a) To show that S ( x ) = π ( r + x ) 1 + ( r − x ) 2

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Answer 1

Question

Chapter 4.7, Problem 82E

To determine

a)

To show that $S (x) = π (r + x) \sqrt{1 + {(r - x)}^{2}}$

To determine

b)

To show that $r < \sqrt{2}$ , then $S (x)$ is an increasing function.

To determine

c)

Assume that $r > \sqrt{2}$ show that $S$ has two critical point $x_{1} < x_{2}$ in $(0, r)$ and that is a local maximum and $S (x_{2})$ is a local minimum

To determine

d)

Conclude that the minimum occurs at $x = 0$ or $x_{2}$

To determine

e)

Find the minimum in the cases $r = 1.5 and r = 2$

To determine

f)

Challenge let $c = \sqrt{(5 + 3 \sqrt{3}}) / 4 \approx 1.597$ prove that the minimum occurs at $x = 0 (c o n e)$

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Answer 2

Question

Chapter 4.7, Problem 82E

To determine

a)

To show that $S (x) = π (r + x) \sqrt{1 + {(r - x)}^{2}}$

To determine

b)

To show that $r < \sqrt{2}$ , then $S (x)$ is an increasing function.

To determine

c)

Assume that $r > \sqrt{2}$ show that $S$ has two critical point $x_{1} < x_{2}$ in $(0, r)$ and that is a local maximum and $S (x_{2})$ is a local minimum

To determine

d)

Conclude that the minimum occurs at $x = 0$ or $x_{2}$

To determine

e)

Find the minimum in the cases $r = 1.5 and r = 2$

To determine

f)

Challenge let $c = \sqrt{(5 + 3 \sqrt{3}}) / 4 \approx 1.597$ prove that the minimum occurs at $x = 0 (c o n e)$

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 4.7, Problem 82E

To determine

a)

To show that $S (x) = π (r + x) \sqrt{1 + {(r - x)}^{2}}$

To determine

b)

To show that $r < \sqrt{2}$ , then $S (x)$ is an increasing function.

To determine

c)

Assume that $r > \sqrt{2}$ show that $S$ has two critical point $x_{1} < x_{2}$ in $(0, r)$ and that is a local maximum and $S (x_{2})$ is a local minimum

To determine

d)

Conclude that the minimum occurs at $x = 0$ or $x_{2}$

To determine

e)

Find the minimum in the cases $r = 1.5 and r = 2$

To determine

f)

Challenge let $c = \sqrt{(5 + 3 \sqrt{3}}) / 4 \approx 1.597$ prove that the minimum occurs at $x = 0 (c o n e)$

Expert Solution & Answer

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See solution

Answer 4

Question

Chapter 4.7, Problem 82E

To determine

a)

To show that $S (x) = π (r + x) \sqrt{1 + {(r - x)}^{2}}$

To determine

b)

To show that $r < \sqrt{2}$ , then $S (x)$ is an increasing function.

To determine

c)

Assume that $r > \sqrt{2}$ show that $S$ has two critical point $x_{1} < x_{2}$ in $(0, r)$ and that is a local maximum and $S (x_{2})$ is a local minimum

To determine

d)

Conclude that the minimum occurs at $x = 0$ or $x_{2}$

To determine

e)

Find the minimum in the cases $r = 1.5 and r = 2$

To determine

f)

Challenge let $c = \sqrt{(5 + 3 \sqrt{3}}) / 4 \approx 1.597$ prove that the minimum occurs at $x = 0 (c o n e)$

Expert Solution & Answer

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See solution

Answer 5

Chapter 4.7, Problem 82E

To determine

a)

To show that $S (x) = π (r + x) \sqrt{1 + {(r - x)}^{2}}$

To determine

b)

To show that $r < \sqrt{2}$ , then $S (x)$ is an increasing function.

To determine

c)

Assume that $r > \sqrt{2}$ show that $S$ has two critical point $x_{1} < x_{2}$ in $(0, r)$ and that is a local maximum and $S (x_{2})$ is a local minimum

To determine

d)

Conclude that the minimum occurs at $x = 0$ or $x_{2}$

To determine

e)

Find the minimum in the cases $r = 1.5 and r = 2$

To determine

f)

Challenge let $c = \sqrt{(5 + 3 \sqrt{3}}) / 4 \approx 1.597$ prove that the minimum occurs at $x = 0 (c o n e)$

Answer 6

Chapter 4.7, Problem 82E

To determine

a)

To show that $S (x) = π (r + x) \sqrt{1 + {(r - x)}^{2}}$

Answer 7

Chapter 4.7, Problem 82E

To determine

a)

To show that $S (x) = π (r + x) \sqrt{1 + {(r - x)}^{2}}$

Answer 8

To determine

b)

To show that $r < \sqrt{2}$ , then $S (x)$ is an increasing function.

Answer 9

To determine

b)

To show that $r < \sqrt{2}$ , then $S (x)$ is an increasing function.

Answer 10

To determine

c)

Assume that $r > \sqrt{2}$ show that $S$ has two critical point $x_{1} < x_{2}$ in $(0, r)$ and that is a local maximum and $S (x_{2})$ is a local minimum

Answer 11

To determine

c)

Assume that $r > \sqrt{2}$ show that $S$ has two critical point $x_{1} < x_{2}$ in $(0, r)$ and that is a local maximum and $S (x_{2})$ is a local minimum

Answer 12

To determine

d)

Conclude that the minimum occurs at $x = 0$ or $x_{2}$

Answer 13

To determine

d)

Conclude that the minimum occurs at $x = 0$ or $x_{2}$

Answer 14

To determine

e)

Find the minimum in the cases $r = 1.5 and r = 2$

Answer 15

To determine

e)

Find the minimum in the cases $r = 1.5 and r = 2$

Answer 16

To determine

f)

Challenge let $c = \sqrt{(5 + 3 \sqrt{3}}) / 4 \approx 1.597$ prove that the minimum occurs at $x = 0 (c o n e)$

Answer 17

To determine

f)

Challenge let $c = \sqrt{(5 + 3 \sqrt{3}}) / 4 \approx 1.597$ prove that the minimum occurs at $x = 0 (c o n e)$

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

a) To show that S ( x ) = π ( r + x ) 1 + ( r − x ) 2