We need to determine which of the following curves pass through the point ( 1 , 4 ) .

Question

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Answer 1

Question

Chapter 11, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

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Answer 2

Question

Chapter 11, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

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Answer 3

Question

Chapter 11, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

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Answer 4

Question

Chapter 11, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

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Answer 5

Chapter 11, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Answer 6

Chapter 11, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Answer 7

Chapter 11, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Answer 8

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Answer 12

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 6PQ Ch. 11.1 - Prob. 7PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E

We need to determine which of the following curves pass through the point ( 1 , 4 ) .

We need to determine which of the following curves pass through the point (1,4).

Answer to Problem 1CRE

Explanation of Solution

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Chapter 11 Solutions

We need to determine which of the following curves pass through the point $(1, 4)$ .