest when $x = - 2.74$ or $x = 2.74$ .

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Answer 3

Question

Chapter 3.6, Problem 1AE

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

a. $d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

a. Distance $d$ as a function of $x$

Let, $P = (x, y)$ be the point on the graph of $y = x^{2} - 8$ . The distance from $O$ to $P$ is

$d = \sqrt{{(x - 0)}^{2} + {(y - 0)}^{2}}$

$= \sqrt{{(x)}^{2} + {(y)}^{2}}$

Substituting $y = x^{2} - 8$ for $y$ , then

$d (x) = \sqrt{{(x)}^{2} + {(x^{2} - 8)}^{2}}$

$d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

b. $d (0) = 8$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

b. Value of $d$ if $x = 0$

Substituting $x = 0$ , the distance $d$ is

$d (0) = \sqrt{0^{4} - 15 {(0)}^{2} + 64}$

$d (0) = 8$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

c. $d (1) = 7.07$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

c. Value of $d$ if $x = 1$

Substituting $x = 1$ , the distance $d$ is

$d (1) = \sqrt{1 - 15 + 64}$

$d (1) = \sqrt{50} ≅ 7.07$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 1

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

d. Graph

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 2

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

(e) $x = - 2.74$ or $x = 2.74$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

(e) Smallest $d$

The value of $d$ is smallest when $x = - 2.74$ or $x = 2.74$ .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 3.6, Problem 1AE

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

a. $d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

a. Distance $d$ as a function of $x$

Let, $P = (x, y)$ be the point on the graph of $y = x^{2} - 8$ . The distance from $O$ to $P$ is

$d = \sqrt{{(x - 0)}^{2} + {(y - 0)}^{2}}$

$= \sqrt{{(x)}^{2} + {(y)}^{2}}$

Substituting $y = x^{2} - 8$ for $y$ , then

$d (x) = \sqrt{{(x)}^{2} + {(x^{2} - 8)}^{2}}$

$d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

b. $d (0) = 8$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

b. Value of $d$ if $x = 0$

Substituting $x = 0$ , the distance $d$ is

$d (0) = \sqrt{0^{4} - 15 {(0)}^{2} + 64}$

$d (0) = 8$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

c. $d (1) = 7.07$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

c. Value of $d$ if $x = 1$

Substituting $x = 1$ , the distance $d$ is

$d (1) = \sqrt{1 - 15 + 64}$

$d (1) = \sqrt{50} ≅ 7.07$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 1

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

d. Graph

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 2

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

(e) $x = - 2.74$ or $x = 2.74$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

(e) Smallest $d$

The value of $d$ is smallest when $x = - 2.74$ or $x = 2.74$ .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 3.6, Problem 1AE

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

a. $d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

a. Distance $d$ as a function of $x$

Let, $P = (x, y)$ be the point on the graph of $y = x^{2} - 8$ . The distance from $O$ to $P$ is

$d = \sqrt{{(x - 0)}^{2} + {(y - 0)}^{2}}$

$= \sqrt{{(x)}^{2} + {(y)}^{2}}$

Substituting $y = x^{2} - 8$ for $y$ , then

$d (x) = \sqrt{{(x)}^{2} + {(x^{2} - 8)}^{2}}$

$d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

b. $d (0) = 8$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

b. Value of $d$ if $x = 0$

Substituting $x = 0$ , the distance $d$ is

$d (0) = \sqrt{0^{4} - 15 {(0)}^{2} + 64}$

$d (0) = 8$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

c. $d (1) = 7.07$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

c. Value of $d$ if $x = 1$

Substituting $x = 1$ , the distance $d$ is

$d (1) = \sqrt{1 - 15 + 64}$

$d (1) = \sqrt{50} ≅ 7.07$

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 1

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

d. Graph

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 2

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

(e) $x = - 2.74$ or $x = 2.74$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

(e) Smallest $d$

The value of $d$ is smallest when $x = - 2.74$ or $x = 2.74$ .

Answer 6

Chapter 3.6, Problem 1AE

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

a. $d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

a. Distance $d$ as a function of $x$

Let, $P = (x, y)$ be the point on the graph of $y = x^{2} - 8$ . The distance from $O$ to $P$ is

$d = \sqrt{{(x - 0)}^{2} + {(y - 0)}^{2}}$

$= \sqrt{{(x)}^{2} + {(y)}^{2}}$

Substituting $y = x^{2} - 8$ for $y$ , then

$d (x) = \sqrt{{(x)}^{2} + {(x^{2} - 8)}^{2}}$

$d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Answer 7

Chapter 3.6, Problem 1AE

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Answer 8

Expert Solution

Answer to Problem 1AE

a. $d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

a. Distance $d$ as a function of $x$

Let, $P = (x, y)$ be the point on the graph of $y = x^{2} - 8$ . The distance from $O$ to $P$ is

$d = \sqrt{{(x - 0)}^{2} + {(y - 0)}^{2}}$

$= \sqrt{{(x)}^{2} + {(y)}^{2}}$

Substituting $y = x^{2} - 8$ for $y$ , then

$d (x) = \sqrt{{(x)}^{2} + {(x^{2} - 8)}^{2}}$

$d (x) = \sqrt{x^{4} - 15 x^{2} + 64}$

Answer 13

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

b. $d (0) = 8$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

b. Value of $d$ if $x = 0$

Substituting $x = 0$ , the distance $d$ is

$d (0) = \sqrt{0^{4} - 15 {(0)}^{2} + 64}$

$d (0) = 8$

Answer 14

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Answer 15

Expert Solution

Answer to Problem 1AE

b. $d (0) = 8$

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

b. Value of $d$ if $x = 0$

Substituting $x = 0$ , the distance $d$ is

$d (0) = \sqrt{0^{4} - 15 {(0)}^{2} + 64}$

$d (0) = 8$

Answer 20

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

c. $d (1) = 7.07$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

c. Value of $d$ if $x = 1$

Substituting $x = 1$ , the distance $d$ is

$d (1) = \sqrt{1 - 15 + 64}$

$d (1) = \sqrt{50} ≅ 7.07$

Answer 21

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Answer 22

Expert Solution

Answer to Problem 1AE

c. $d (1) = 7.07$

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

c. Value of $d$ if $x = 1$

Substituting $x = 1$ , the distance $d$ is

$d (1) = \sqrt{1 - 15 + 64}$

$d (1) = \sqrt{50} ≅ 7.07$

Answer 27

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 1

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

d. Graph

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 2

Answer 28

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Answer 29

Expert Solution

Answer to Problem 1AE

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 1

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

d. Graph

College Algebra (10th Edition), Chapter 3.6, Problem 1AE , additional homework tip 2

Answer 34

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Expert Solution

Answer to Problem 1AE

(e) $x = - 2.74$ or $x = 2.74$

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

(e) Smallest $d$

The value of $d$ is smallest when $x = - 2.74$ or $x = 2.74$ .

Answer 35

To determine

To answer: The questions related to the function, $y = x^{2} - 8$ .

Answer 36

Expert Solution

Answer to Problem 1AE

(e) $x = - 2.74$ or $x = 2.74$

Answer 37

Expert Solution

Answer 38

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given:

$y = x^{2} - 8$

$P = (x, y)$

Calculation:

(e) Smallest $d$

The value of $d$ is smallest when $x = - 2.74$ or $x = 2.74$ .

Answer 41

Ch. 3.1 - Prob. 1AYP Ch. 3.1 - Prob. 2AYP Ch. 3.1 - Prob. 3AYP Ch. 3.1 - Prob. 4AYP Ch. 3.1 - Prob. 5AYP Ch. 3.1 - Prob. 6AYP Ch. 3.1 - Prob. 7CV Ch. 3.1 - Prob. 8CV Ch. 3.1 - Prob. 9CV Ch. 3.1 - Prob. 10CV

To answer: The questions related to the function, y = x 2 − 8 .

To answer: The questions related to the function, y = x 2 − 8 .

Answer to Problem 1AE

Explanation of Solution

To answer: The questions related to the function, y = x 2 − 8 .

Answer to Problem 1AE

Explanation of Solution

To answer: The questions related to the function, y = x 2 − 8 .

Answer to Problem 1AE

Explanation of Solution

To answer: The questions related to the function, y = x 2 − 8 .

Answer to Problem 1AE

Explanation of Solution

To answer: The questions related to the function, y = x 2 − 8 .

Answer to Problem 1AE

Explanation of Solution

Want to see more full solutions like this?

Chapter 3 Solutions

To answer: The questions related to the function, $y = x^{2} - 8$ .

To answer: The questions related to the function, $y = x^{2} - 8$ .

To answer: The questions related to the function, $y = x^{2} - 8$ .

To answer: The questions related to the function, $y = x^{2} - 8$ .

To answer: The questions related to the function, $y = x^{2} - 8$ .